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Mircea Dinescu

Mircea Dinescu (born November 11, 1950) is a Romanian poet, journalist, and editor.

Early life and poetry
He was born in Slobozia, the son of Ștefan Dinescu, a metalworker, and Aurelia (born Badea). Dinescu studied at the Faculty of Journalism of the Ștefan Gheorghiu Academy, and was considered a gifted young poet during his youth, with several poetry volumes published.

Dissidency
In August 1988, Dinescu was invited by the Union of Soviet Writers in the Soviet Union and on August 25, he gave an interview to the Romanian section of the Voice of Russia. During the interview, he expressed his support for the Glasnost and Perestroika policies of the Soviet Union.

After returning to Bucharest, he invited some friends (including Gabriel Liiceanu, Alexandru Paleologu, and Andrei Pleșu) to write a protest against Ceaușescu's policies that were destroying Romanian culture and villages, but they failed to reach a consensus on the text and Dinescu decided to write his own protest. The members of the group were then visited by the Securitate, which argued that their actions were done under KGB orders as an attack against Romania, not against Ceaușescu.

His book, Moartea citește ziarul ("Death is reading the newspaper") was turned down in 1988 by the Communist regime's censorship apparatus, and was then published in Amsterdam.

On March 17, 1989, he was fired from România Literară literary magazine, as a result of an anti-totalitarian interview against President Nicolae Ceaușescu, which Dinescu had granted to the French newspaper Libération in December 1988. According to him, the reason for dismissal was "receiving visits from diplomats and journalists from Socialist and capitalist countries without permission". He was expelled from the Romanian Communist Party (PCR), held under house arrest, with his house guarded around the clock, all visits banned; he was allowed to go outside just for shopping, but always flanked by two Securitate officers.

Dinescu got support from seven writers (Geo Bogza, Ștefan Augustin Doinaș, Dan Hăulică, Octavian Paler, Andrei Pleșu, Alexandru Paleologu, and Mihai Șora), who wrote a letter to Dumitru Radu Popescu, the President of the Writers' Union, asking him "to undo an injustice". Despite the original authors' secrecy (they didn't publish it abroad), six of them (all, except for Geo Bogza, a veteran socialist) were forbidden to publish. He got additional support from poet Doina Cornea, literary critics Alexandru Călinescu and Radu Enescu, and, in November 1989, a collective of 18 young academics and writers, who also wrote letters to Popescu.

Despite being isolated, Dinescu noticed that with a handful of exceptions, the writers did not protest against the oppression of the regime. On November 11, he wrote a statement in which he attacked the Romanian intelligentsia for their sycophancy for Ceaușescu, the Romanian Orthodox Church for being "trade unionists in religious vestments", journalists for being 'apostles of the personality cult", and writers for being "trusted handmaidens of the party".

Revolution
In December 1989 he had a preeminent role in the Romanian Revolution, taking part in the occupation of the National Television building by the people of Bucharest. According to popular rumors, his fellow revolutionary Ion Caramitru, unaware that he was being filmed, said to Dinescu something that was taken to be "Mircea, fă-te că lucrezi!" ("Mircea, pretend you are working!"); this was to be proof that the Revolution was a carefully staged front for a coup d'état. According to the investigation of Alex Mihai Stoenescu, Caramitru actually said "Mircea, arată că lucrezi" ("Mircea, show that you're working [on something]" – while holding Dinescu's booklet in front of camera), to which Dinescu replied "La un apel" ("[I'm working] on an appeal [to the people]") – which was indicative of their ill-preparedness and preoccupation in quickly drafting a single revolutionary proclamation on the spot.

Journalist after 1989
After the fall of Communism, he co-founded Academia Cațavencu, the most famous Romanian satirical magazine. He quit the publication in 1998 and went on founding his own publications, Plai cu Boi (loosely translated as "Land of the Dumb") – a satirical Playboy-style magazine and Aspirina Săracului (The Poor Man's Aspirin – a humorous reference to sexual intercourse) – a weekly satirical magazine.

He invested a part of the money he earned from the books published into agriculture. His estate makes a wine sold under the name Vinul Moșierului ("Landlord's wine") – the name is a tongue-in-cheek reference to an ironic comment President Ion Iliescu had made about Dinescu's social status.

Dinescu remains a strong and charismatic voice of the civil society. As member of Consiliul Național pentru Studierea Arhivelor Securității (National Council for the Study of the Securitate Archives), he is particularly concerned with exposing the former officers and collaborators of the Securitate. He is also a strong critic of Communism and of Romanian leaders that had connections with the Communist regime.

Although not politically involved, he openly supported Traian Băsescu's candidature for President of Romania during the 2004 elections.

In May 2005, in collaboration with the journalist Cristian Tudor Popescu, he started a new newspaper called Gândul, with an initial circulation of 100,000 copies, but he sold his shares in July 2006. He and Stelian Tănase host a talk show on Realitatea TV, Tănase și Dinescu.

Dinescu was appointed a Commander of the Order of the Star of Romania. In 1991, he became an Honorary Member of the University of Augsburg.

Presence in English language anthologies

 * Testament - Anthology of Romanian Verse - American Edition - monolingual English language edition - Daniel Ioniță (editor and principal translator) with Eva Foster, Daniel Reynaud and Rochelle Bews - Australian-Romanian Academy for Culture - 2017 - ISBN 978-0-9953502-0-5
 * Born in Utopia - An anthology of Modern and Contemporary Romanian Poetry - Carmen Firan and Paul Doru Mugur (editors) with Edward Foster - Talisman House Publishers - 2006 - ISBN 1-58498-050-8
 * From the Republic of Conscience - An International Anthology of Poetry - Kerry Flattley and Chris Wallace-Crabbe (editors) with Edward Foster - White Pine Press - 1993 - ISBN 1-877727-26-1
 * 2019 -Testament - 400 Years of Romanian Poetry/400 de ani de poezie românească - Minerva Publishing 2019 - Daniel Ioniță (editor and principal translator) assisted by Daniel Reynaud, Adriana Paul and Eva Foster. ISBN 978-973-21-1070-6
 * 2020 - Romanian Poetry from its Origins to the Present - bilingual edition - Daniel Ioniță (editor and principal translator) with Daniel Reynaud, Adriana Paul and Eva Foster - Australian-Romanian Academy Publishing - 2020 - ISBN 978-0-9953502-8-1 ;

title: Mircea Dinescu


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Save Me the Waltz

Save Me the Waltz is a 1932 novel by American writer Zelda Fitzgerald. It is a semi-autobiographical account of her life in the Deep South during the Jim Crow era and her marriage to F. Scott Fitzgerald. The novel recounts the lives of Jazz Age hedonists Alabama Beggs and her husband David Knight, thinly-disguised alter-egos of their real-life counterparts. An aging Alabama aspires to become a prima ballerina, but an infected blister from her pointe shoe leads to blood poisoning, forever ending her dreams of fame.

Following the decline of her mental health in 1929, Zelda wrote the novel while a voluntary patient at Johns Hopkins Hospital's Phipps Clinic in Baltimore. She sent the manuscript to her husband's editor, Maxwell Perkins. Unimpressed by her manuscript, Perkins nevertheless published the novel at the urging of her husband Scott Fitzgerald in order for him to repay his financial debt to his publisher Scribner's, much of which resulted from Zelda's medical bills for her voluntary stays in psychiatric institutions.

Although F. Scott Fitzgerald touted the novel's quality, the novel garnered negative reviews upon its publication. The book sold approximately 1,300 copies for which Zelda earned a grand total of $120.73. Its critical and commercial failure dispirited Zelda and led her to pursue other interests as a playwright and a painter. After Broadway investors declined to produce her plays, her husband Scott arranged an exhibition of her paintings, but the critical response proved equally disappointing.

In 1959, a decade after her death, Zelda's friend and literary critic Edmund Wilson wrote in The New Yorker magazine that readers should not infer too much about the Fitzgeralds' personal lives based on Save Me the Waltz as the semi-fictional novel merely reflects the glamorous fantasy that Zelda and Scott shared together. Wilson later stated that acquaintance Morley Callaghan's 1963 memoir That Summer in Paris provided a far more accurate depiction of the Fitzgeralds' lives while in Europe.

In 1970, forty years after its publication, biographer Nancy Milford speculated that Zelda's husband Scott Fitzgerald rewrote the novel prior to publication. However, later scholarly examinations of Zelda's drafts and the published version debunked this speculation. Contrary to Milford's claims, Scott did not rewrite the manuscript, and Zelda herself made only minor editorial revisions.

Background
In Winter of 1929, Zelda Fitzgerald's mental health abruptly deteriorated. Soon after, during an automobile trip to Paris along the mountainous roads of the Grande Corniche, Zelda seized the car's steering wheel and tried to kill herself, her husband F. Scott Fitzgerald, and their 9-year-old daughter Scottie by driving over a cliff.

After this homicidal and suicidal incident, Zelda sought psychiatric treatment, and doctors diagnosed her with schizophrenia in June 1930. Zelda's biographer, Nancy Milford, quotes Dr. Oscar Forel's contemporary psychiatric diagnosis: "The more I saw Zelda, the more I thought at the time [that] she is neither [suffering from] a pure neurosis nor a real psychosis—I considered her a constitutional, emotionally unbalanced psychopath—she may improve, [but] never completely recover." Zelda and her husband Scott traveled to Switzerland where she underwent further treatment at a clinic.

After Dr. Forel's initial hypothesis of psychopathic tendencies, Zelda remained in and out of psychiatric institutions. After yet another mental health episode, Zelda insisted that she be admitted to the Phipps Clinic at Johns Hopkins Hospital in Baltimore, despite her husband's objections. The Phipps Clinic in Baltimore admitted Zelda on February 12, 1932. Dr. Adolf Meyer, an expert on schizophrenia, oversaw her daily treatment. As part of her recovery routine, she spent two hours a day writing a novel.

At Phipps Clinic, Zelda developed a bond with Mildred Squires, a female resident. Toward the end of February, she shared fragments of her inchoate novel with Squires, who wrote to Scott that her writing had a certain charm. Zelda wrote to Scott: "I am proud of my [unfinished] novel, but I can hardly restrain myself enough to get it written. You will like it—It is distinctly École Fitzgerald, though more ecstatic than yours—perhaps too much so." Zelda wrote each day and finished the novel on March 9. She sent the unaltered manuscript to Scott's editor, Maxwell Perkins, at Scribner's.

Surprised to receive an unannounced novel in the mail from Zelda, Max Perkins carefully perused her original and unaltered manuscript. Perkins thought the work had "a slightly deranged quality which gave him the impression that the author had difficulty in separating fiction from reality." Although the famous editor believed the manuscript contained a few promising sections, he deemed its overall tone to be hopelessly "dated" and hearkened back to the glamorous Jazz Age hedonism recounted in Fitzgerald's 1922 work, The Beautiful and Damned. Perkins hoped that her husband Scott might be able to improve its overall quality with his criticism.

Upon learning that Zelda had submitted her manuscript to his editor, Scott became perturbed that she had not shown a draft to him beforehand. After reading the manuscript, he objected to her plagiarism of his character Amory Blaine, the protagonist of This Side of Paradise. He expressed surprise that her novel featured the same plot as his upcoming work, Tender Is the Night.

After receiving a letter from Scott delineating these objections, Zelda wrote to Scott that she feared "we might have touched the same material." Despite Scott's initial annoyance, a debt-ridden Fitzgerald concluded that Zelda's book might earn a profit. Consequently, his requested revisions were "relatively few," and "the disagreement was quickly resolved, with Scott recommending the novel to Perkins." Several weeks later, Scott wrote enthusiastically to Perkins: ""Here is Zelda's novel. It is a good novel now, perhaps a very good novel—I am too close to tell. It has the faults and virtues of a first novel. It is more the expression of a powerful personality, like Look Homeward Angel, than the work of a finished artist like Ernest Hemingway. It should interest the many thousands in dancing. It is about something and absolutely new, and should sell.""

Although still unimpressed by Zelda's revised manuscript, Perkins nevertheless agreed to publish the work regardless as a way for Fitzgerald to repay his considerable financial debt to Scribner's. At the time, much of Fitzgerald's financial debt to Scribner's resulted from Zelda's medical bills for her extended voluntary stays at the Phipps Clinic and other psychiatric institutions. Perkins arranged for half of Zelda's book royalties to be applied against Scott's debt to Scribner's until at least $5,000 had been repaid.

On June 14, 1932, Zelda signed the contract with Scribner's to publish the book. It was published on October 7 with a printing of 3,010 copies—not unusually low for a first novel in the middle of the Great Depression—on cheap paper, with a cover of green linen. According to Zelda, the book derived its title from a Victor record catalog, and the title evokes the romantic glitter of the lifestyle which F. Scott Fitzgerald and herself experienced during the riotous and insouciant Jazz Age of American history.

Plot summary
Alabama Beggs, a vivacious Southern belle who wants "her own way about things", comes of age in the Deep South during the Jim Crow era. She marries David Knight, a 22-year-old Yankee artist of Irish Catholic stock and an United States Army officer stationed near her Southern town during World War I. Knight becomes a successful painter, and the family moves to the French Riviera where Alabama romances a handsome French aviator named Jacques Chevre-Feuille. In retaliation, David abandons her at a dinner party and spends the night with a famous dancer.

Alabama grows further apart from her alcoholic husband and their young daughter. Obsessed with becoming famous, an aging Alabama aspires to become a renowned prima ballerina and devotes herself to this ambition. She is offered a once-in-a-lifetime opportunity to dance a featured part with a prestigious ballet company in Naples. Alabama journeys to the city alone, and she dances her solo debut in the opera Faust. However, a blister soon becomes infected from the glue in the box of her pointe shoe, leading to blood poisoning, and Alabama can never dance again.

At the novel's end, though outwardly successful to the general public, Alabama and David are both miserable. The unhappy couple returns to Alabama's beloved Deep South during the Great Depression where her father is dying. She searches for meaning in her father's death but finds none. Though she says otherwise, her childhood friends assume she must be happy, and they envy her privileged lifestyle. The last paragraph depicts the unhappy Knights immobile and dissipated as a couple: ""They sat in the pleasant gloom of late afternoon, staring at each other through the remains of the party; the silver glasses, the silver tray, the traces of many perfumes; they sat together watching the twilight flow through the calm living-room that they were leaving like the clear cold current of a trout stream.""

Contemporary reception
Upon its publication, the novel received overwhelmingly negative reviews. Critics savaged Zelda's prose as overwritten, attacked her characters as weak and uninteresting, and declared her tragic scenes to be grotesquely "harlequinade". A particularly harsh review in The New York Times lambasted her editor Max Perkins: ""It is not only that her publishers have not seen fit to curb an almost ludicrous lushness of writing but they have not given the book the elementary services of a literate proofreader.""

The overwhelmingly negative reviews bewildered and distressed Zelda. However, she acknowledged to Maxwell Perkins that a review by William McFee, writing in The New York Sun, contained several accurate criticisms. McFee wrote: ""In this book, with all its crudity of conception, its ruthless purloinings of technical tricks and its pathetic striving after philosophic profundity, there is the promise of a new and vigorous personality in fiction.""

Malcolm Cowley, a friend of the Fitzgeralds, read the book and wrote consolingly to her husband Scott, "It moves me a lot: she has something there that nobody got into words before." Yet another friend, Ernest Hemingway, believed the work lacked artistic merit and warned editor Maxwell Perkins that if he ever published a novel by any of his wives, "I'll bloody well shoot you." Perkins remained privately dismissive of the novel's quality. The book sold approximately 1,300 copies for which Zelda earned a final sum of $120.73.

Post-publication
The critical and commercial failure of Save Me the Waltz temporarily crushed Zelda's spirits. Nevertheless, she attempted to write a farcical stage play titled Scandalabra in the fall of 1932. She submitted the play manuscript to agent Harold Ober, but Broadway investors unanimously declined to produce the play. In an attempt to bolster her spirits, Scott arranged for her play Scandalabra to be staged by a Little Theater group in Baltimore, Maryland, and he sat through long hours of rehearsals of the play. This independent production ultimately proved to be a failure.

One year later, during a tense group therapy session with her husband and a psychiatrist, Fitzgerald remarked that she was "a third-rate writer and a third-rate ballet dancer." Zelda next attempted to paint watercolors while in and out of sanatoriums but, when her husband Scott arranged their exhibition in 1934, the critical response proved equally disappointing. As with the negative reception of her book, New York critics disliked her paintings. The New Yorker described them merely as "paintings by the almost mythical Zelda Fitzgerald; with whatever emotional overtones or associations may remain from the so-called Jazz Age." No actual description of her paintings appeared in any reviews.

In January 1959, over a decade after Zelda's death, her friend and literary critic Edmund Wilson wrote in The New Yorker magazine that readers should not infer too much about the Fitzgeralds' supposedly glamorous existence based on Save Me the Waltz as the semi-fictional novel merely offered "a reflection of the fantasy that he and she lived together". Wilson later stated that Morley Callaghan's 1963 memoir That Summer in Paris, which recounted Callaghan's friendship with the Fitzgeralds during their sojourn abroad, provided a more accurate representation of the actual lives of Zelda and her husband Scott while in Europe.

In later decades, critics reevaluated the novel in light of the time constraints placed upon the writer and offered more charitable opinions. In 1991, The New York Times literary critic Michiko Kakutani reviewed the work and opined "that the novel was written in two months is amazing. That for all its flaws it still manages to charm, amuse and move the reader is even more remarkable. Zelda Fitzgerald succeeded, in this novel, in conveying her own heroic desperation to succeed at something of her own, and she also managed to distinguish herself as a writer".

Authorship
In 1970, forty years after the novel's original publication, Zelda's first biographer Nancy Milford posited that novelist F. Scott Fitzgerald had extensively rewritten his spouse's manuscript prior to its publication. Contrary to this unfounded speculation, later scholarly examinations of Zelda's earlier drafts of Save Me the Waltz and the revised version of her novel discerned fewer alterations than previously assumed.

According to Fitzgerald scholar Matthew J. Bruccoli, Milford's assumption that Scott "actually rewrote Save me the Waltz is false", and "the available documents indicate that his work was advisory." The revised galleys were "worked over, but almost all the marks are in Zelda Fitzgerald's hand. F. Scott Fitzgerald did not systematically work on the surviving proofs: only eight of the words written on them are clearly in his hand." Furthermore, the revisions requested by Fitzgerald were determined to be relatively minor.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Save Me the Waltz


text:
Nomogram

A nomogram (from Greek νόμος, "law" and  γραμμή, "line"), also called a nomograph, alignment chart, or abac, is a graphical calculating device, a two-dimensional diagram designed to allow the approximate graphical computation of a mathematical function. The field of nomography was invented in 1884 by the French engineer Philbert Maurice d'Ocagne (1862–1938) and used extensively for many years to provide engineers with fast graphical calculations of complicated formulas to a practical precision. Nomograms use a parallel coordinate system invented by d'Ocagne rather than standard Cartesian coordinates.

A nomogram consists of a set of n scales, one for each variable in an equation. Knowing the values of n-1 variables, the value of the unknown variable can be found, or by fixing the values of some variables, the relationship between the unfixed ones can be studied. The result is obtained by laying a straightedge across the known values on the scales and reading the unknown value from where it crosses the scale for that variable. The virtual or drawn line created by the straightedge is called an index line or isopleth.

Nomograms flourished in many different contexts for roughly 75 years because they allowed quick and accurate computations before the age of pocket calculators. Results from a nomogram are obtained very quickly and reliably by simply drawing one or more lines. The user does not have to know how to solve algebraic equations, look up data in tables, use a slide rule, or substitute numbers into equations to obtain results. The user does not even need to know the underlying equation the nomogram represents. In addition, nomograms naturally incorporate implicit or explicit domain knowledge into their design. For example, to create larger nomograms for greater accuracy the nomographer usually includes only scale ranges that are reasonable and of interest to the problem. Many nomograms include other useful markings such as reference labels and colored regions. All of these provide useful guideposts to the user.

Like a slide rule, a nomogram is a graphical analog computation device. Also like a slide rule, its accuracy is limited by the precision with which physical markings can be drawn, reproduced, viewed, and aligned. Unlike the slide rule, which is a general-purpose computation device, a nomogram is designed to perform a specific calculation with tables of values built into the device's scales. Nomograms are typically used in applications for which the level of accuracy they provide is sufficient and useful. Alternatively, a nomogram can be used to check an answer obtained by a more exact but error-prone calculation.

Other types of graphical calculators—such as intercept charts, trilinear diagrams, and hexagonal charts—are sometimes called nomograms. These devices do not meet the definition of a nomogram as a graphical calculator whose solution is found by the use of one or more linear isopleths.

Description
A nomogram for a three-variable equation typically has three scales, although there exist nomograms in which two or even all three scales are common. Here two scales represent known values and the third is the scale where the result is read off. The simplest such equation is u1 + u2 + u3 = 0 for the three variables u1, u2 and u3. An example of this type of nomogram is shown on the right, annotated with terms used to describe the parts of a nomogram.

More complicated equations can sometimes be expressed as the sum of functions of the three variables. For example, the nomogram at the top of this article could be constructed as a parallel-scale nomogram because it can be expressed as such a sum after taking logarithms of both sides of the equation.

The scale for the unknown variable can lie between the other two scales or outside of them. The known values of the calculation are marked on the scales for those variables, and a line is drawn between these marks. The result is read off the unknown scale at the point where the line intersects that scale. The scales include 'tick marks' to indicate exact number locations, and they may also include labeled reference values. These scales may be linear, logarithmic, or have some more complex relationship.

The sample isopleth shown in red on the nomogram at the top of this article calculates the value of T when S = 7.30 and R = 1.17. The isopleth crosses the scale for T at just under 4.65; a larger figure printed in high resolution on paper would yield T = 4.64 to three-digit precision. Note that any variable can be calculated from values of the other two, a feature of nomograms that is particularly useful for equations in which a variable cannot be algebraically isolated from the other variables.

Straight scales are useful for relatively simple calculations, but for more complex calculations the use of simple or elaborate curved scales may be required. Nomograms for more than three variables can be constructed by incorporating a grid of scales for two of the variables, or by concatenating individual nomograms of fewer numbers of variables into a compound nomogram.

Applications
Nomograms have been used in an extensive array of applications. A sample includes:

 * The original application by d'Ocagne, the automation of complicated cut and fill calculations for earth removal during the construction of the French national railway system. This was an important proof of concept, because the calculations are non-trivial and the results translated into significant savings of time, effort, and money.
 * The design of channels, pipes and wires for regulating the flow of water.
 * The work of Lawrence Henderson, in which nomograms were used to correlate many different aspects of blood physiology. It was the first major use of nomograms in the United States and also the first medical nomograms anywhere.
 * Medical fields, such as pharmacy and oncology.
 * Ballistics calculations prior to fire control systems, where calculating time was critical.
 * Machine shop calculations, to convert blueprint dimensions and perform calculations based on material dimensions and properties. These nomograms often included markings for standard dimensions and for available manufactured parts.
 * Statistics, for complicated calculations of properties of distributions and for operations research including the design of acceptance tests for quality control.
 * Operations Research, to obtain results in a variety of optimization problems.
 * Chemistry and chemical engineering, to encapsulate both general physical relationships and empirical data for specific compounds.
 * Aeronautics, in which nomograms were used for decades in the cockpits of aircraft of all descriptions. As a navigation and flight control aid, nomograms were fast, compact and easy-to-use calculators.
 * Astronomical calculations, as in the post-launch orbital calculations of Sputnik 1 by P.E. Elyasberg.
 * Engineering work of all kinds: Electrical design of filters and transmission lines, mechanical calculations of stress and loading, optical calculations, and so forth.
 * Military, where complex calculations need to be made in the field quickly and with reliability not dependent on electrical devices.
 * Seismology, where nomograms have been developed to estimate earthquake magnitude and to present results of probabilistic seismic hazard analyses

Parallel-resistance/thin-lens
The nomogram below performs the computation:

$$f(A,B)=\frac{1}{1/A+1/B}=\frac{AB}{A+B}$$

This nomogram is interesting because it performs a useful nonlinear calculation using only straight-line, equally graduated scales. While the diagonal line has a scale $$\sqrt{2}$$ times larger than the axes scales, the numbers on it exactly match those directly below or to its left, and thus it can be easily created by drawing a straight line diagonally on a sheet of graph paper.

A and B are entered on the horizontal and vertical scales, and the result is read from the diagonal scale. Being proportional to the harmonic mean of A and B, this formula has several applications. For example, it is the parallel-resistance formula in electronics, and the thin-lens equation in optics.

In the example, the red line demonstrates that parallel resistors of 56 and 42 ohms have a combined resistance of 24 ohms. It also demonstrates that an object at a distance of 56 cm from a lens whose focal length is 24 cm forms a real image at a distance of 42 cm.

Chi-squared test computation
The nomogram below can be used to perform an approximate computation of some values needed when performing a familiar statistical test, Pearson's chi-squared test. This nomogram demonstrates the use of curved scales with unevenly spaced graduations.

The relevant expression is:

$$\frac{(OBS - EXP)^2}{EXP}$$

The scale along the top is shared among five different ranges of observed values: A, B, C, D and E. The observed value is found in one of these ranges, and the tick mark used on that scale is found immediately above it. Then the curved scale used for the expected value is selected based on the range. For example, an observed value of 9 would use the tick mark above the 9 in range A, and curved scale A would be used for the expected value. An observed value of 81 would use the tick mark above 81 in range E, and curved scale E would be used for the expected value. This allows five different nomograms to be incorporated into a single diagram.

In this manner, the blue line demonstrates the computation of:

(9 − 5)2 / 5 = 3.2

and the red line demonstrates the computation of:

(81 − 70)2 / 70 = 1.7

In performing the test, Yates's correction for continuity is often applied, and simply involves subtracting 0.5 from the observed values. A nomogram for performing the test with Yates's correction could be constructed simply by shifting each "observed" scale half a unit to the left, so that the 1.0, 2.0, 3.0, ... graduations are placed where the values 0.5, 1.5, 2.5, ... appear on the present chart.

Food risk assessment
Although nomograms represent mathematical relationships, not all are mathematically derived. The following one was developed graphically to achieve appropriate end results that could readily be defined by the product of their relationships in subjective units rather than numerically. The use of non-parallel axes enabled the non-linear relationships to be incorporated into the model.

The numbers in square boxes denote the axes requiring input after appropriate assessment.

The pair of nomograms at the top of the image determine the probability of occurrence and the availability, which are then incorporated into the bottom multistage nomogram.

Lines 8 and 10 are 'tie lines' or 'pivot lines' and are used for the transition between the stages of the compound nomogram.

The final pair of parallel logarithmic scales (12) are not nomograms as such, but reading-off scales to translate the risk score (11, remote to extremely high) into a sampling frequency to address safety aspects and other 'consumer protection' aspects respectively. This stage requires political 'buy in' balancing cost against risk. The example uses a three-year minimum frequency for each, though with the high risk end of the scales different for the two aspects, giving different frequencies for the two, but both subject to an overall minimum sampling of every food for all aspects at least once every three years.

This risk assessment nomogram was developed by the UK Public Analyst Service with funding from the UK Food Standards Agency for use as a tool to guide the appropriate frequency of sampling and analysis of food for official food control purposes, intended to be used to assess all potential problems with all foods, although not yet adopted.

Other quick nomograms
Using a ruler, one can readily read the missing term of the law of sines or the roots of the quadratic and cubic equation.

title: Nomogram


text:
Talk:Frequency modulation

Some another dialog
why the radio based on frequency modulation has very small transmission area?

 * It's nothing to do with the FM modulation, it's to do with the higher frequency used for FM radio broadcasts, compared with AM radio broadcasts. AM radio is on a lower frequency, so it travels further. The lower longer-range AM radio channels were handed out first, so they use the older (and more frequency-efficient, but less interference-tolerant) modulation. -- The Anome 11:04 18 Jul 2003 (UTC)

 * Actually, FM is more frequency efficent than AM, except that commercial FM uses wide FM to get more audio bandwidth into the signal. If FM used the same audio bandwidth as AM, it would use the same or less RF bandwidth than AM.  Commercial frequencies (i.e., public safety) and amateur frequencies that use FM use narrow FM. --ssd 03:59, 23 Jun 2004 (UTC)

 * Note: we should have a radio propagation to explain why the lower frequency radio waves travel further. -- The Anome

 * I've started one, but there may be lots of factual inaccuracies, I'm not sure, I haven't done radio stuff in ages :) Dysprosia 11:26 18 Jul 2003 (UTC)

 * I started Category:Radio frequency propagation with the intent of writing an article including as many of those terms as sane. Feel free to use it as a seed. --ssd 03:59, 23 Jun 2004 (UTC)

Could we please stop moving the disambiguation page and setting to FM. FM does stand for more than one thing. Thank you. --Numerousfalx 23:51, 15 Dec 2004 (UTC)

Example
Can someone give an example for frequency modulation? let's say there is a test signal low tone, high tone, and a sweep. this composed audio signal is supposed to be put on FM radio - how would the modulated tone look like? how much bandwidth does FM radio need? When I detune my favorite radio station "92.2 MHz Rock" by, let's say +0.2 MHz, will the music and all transmitted acoustics be pitched to higher frequencies (so that radio moderators talk like Mickey Mouse) - or is FM resistant against those mistunings.

It would be great if someone could work my (answered) questions into the article. Thanks, --Abdull 21:41, 17 Jan 2005 (UTC)
 * I agree this sort of information should be covered by the article, preferably with diagrams. Answering these questions (for FM) is somewhat tricky, though, and involves a lot of math.
 * I can answer your last question here: no, tuning away from an FM station does not shift the frequency components of the output, so you won't hear "Mickey Mouse" voices like you would with SSB. The capture effect inherent to analog FM receivers means that slight mistunings are "automatically" compensated for.  Tune far enough away and you hear static-y, distorted sound; tune further away and you hear only static.
 * Simon 18:20, 23 Jan 2005 (UTC)
 * Simon is correct about detuning an FM receiver that has no AFC (Automatic Frequency Control) or has AFC switched off. However most FM receivers do have AFC (because it is quite easy to implement) which truly compensates for mistuning. Try to tune away and the sound remains good, until you reach the limit of the AFC and suddenly lose the signal completely. Then the sound changes to the hiss heard between stations. Some receivers have an additional "squelch" function that mutes the hiss noise. Note: all the above observations are for home VHF FM radios, which the frequency Abdull mentions indicates.Cuddlyable3 18:50, 12 February 2007 (UTC)
 * In theory, detuning adds a DC offset to the output. There is always at least one capacitor in the path, that will block DC. Gah4 (talk) 17:56, 27 November 2023 (UTC)
 * Simon is correct about detuning an FM receiver that has no AFC (Automatic Frequency Control) or has AFC switched off. However most FM receivers do have AFC (because it is quite easy to implement) which truly compensates for mistuning. Try to tune away and the sound remains good, until you reach the limit of the AFC and suddenly lose the signal completely. Then the sound changes to the hiss heard between stations. Some receivers have an additional "squelch" function that mutes the hiss noise. Note: all the above observations are for home VHF FM radios, which the frequency Abdull mentions indicates.Cuddlyable3 18:50, 12 February 2007 (UTC)
 * In theory, detuning adds a DC offset to the output. There is always at least one capacitor in the path, that will block DC. Gah4 (talk) 17:56, 27 November 2023 (UTC)
 * In theory, detuning adds a DC offset to the output. There is always at least one capacitor in the path, that will block DC. Gah4 (talk) 17:56, 27 November 2023 (UTC)

Too focused on radio
The article reads as "FM as used in radio" with a little theory thrown in at the last minute. Shouldn't an article titled "Frequency Modulation" primarily cover the theory and link to separate articles on radio/data transmission/encoding (and FM synthesis)? The FM synth article has almost no theory at all.

That might be because the authors of the FM Synth article are unaware of that FM-synthesis á la Yamaha is based on phase-modulation. /ja

The first sentence "...represents information as variations in the instantaneous frequency of a carrier wave" makes sense if you're reading about radio, but is hard to "get" if you're coming at this from the FM synth perspective.

Please have a look at the discussion page under "phase modulation" where I present a few C like oneliners to make the point. /ja

I suppose it makes sense to add a bit more on the theory, whether the article should have its current focus or not; I'd do it myself, except for the fact that I don't really understand FM all that well yet.

magetoo 14:16, 27 Apr 2005 (UTC)

But why not add a see also in both articles Theking2 (talk) 16:52, 27 November 2023 (UTC)

english lesson
"The phrase frequency-modulated, an adjective, should have a hyphen when used attributively."

 * Is this significant to FM for some reason? - Omegatron 21:39, May 25, 2005 (UTC)

font
Could the author consider changing the font on the maths? I found it very difficult to see on a computer screen whether I was reading "t" for time or "f" for frequency. Otherwise found the article well balanced.

 * I agree that the font used makes the formulae very hard to read, but the author correctly used TeX to create them; there is nothing to fix on this page.

 * In my opinion there is a problem with the HTML generation of formulae (it was just as unreadable in IE as Firefox). I will look around and see if there is somewhere I can raise this issue. In the meantime, I recommend changing your wikipedia math preferences to use png for all formulae (the default is to use HTML for 'simple' formulae and png for everything else). Happyharris 18:40, 18 August 2005 (UTC)

 * After reading some more doc, it seems that individual formula can be forced to PNG. That seems appropriate here so I did it (although I still think the default use of HTML is a wikepedia-wide fault) Happyharris 18:44, 30 August 2005 (UTC)

 * Happyharris, i really agree and have had some of my PNG converted to HTML like in Plank units at the bottom. but i think that consistency in notation and appearance is important.  ironically, i was recently editing and was putting in in-line HTML math instead of the usual PNG.  so maybe i got infected with WP orthodoxy. r b-j 05:15, 20 October 2005 (UTC)

Formula Error
The main theory discussion has a very common mistake in deriving frequency modulation. I picked up on it because I make the same mistake every time I start to review FM, and have to fix it. The formula x(t) = A*cos(2*pi*f(t)*t) is incorrect. It arises because A*cos(2*pi*f*t) is correct when f is a constant - f is the frequency. However, frequency is the rate of change of the cos argument. If f(t) is time varying, then the rate of change of f(t)*t is not f(t), it is some complex derivative that is no fun at all.

A better derivation is to start with x(t) = A*cos(phi(t)). Frequency is defined as the rate of change of phi(t). To get sinusoidal FM, we need some phi(t) such that the derivative of phi(t) is 2*pi*deviation*cos(2*pi*rate*t). That isn't so hard - we know the derivative of sin(kt) is k*cos(kt), so we postulate phi(t) = deviation/rate *sin(2*pi*rate*t). It is inconvenient to carry the ratio of deviation/rate, so it is often called Beta. The final formula, then, is x(t)=A*cos(Beta * sin(2*pi*rate*t)) where Beta is deviation/rate, and both deviation and rate are in Hz.

This leads nicely to the Bessel functions, which are a formalized way of working out equations like cos(m sin(x)).

References: "Analog and Digital Communications" by Hwei Hsu (Schaum's Outline) and "Fundamentals of Electronics" by Aldo Vieira da Rosa. (above written by Doug olney)

 * In response to the above, I don't think anybody said that x(t) = A*cos(2*pi*f(t)*t) is even used for teaching FM, unless f(t) is defined as fo + m(t). I would expect that the formula should be something like x(t) = A*cos[ {wc + k.m(t)}.t ], where the message k.m(t) somehow alters the frequency inside the brackets { }. The issue here is: if we apply the formula to obtain the instantaneous frequency of x(t) = A*cos( {wc + km(t)}.t ), then it turns out we will get the instantaneous frequency to be something like: wc + k.{m(t) + t.dm(t)/dt}, which is nothing like what we 'hoped' to get for the instantaneous frequency, such as: wc + k.m(t). This sort of thing is absolutely confusing to people that are learning about frequency modulation. For example, why do they not begin with this particular expression x(t) = A*cos[ {wc + k.m(t)}t ] ? And why do they side-step it by beginning with phase modulation? Maybe because they are conveniently able to get the instantaneous frequency to become what they want to see when beginning with a phase modulation expression, ie. they are able to get the instantaneous frequency to be wc + k.m(t) when they start with phase modulation expressions. It really is something unusual. This really needs to be addressed in the Frequency Modulation Wikipedia page. It needs to be told straight-up to people. That is, why do they not begin with x(t) = A*cos( {wc + km(t)}.t )? The answer is of course, the equation does not model instantaneous frequency being proportional to message amplitude, even though one might incorrectly 'intuitively' or 'instinctively' assume this is the right model. You are right, it is not the right model. KorgBoy (talk) 00:48, 23 March 2017 (UTC)

 * Without thinking about it in too much detail, it seems to me that the wrong form should be close enough when the modulation frequencies are much smaller than the carrier frequency. That is, we can ignore the higher terms. That is, do a first order approximation. In theory, FM has infinite sidebands, which would preclude multiple stations, but in the practical case the sidebands fall off fast enough. Even when the modulating frequency isn't so small, such as the luminance signal in video tape, it will be filtered after the modulator to remove excess sidebands, which likely makes more difference than getting it right in the first place.  Gah4 (talk) 06:12, 20 November 2019 (UTC)
 * I think that the angle modulation page does it right. It defines angle-modulated signals in terms of A cos(wt + phi(t)).  Then it defines instantaneous phase and instantaneous frequency.  It then shows how in FM the instantaneous frequency is linearly related to the modulating signal, and how in PM the instantaneous phase is linearly related to the modulating signal.  That page is much less confusing than this one.  Maybe this page should reference the angle modulation page, or adopt a similar approach. DigitalCommsEngineer (talk) 16:45, 11 July 2024 (UTC)

FM recording
"FM is also used at intermediate frequencies by most analog VCR systems, including VHS, to record the luminance (black and white) portion of the video signal."

Has this method ever been tried for audio recording, aside from the HiFi modes on some analog VCR systems such as VHS and Betamax?144.139.87.8
 * On magnetic tape, the common method of adding a supersonic frequency to the audio signal reduces distortion very effectively, and exploits the dynamic range of the tape to the full. An FM signal with its sidebands would demand a faster tape speed, hence allow less recording time.

FM of an audio-frequency carrier has been useful as a means of recording low-rate digital data on audio tape (cassette) recorders. Such audio equipment could not handle long strings of repeated 0's or 1's directly because of limited low-frequency response.Cuddlyable3 19:01, 12 February 2007 (UTC)

"FM is the only feasible method of recording video to and retrieving video from magnetic tape without extreme distortion, as video signals have a very large range of frequency components — from a few hertz to several megahertz, too wide for equalisers to work with due to electronic noise below -60 dB. This sentence tries to say too many things and needs attention. The megahertz-wide frequency range of video does not force any particular choice of modulation method, nor is it difficult to "equalise" over the video frequency range. I think the subject of FM in video recording belongs in a new section, where the significant issues treated are linearity, pre- and post-emphasis, tape speed, head gaps and noise distribution.Cuddlyable3 18:53, 9 February 2007 (UTC)

 * It is that the frequency goes down to almost zero that is what makes it hard to do other than FM. I suppose another possibility would be to mix it up to a much higher frequency, but higher frequencies are also hard to record. Gah4 (talk) 22:29, 16 July 2018 (UTC)

The statement of "Commonly, the chrominance component is recorded as a conventional AM signal, using the higher-frequency FM signal as bias." of appears to be referring to the VHS system and this isn't true. The chrominance signal is recorded using the "color under" system. The 3.58 MHz subcarrier is simply downconverted to a lower frequency and recorded along with the luminance signal. Maybe this whole section should be scrapped and links given to FM video recording systems such as VHS and data recording such as the Kansas City Standard. (Even though the latter is rarely used these days.) — Preceding unsigned comment added by 96.240.175.232 (talk) 01:31, 20 December 2013 (UTC)

 * After mixing down, it is then recorded as conventional recording. I suppose you could even include the mixing done by an AM modulator in the comparison. Gah4 (talk) 22:29, 16 July 2018 (UTC)

AM and FM compared
The animation is nice. However the AM example is jerky, gives an impression that carrier cycles are individually modulated, and they don't look sinusoidal. There is also redundant text "modulatie", not even in English (the M's stand for modulation already). I think we have to look extra critically at animated drawings because of the relatively high data overhead they represent.Cuddlyable3 15:19, 15 February 2007 (UTC)

I have fixed the above with a new animation. Besides being accurate and non-language specific, it is a much smaller file, and we all like pages to load quickly, don't we?Cuddlyable3 01:04, 18 February 2007 (UTC)

FM
I may be wrong, since I'm still studying elementary physics, but does the first graph show a frequency over time (signal) superimposed on an amplitude over time (carrier)? To remain consistent, I would think that the two graphs should have the same two variables. --Pyg 01:09, 11 March 2006 (UTC)
 * Your question confuses me but the graphs do not. They all have the variables voltage (vertical) and time (horizontal).Cuddlyable3 18:18, 9 February 2007 (UTC)
 * The red curve shows the signal as advertised, which is a varying voltage input to the modulator. Only after the modulation does the carrier frequency over time take on the same curve (or it could be inverted since there is no fixed convention about the direction of frequency deviation).Cuddlyable3 21:22, 11 March 2007 (UTC)

I think the first image (AM, green waveform) is incorrect - it should be showing a varying signal amplitude (vertical scale) at a fixed frequency. Nogami 00:47, 12 August 2006 (UTC)
 * It is correct. The carrier drawn in green has neither AM nor FM.Cuddlyable3 18:18, 9 February 2007 (UTC)

Theory
There seems to be something wrong with the formula. It is different from the one shown in one of the external links (http://www.fas.org/man/dod-101/navy/docs/es310/FM.htm). In this page the formula does not involve an integral at all. It seems to me that the formula as it is now requires the time integral of the signal Xm(t) from 0 to t to be restricted to [-1,1] for all t. This is not necessarily true even if |Xm(t)| < 1. Also it would be interesting to know how to recover the transmitted signal from the modulated carrier wave.

 * The integral is correct - it comes from the fact that FM is actually a special case of PM (phase modulation), and phase is the integral of frequency w.r.t. time. Also, I don't see why the time integral must be restricted to [-1,+1].  The only reason that the restriction $$|X_m(t)| < 1$$ exists is so that the frequency is restricted to $$f_c \pm f_\Delta$$. Oli Filth 09:58, 22 January 2007 (UTC)

Could someone expand the theory section significantly? I think it could use more math/physics background and a sub-section on the engineering of actually accomplishing frequency modulation. Ryanluck 15:55, 6 November 2006 (UTC)

I disagree that the theory section needs more math/physics background. FM and radio is essentially the product of engineering and the mathematics behind it is nice to understand - but not fundamental. The explanation of FM given here is equivalent to asking someone the time and getting and answer on how his watch was built with a precise explanation of the location of every cog in the structure. It may in fact include the information being sought, however more than likely the questioner still won't know what time it is. A far more practical explanation of the theory of frequency modulation is given in the reference http://www.fas.org/man/dod-101/navy/docs/es310/FM.htm:

Frequency modulation uses the information signal, Vm(t) to vary the carrier frequency within some small range about its original value. Here are the three signals in mathematical form:

* Information: Vm(t) * Carrier: Vc(t) = Vco sin ( 2 p fc t + f ) * FM: VFM (t) = Vco sin (2 p [fc + (Df/Vmo) Vm (t) ] t + f)

Df is the peak frequency deviation. In this form, you should be able to see that the carrier frequency term: fc + (Df/Vmo) Vm (t) now varies between the extremes of fc - Df and fc + Df. The interpretation of Df becomes clear: it is the farthest away from the original frequency that the FM signal can be. Sometimes it is referred to as the "swing" in the frequency.

We can also define a modulation index for FM, analogous to AM:

b = Df/fm, where fm is the maximum modulating frequency used.

The simplest interpretation of the modulation index, b, is as a measure of the peak frequency deviation, Df. In other words, b represents a way to express the peak deviation frequency as a multiple of the maximum modulating frequency, fm, i.e. Df = b fm.

Example: suppose in FM radio that the audio signal to be transmitted ranges from 20 to 15,000 Hz (it does). If the FM system used a maximum modulating index, b, of 5.0, then the frequency would "swing" by a maximum of 5 x 15 kHz = 75 kHz above and below the carrier frequency.

Here is a simple FM signal:

Here, the carrier is at 30 Hz, and the modulating frequency is 5 Hz. The modulation index is about 3, making the peak frequency deviation about 15 Hz. That means the frequency will vary somewhere between 15 and 45 Hz. How fast the cycle is completed is a function of the modulating frequency. —Preceding unsigned comment added by 67.142.130.42 (talk) 18:26, 5 October 2007 (UTC)

How to demodulate FM ?
There is no explanation given of how the transmitted signal is recovered. That is cheating the reader after promising "The rest of this article...concentrates on the FM modulation [sic] and demodulation process." A solution could be instead to link to descriptions of the established FM detectors (Ratio, Foster-Seeley, Slope and PLL) in the article on Detector (radio).Cuddlyable3 17:54, 9 February 2007 (UTC)
 * Common methods used in FM receiver are slope detection and phase-locked loops.

The above is not true if by "common" we understand the majority of domestic radios.Cuddlyable3 19:06, 12 February 2007 (UTC)
 * That's what Carlson mentions. Please update the article if you have a more up-to-date reference. Alinja 21:16, 14 February 2007 (UTC)
 * Please help me by identifying what you mean by "Carlson". Until I check that, I like the solution I proposed i.e. a link to Detector (radio). BTW I have the impression that Slope detection of FM is too unwieldy for common use and is only kept mentioned in textbooks.Cuddlyable3 15:30, 15 February 2007 (UTC)
 * By Carlson I mean 'A. Bruce Carlson: "Communication systems, 2nd edition", McGraw-Hill, Inc, 1981'. A link to a more complete article about detectors is of course ok, but we want some kind of mention of how FM can be detected here anyway. Alinja 19:28, 15 February 2007 (UTC)
 * Thank you Alinja for that book reference. However FM signals having no amplitude variation are rather incompatible with AM detectors. The phenomenon called slope detection must have been an accidental discovery that AM radios nevertheless register some sound from FM transmissions. Slope detection is inferior in distortion, noise rejection and adjacent signal rejection compared to the established FM detectors and seems to be kept in textbooks only for its educational value.Cuddlyable3 00:48, 18 February 2007 (UTC)
 * I have tidied up the references to FM detection, relegating the explanation of actual detector circuits to Detector (radio).84.210.139.189 18:26, 9 March 2007 (UTC)

The most common method used in commercial FM broadcast band radio receivers is the quadrature detector. See LM3189 datasheet for an IC that used to be the workhorse of FM detectors. Motorola AN189 gives some theory on how a quadrature detector works. The Foster-Seeley detector was common before ICs became common. — Preceding unsigned comment added by 96.240.175.232 (talk) 01:24, 20 December 2013 (UTC)

Assignments
Could this article include the assigned frequencies for the different uses? Such as 118.00 – 136.975 for Aviation, 108.000-117.975 Navigation, 151.5125- 158.400 BRS. I think a side bar would be best served for this purpose. —The preceding unsigned comment was added by 70.41.64.103 (talk) 00:50, 15 February 2007 (UTC).
 * There should be a linking with Radio frequency and Frequency allocation pages to avoid duplication. Probably Wikipedia should only link to the most detailed frequency allocations with their national variations, found on the web. I would like it kept clear that FM is a modulation type, and not intrinsically any frequency range.Cuddlyable3 15:42, 15 February 2007 (UTC)
 * ...although FM broadcasting is better allocated to higher frequencies than those historically allocated to AM broadcasting, because of issues of coverage and bandwidth.Cuddlyable3 21:29, 11 March 2007 (UTC)

Math confusing - statements about circuit design would be complimentary
Specifically, $$A \cos \left( 2 \pi \int_{0}^{t} \left[ f_c + f_\Delta x_m(\tau) \right] \, d \tau \right) $$

makes it difficult to understand the underlying circuitry.

$$ \int_{0}^{t} \left[ f_c + f_\Delta x_m(\tau) \right] \, d \tau  =   t \times f_c + \int_{0}^{t} f_\Delta x_m(\tau)  \, d \tau  $$

There's no electronic circuit that can indefinitely accumulate a non-zero average input as implied by this equation; while the equation may or may not be correct, it will inevitably be an indirect parallel to the physical model. Also, $$ f_\Delta x_m\left(\tau\right) $$ is not clearly defined; the reader must infer it's nature from the integral, which may be incorrect.

$$A \cos \left( 2 \pi \times f(t) \times t \right) $$ would be a simpler, more direct mathematical model. It has a constant amplitude with a varying frequency.

$$f(t) =  \left( f_c + k \times input(t) \right) $$ is a possible scenario; however, the article does not state (though it implies) that this the actual modulation.

The set of possible modulations is covered by $$f_c + m\left(input(t)\right) $$where$$ input\left(t\right)$$ is flat long-term.

note: I don't know how to get a proper multiplication dot; hence my multiplication looks like a cross-product; feel free to fix that if you know how.

It would be more helpful to state the exact modulation, or the exact circuit.

—Preceding unsigned comment added by 66.245.28.149 (talk • contribs) 09:06, 4 July 2007

 * The simpler mathematical model that you propose hides the continuous-phase nature of most frequency-modulation schemes. You're right that the existing model is not the easiest of equations to understand (in terms of intuition); however all the terms are clearly defined.

 * In most circumstances, it will be a direct representation of what's going on in the circuit. A VCO (or NCO) accumulates phase indefinitely; that's exactly what the equation shows.  Oli Filth 11:33, 4 July 2007 (UTC)

Thank you for your help; I found one of the external links (www.fas.org) presented FM in a set of equations that cleared everything up for me personally. The confusion in the Wikipedia article is the result of the definition for $$f_\Delta$$ as "instantaneous maximum deviation": it's actually just a constant, but 'instantaneous implies that it is a variable in time.
 * The integral form might be mathematically correct, but it isn't physical. Its Fourier components go to infinity, which real radio transmitters can't do. For low modulation index, the f(t) form is close enough. The other terms get small really fast! Usual is an oscillator with a varicap diode in it, instead of a fixed capacitor. So simple to build! Gah4 (talk) 18:23, 27 November 2023 (UTC)
 * The integral form might be mathematically correct, but it isn't physical. Its Fourier components go to infinity, which real radio transmitters can't do. For low modulation index, the f(t) form is close enough. The other terms get small really fast! Usual is an oscillator with a varicap diode in it, instead of a fixed capacitor. So simple to build! Gah4 (talk) 18:23, 27 November 2023 (UTC)

Bessel Function table
After Carson's rule, Bessel Functions and their role in calculating aspects of the sidebands created by FM needs to be added. I have added it, but it needs more explanation, and the table title needs repair as below. Phillipbeynon 04:24, 1 August 2007 (UTC)

 * I don't think this table is a good (so-called) illustration. A graph would show better that:

 * Sidebands shown blank in the table are not non-existent, they are merely below an arbitrary quantising limit. The sidebands produced by sinusoidal FM are an infinite series.
 * A graph shows that particular sideband pairs are zero at particular modulation indices, which gives a common method of calibrating frequency modulators using a spectrum analyzer. Please sign your posts. Cuddlyable3 10:09, 30 July 2007 (UTC)
 * Valid point about the undefined values. The harmonics produced by changing frequency continue ad infinitum; however, the arbitrary limit defining what are significant sidebands is 2% using Carson's rule and 1% for Bessel table values. I found it important to include the table for reference, as I myself was looking for it when I first read this page. A spectrograph would illustrate this infinite series better.--Phillipbeynon 04:24, 1 August 2007 (UTC)
 * I agree that a spectrograph would help explain the sideband behaviour. I notice that your table does identify the special values of modulation index where the carrier disappears, something which can surprise folks. I have another thought: since no FM radio channel can pass ALL the infinite sideband harmonics, every practical FM radio channel distorts a sine signal. I think Carson's rule is intended to be used to design the overall half-power bandwidth of a radio channel. Can we quote the maximum signal distortion that results? Cuddlyable3 13:49, 1 August 2007 (UTC)

I think this table is valid only when the modulating signal is a sinusoid - isn't it so? This should be mentioned. If the table has some meaning for non-sinusoidal modulating signals (as some kind of rule of thumb) it should be explicitly said. Matteosistisette (talk) 13:31, 17 February 2010 (UTC)

FM capture and hearing 2 stations at once
Why is it that most sources claim that an FM receiver only demodulates the strongest signal available, and yet one will sometimes hear two stations simultaneously? Does this indicate something is wrong with the receiver or is this 'normal' if the signals' strengths are the same order of magnitude? I have a few times been able to enjoy a talk and music at the same time using my car radio (KXBL 99.5 FM and KAKS 99.5 FM).

-User: Nightvid
 * That is normal and does not indicate anything wrong with your receiver. Unlike AM signals, only a small increase in the received power from the stronger station is needed for it to "overpower" (make inaudible) the weaker station. Descriptions of this capture effect are sometimes exaggerated.Cuddlyable3 23:12, 7 October 2007 (UTC)

Merge FM and PM?
FM and PM are really the same thing, separated only by the mathematical viewpoint. Perhaps they should be merged into one article and then have FM treated as a special case? HatlessAtless (talk) 21:48, 23 April 2008 (UTC)
 * One might equally argue that PM is a special case of FM. The naming of the Wikipedia articles is influenced by the fact that AM and FM are worldwide broadcasting standards whereas PM outside narrow technical fields is relatively little known or used. Cuddlyable3 (talk) 06:01, 24 April 2008 (UTC)
 * There actually are practical differences between the two. Noise effects arising from demodulation is one difference. A second is the modulation constant: phase modulation wraps after 2 pi radians, but frequency modulation does not, so the bandwidth spreading isn't limited in FM.

Serrano24 (talk) 15:37, 20 June 2008 (UTC)

Improve Noise Quieting and Wideband Noise Reduction sections
There should be a more intuitive way to explain these phenomenon. The derivations of the SNR's are horribly complicated. Does anyone have an easy way to explain this? Maybe we can even have a whole section on calculating SNR? —Preceding unsigned comment added by Daviddoria (talk • contribs) 22:14, 15 September 2008 (UTC)

 * I have removed this section:

 * Wideband noise reduction
 * Since $$B_T$$ increases with the deviation ratio and the SNR is proportional to the deviation ratio, we can reduce signal power and keep the SNR constant as long as we increase the bandwidth.
 * The above is not correct. Thermal noise power at a receiver increases proportionally to its bandwidth. The implication that one can always maintain a SNR while reducing signal power is wrong. Cuddlyable3 (talk) 09:49, 26 November 2008 (UTC)

Too many animations
This page has attracted several versions of animated diagrams that all attempt to illustrate the same thing. Animation "C" (see right) has recently been inserted without explanation for the change. We should now compare the available diagrams and gain a consensus on which one to use. (Please see some earlier discussion above.) Below is my assessment.
 * Animation A
 * Oppose It is a jerky animation. The waves are not sinusoidal. The modulating signal is not shown but is different for the two carriers. The FM wave is not continuous. —Preceding unsigned comment added by Cuddlyable3 (talk • contribs)
 * Oppose for the same reasons. Mange01 (talk) 15:00, 5 November 2008 (UTC)
 * Oppose. No time, no source signal.--Berserkerus (talk) 19:13, 21 November 2008 (UTC)

 * Animation B
 * Support Two editors have worked on this animation which was nominated for FP. —Preceding unsigned comment added by Cuddlyable3 (talk • contribs)

 * Oppose It presumes that the reader understands the oscilloscope horizontal sync mechanism. It is hard to understand for many readers why the that there are two time scales, one fine scale on the horizontal axis, and one course scale illustrated by the animated waveform change. Mange01 (talk) 15:00, 5 November 2008 (UTC)
 * A, B and C all purport to show what might be seen on an oscilloscope. Certainly one reader labours under a misunderstanding that B has both a fine and a course[sic] time scale. There is only one horizontal time scale common to all 3 waveforms. Cuddlyable3 (talk) 22:15, 6 November 2008 (UTC)
 * Oppose. FM wave have abnormal phase speed directions. --Berserkerus (talk) 19:13, 21 November 2008 (UTC)
 * Abnormal? Not really. You see a similar effect to the wagon wheels in cowboy films that seem to turn backwards. The equations are:
 * s = $$pi$$ frame / 16
 * audio = - sin( x/15 + s )
 * am = 1.25 cos( x / 3 ) ( 1 + .7 sin ( x/15 + s ))
 * fm = 1.25 cos ( p / 2 ),
 * p = p + x ( 1 + .5 sin ( x/15 + s ))
 * Cuddlyable3 (talk) 21:09, 25 January 2009 (UTC)

 * Animation C
 * Weak support Doubtful See below. While mathematically correct, this animation has the signal and carrier phase locked together; this is not true in normal broadcasting. The movement and the use of colour does not add any information to what could be a simple diagram. The file size is large at over half a megabyte . I appreciate that the file size is now reduced. I withdraw my weak support and agree with Dicklyon that animation adds nothing to this diagram. Showing unrealistically synchronised waves in an animation encourages the sort of misunderstanding seen above. I would weakly support a non-animated version of this diagram. Cuddlyable3 (talk) 21:09, 25 January 2009 (UTC) (updated)
 * 84 KB now--Berserkerus (talk) 19:13, 21 November 2008 (UTC)
 * Support The "sliding window" makes it easy to understand. Of course it could be made more realistic if the two signals were out of sync, but that is not important. An unmodulated carrer could be added as a forth signal, to illustrate to concept of carrier waveform. A version that shows the difference between AM-UC and AM-SC (both DSB) would also be interesting, as well as a version that shows the difference between FM and PM. Mange01 (talk) 15:00, 5 November 2008 (UTC)
 * That is a nice wish list for new diagrams. Are you offering to provide some? Cuddlyable3 (talk) 22:15, 6 November 2008 (UTC)
 * Hmmm, no answer yet. Perhaps answering is another thing that Mange01 dismisses as not important. Actually providing realistic information is important and is what Wikipedia is supposed to do.Cuddlyable3 (talk) 17:01, 17 February 2010 (UTC)s
 * Hm. "Another thing"? If I was convinced my suggestion were supported, and if the original source code was available on the picture description page, I might make an attempt. Mange01 (talk) 22:45, 18 February 2010 (UTC)
 * Support. I am author:)--Berserkerus (talk) 19:13, 21 November 2008 (UTC)
 * Oppose. When the modulating signal is phase locked to the carrier the FM transmitter will be unable to handle a continuous analog waveform! Since there is no sign of this unrealism being corrected in this animation I withdraw my "support" and "doubtful" votes. I apologise for this turnaround! The animation in the article should not have been changed from B which is correctly realistic. Cuddlyable3 (talk) 10:25, 12 May 2010 (UTC)

What do other editors think? —Preceding unsigned comment added by Cuddlyable3 (talk • contribs)
 * Oppose all – none of these adds any clarity to what you can get from a static diagram. Dicklyon (talk) 05:10, 6 November 2008 (UTC)

The diagram with the green curve is wrong
Specifically, the diagram FM Message and Modulated Signals.svg.

Which I clicked on the diagram, it says that f_delta = 0.15. I tried my best to work out and plot the equation of the green curve on my computer, but somehow it didn't work out. On closer examination, if f_c is 3 as stated on the file page, then f_delta of 0.15 seems too small for its effect to be noticeable on the graph. Are we sure f_delta is 0.15?

Also, I tried using other values of f_delta like 0.5, 1.5 etc and I couldn't get the green curve on the diagram.

Now let's say I simply made a mistake somewhere in my workings and that's why I have been unable to get the green curve, but there's something I've seen that doesn't seem quite right about the curve. If we examine equation (1) as referred to in the article, y(t) = A_c*cos(2*pi*f_c*t + 2*pi*f_delta*∫x_m(τ)dτ, the integral ∫x_m(τ)dτ represents the signed area of the region bounded within the data signal curve. Now, let's assume that this area between τ=0 and τ=t is represented by an average value of x_m_ave(t), so that ∫x_m(τ)dτ between τ=0 and τ=t equals x_m_ave(t)*t. Going back to Equation (1), it can be rewritten as

y(t) = A_c*cos[2*pi*(f_c + x_m_ave(t)*f_delta)*t]

What the above equation shows is that at time t, the instantaneous deviation between the frequency of the transmitted signal and f_c is dependent on the instantaneous amplitude of the data signal (i.e. x_m(t)). That is, at time t, the larger the value of x_m(t), the higher the instantaneous frequency of the transmitted signal; the smaller the value of x_m(t), the smaller the frequency.

After having said all that, if we look back at the green curve in question, it is at odd with the above conclusion. Can someone please comment on this? 222.152.22.151 (talk) 14:34, 13 April 2010 (UTC)
 * This shows the equations and you can contact the artist here.Cuddlyable3 (talk) 16:27, 30 May 2010 (UTC)
 * The "green curve" is wrong by inspection! Unless there is significant audio filtering, the instantaneous frequency of the modulated signal must be the carrier freq. plus the modulation input times a freq. deviation, as in the animated figure.  This is clearly not the case in the figure.  (The equations given along with the SVG file have an erroneous integration - and no references.) Furthermore the "red curve" is misleading and unhelpful.  Superimposing the carrier and the modulating waveform this way suggests that they are co-present at some point in the system, and they are not.   I suggest deleting both red and green figures. Even if they were fixed, they would not add anything compared with the animation.  --Albany45 (talk) 14:52, 18 September 2010 (UTC)

 * I took it out. If someone wants to redo it correctly and put it back, that might be OK.  Dicklyon (talk) 16:14, 18 September 2010 (UTC)

Target of FM Redirect
FM is currently a redirect to this article. That said, an non-exhaustive survey suggests that majority of incoming links are really referring to (the related) FM broadcasting article.

In this context, User:Georgia guy and I have been having a conversation over at Talk:FM about where the FM redirect should point.

If folks have a moment to read the conversation so far, we'd love some additional thoughts from other involved Wikipedians. Thanks in advance! —m a k o ๛  05:44, 27 September 2011 (UTC)

Stray sentence in penultimate paragraph
"The rest of this article concentrates on the FM modulation and demodulation process, which is identical in stereo and monaural processes." – No, it doesn't. Does anyone know where this sentence is supposed to go; it is now almost at the end of the article... -- megA (talk) 21:55, 6 November 2011 (UTC)

 * It was originally in an early "Stereo FM" section, when it was inserted in 2003, here. I fixed it. Dicklyon (talk) 22:41, 6 November 2011 (UTC)

Contradicting statements
This article says "In analog applications, the difference between the instantaneous and the base frequency of the carrier is not directly proportional to the instantaneous value of the input-signal amplitude but it is proportional to frequency." where as article on FM Broadcasting says "In analog applications, the instantaneous frequency of the carrier is directly proportional to the instantaneous value of the input signal. This form of modulation is commonly used in the FM broadcast band." They are contradicting. Which is right? wikieinstein (talk) 13:03, 17 January 2013 (UTC)

 * Good catch, I think. I can't figure out what the Wikipedia statement is getting at.  --Bob K (talk) 14:23, 17 January 2013 (UTC)

 * In simple FM, the frequency is strictly proportional to modulating voltage. FM broadcasting uses pre-emphasis, however to boost SNR by increasing modulation at high frequencies.  Maybe that's what our writer had in mind, but it's a mistake to generalize it to all of FM.--Albany45 (talk) 22:20, 3 February 2013 (UTC)

My BIGGEST question
Hello, could anyone explain, what about non-sinusoidal (and maybe non-periodic) carrier? Could we assume some FM( A(t), B(t) ) function, which modulates carrier, given by abstract function A(t) with signal, given by abstract function B(t)? could anyone write/explain something about that? what will formula look like in that most common case? I want some kind of recursive formula in terms, like "A(t-1)". Or either some explanation, if that is not possible and why. I was not able to find any info related to my question on the internet, so im here, asking people... — Preceding unsigned comment added by 95.143.213.249 (talk • contribs)
 * Just replace the cos with A. But why? Dicklyon (talk) 02:39, 2 February 2013 (UTC)
 * And why would that still be called "frequency modulation"? I.e. cos is a periodic function, which gives meaning to the word "frequency". The same can't be said for A(t). --Bob K (talk) 05:10, 2 February 2013 (UTC)
 * With A(t) being "maybe non-periodic", it's maybe frequency modulation; and maybe rate modulation would be a better term otherwise. Dicklyon (talk) 06:16, 2 February 2013 (UTC)

"rate modulation" is unsuitable, because i have no "future". I mean, i am not playing wav file, and i cannot just speed up it's playback. In other words, i'd say, i want to make "pitch modulation without rate increase" I am trying to code such dsp algorithm. It's heart is some discrete so-called "now" moment - you only have At and Bt sample, you must return Result sample value. Okay, you may have "past" if you want. You may succesfully obtain its previously stored "prev" values Aprev=A(t-1), Bprev=B(t-1), required for example in simple lowpass/hipass. You may store whole array and make delay line easily. You have "past", but you have no "future", which can become ONLY after calculation. And that's the task - to calculate the out result. What should we do, to "pitch-modulate" signal A(t) with B(t) in such enviroment& Where B(t) / B(t-1) == 2 means that A's pitch must be increased twice, resulting in 2 times higher percepted tone, but without "speeding up" playback. — Preceding unsigned comment added by 95.143.213.249 (talk) 14:38, 3 February 2013 (UTC)

Armstrong and "wideband" FM?
The article claims that Armstrong invented wideband FM. I'm not sure why "wideband". His early patents mention a modulation index somewhat less than 1 (delta phase at highest modulating frequency) which describes narrowband FM. In any case, the distinction between the two flavors is just a matter of degree, it is not fundamental. For broadcast normally wide band FM is used because of the signal quality benefits, while radio communication uses narrowband FM for spectrum efficiency, but both can be traced back to Armstrong.

Incidentally, Armstrong was not the original inventor of FM, though he arguably is the one whose work became known and led to what we use today. Hanso Idzerda in the Netherlands, the builder of broadcast station PCGG in 1919, invented and patented FM transmission and described its benefits for transmitter simplicity and efficiency. What he did not do (but Armstrong did) is describe receiver technology that takes advantage of the properties of FM, and the "slope detection" that Idzerda's listeners presumably used does not achieve those benefits. Paul Koning (talk) 18:55, 20 December 2017 (UTC)

 * As part of another discussion, I started to look at what Armstrong and Idzerda did. I suspect that Idzerda might have thought about wideband if the technology (high frequency vacuum tubes) existed. As well as I know, Armstrong understood the advantages in noise reduction, and also that the spectrum was available and usable. I don't know how to argue fundamentalness. There is a complicated relationship between bandwidth and S/N of the demodulated signal. Gah4 (talk) 22:39, 16 July 2018 (UTC)

A "baseband modulated signal?" should be "modulating"?
The section titled "Sinusoidal baseband signal" begins, "Mathematically, a baseband modulated signal may be approximated by a sinusoidal continuous wave signal with a frequency fm". But what is a baseband modulated signal? Up till this point, a baseband signal is equated with a modulating signal. The "frequency fm", as opposed to fc, seems to confirm that we're talking about a baseband signal, i.e. the modulating signal, not the transmitted signal. Huttarl (talk) 15:24, 5 April 2018 (UTC)

contrast this with FM audio broadcasting, where the ratio is around 10,000
The article says: contrast this with FM audio broadcasting, where the ratio is around 10,000. FM broadcasting, in the US at least, is around 100MHz. 10000:1 would be 10kHz. I believe without a stereo subcarrier, broadcast FM can go to 18KHz or so, as long as it is low enough at 19KHz not to trigger the stereo demodulator. With subcarriers such as SCA, it is up to 70KHz or more, so closer to 1400:1. Gah4 (talk) 22:45, 16 July 2018 (UTC)

title: Talk:Frequency modulation


text:
Humat al-Hima

Ḥumāt al-Ḥimá (حماة الحمى, "Defenders of the Homeland") is the national anthem of Tunisia; the text was written by Mostafa Saadeq Al-Rafe'ie and Aboul-Qacem Echebbi.

History
The lyrics come from a poem written in the 1930s by Egyptian poet Mostafa Saadeq Al-Rafe'ie. Although some say the melody of this march was composed by Mohammed Abdel Wahab, Tunisian musicologist Salah El Mahdi claims the melody was composed by the poet Ahmed Kheireddine while the original music for the poem was composed by Zakariyya Ahmad.

The very last verses of the lyrics were written by Aboul-Qacem Echebbi. According to El Mahdi, these verses were appended to the lyrics in June 1955 by nationalist Mongi Slim.

Known as the "Hymn of the Revolution", it was sung during the meetings of the ruling party, the Neo Destour, which later changed its name to the Socialist Destourian Party. "Ḥumat al-Ḥima" was temporarily used as a national anthem between the end of the monarchy on 25 July 1957, when it replaced the "Salam al-Bey", and 20 March 1958, when it was replaced by "Ala Khallidi". "Ḥumat al-Ḥima" was later brought back again following the coup d'état that brought Zine El Abidine Ben Ali to power on 7 November 1987.

Lyrics
On occasions requiring brevity, a short version is sung consisting of the chorus, the third verse (not repeated) and the chorus again.

title: Humat al-Hima


text:
Nectarius of Constantinople

Nectarius (Νεκτάριος; died 17 September 397) was the archbishop of Constantinople from AD 381 until his death, the successor to Saint Gregory Nazianzus and predecessor to St. John Chrysostom.

Life
Born in Tarsus in Cilicia of a noble family, he was widely known for his admirable character. When Gregory resigned as Archbishop of Constantinople, Nectarius was praetor of Constantinople. Preparing for a journey to Tarsus, he called on the Bishop of Tarsus, Diodore, who was attending the First Council of Constantinople (one of the ecumenical councils), to ask if he could take letters for him; his appearance and manners struck Diodorus so forcibly that he at once determined that he should be advanced as a candidate for Bishop; making an excuse of attending to some other business, he took Nectarius to see Meletius.

His unexpected appointment
When the Emperor Theodosius I wanted the Bishops at the Council to suggest new candidates and reserving to himself the right of making the choice, the Bishop of Antioch put at the bottom of his list, Nectarius' name. The Emperor having read the lists, declared Nectarius to be his choice. This caused some amazement amongst the Fathers who wanted to know who and what this Nectarius was. He was still only a catechumen. There was much astonishment at the emperor's unexpected choice, but the people of Constantinople were delighted at the news as was the whole council.

Nectarius was duly baptized and his clothes were changed for the robes of a Bishop of the Imperial city and became at once president of the Second Ecumenical Council.

Nectarius ruled the church for upwards of 16 years, and is thought of as having been a good prelate. His name heads the 150 signatures to the canons of the Second Ecumenical Council. The 3rd canon declares that, "...the Bishop of Constantinople shall hold the first rank after the bishop of Rome, because Constantinople is the new Rome."

Dissent threatens
The Bishops of the West opposed the election result and asked for a common synod of East and West to settle the succession and so the Emperor Theodosius, soon after the close of the second council, summoned the Imperial Bishops to a fresh synod at Constantinople; nearly all of the same bishops who had attended the earlier second council were assembled again in early summer of 382. On arrival they received a letter from the synod of Milan, inviting them to a great general council at Rome; however they indicated that they must remain where they were, because they had not made any preparations for such long a journey. However, they sent three (Syriacus, Eusebius and Priscian) with a synodal letter to Pope Damasus I, archbishop Saint Ambrose and the other bishops assembled in the council at Rome.

The Roman synod to which this letter was addressed was the fifth under Damasus. No formal account remains of its proceedings, nor of how its members treated the question of Nectarius. Theodosius, did however, send commissaries to Rome in support of his synod.

In his 15th letter (to the bishops of Illyria) he indicated that the church in Rome had finally agreed to recognize both Nectarius and Flavian.

Six letters from Nectarius remain extant in the files of his predecessor Gregory Nazianzus. In the first he expresses his hearty good wishes for his episcopate. The last is of great importance, urging him not to be too liberal in tolerating the Apollinarians.

In 383 a third synod at Constantinople was held. In spite of the decrees of bishops and emperor, the Arians and Pneumatomachians continued to spread their doctrines. Theodosius summoned all parties to the Imperial city for a great discussion in June, hoping to reconcile all differences. Before this he had sent for the Archbishop and told him that all questions should be fully debated.

After this, Nectarius returned home, full of anxiety and consulted the Novatianist Bishop Agelius, who felt himself unsuited to arbitrate on such a controversy. However he did have a reader, Sisinnius, a philosopher and theologian, to whom he referred the argument with the Arians. Sisinnius suggested that they should produce the testimonies of the old Fathers of the Church on the doctrine of the Son, and first ask the heads of the several parties whether they accepted these authorities or desired to anathematize them.

Both the Archbishop and the Emperor agreed to this suggestion and when the Bishops met, the Emperor asked whether they respected "...the teachers who lived before the Arian division?" They confirmed that they did and he then asked if they acknowledged, "...them sound and trustworthy witnesses of the true Christian doctrine?".

This question however produced divisions and so the emperor ordered each party to draw up a written confession of its doctrine. When this was done, the Bishops were summoned to the Imperial palace, where the emperor received them with kindness and retired to his study with their written confessions. Theodosius however rejected and destroyed all except that of the orthodox, because he felt that the others introduced a division into the Holy Trinity.

After this, Theodosius forbade all sectaries, except the Novatianists, to hold divine services or to publish their doctrines or to ordain clergy, under threat of severe civil penalties.

In 385 the emperor's wife Aelia Flaccilla (or Placilla) and their daughter Pulcheria died. The archbishop asked Gregory of Nyssa to preach the funeral sermons for both of them.

Towards the close of his episcopate, Nectarius abolished the office of presbyter penitentiary, whose duty appears to have been to receive confessions before communion. His example was followed by nearly all other Bishops. The presbyter penitentiary was added to the ecclesiastical roll about the time of the Novatianist schism, when that party declined to communicate with those who had lapsed in the Decian persecution. Gradually there were fewer lapsed to reconcile, and his duties became more closely connected with preparation for communion. Nectarius abolished the office due to a scandal that had occurred in connection with it.

Nectarius died in office on 17 September 397 (Butler says 27 September) and was succeeded by Saint John Chrysostom.

Veneration
The Eastern Orthodox Church holds Nectarius as Saint, with a feast day of October 11. He was venerated as a saint in the first millennium on October 11.

title: Nectarius of Constantinople


text:
R-39 Rif

The R-39 Rif (Р-39 Риф; NATO reporting name: SS-N-20 Sturgeon; bilateral arms control designation: RSM-52) was a submarine-launched ballistic missile (SLBM) that served with the Soviet Navy from its introduction in 1983 until 1991, after which it served with the Russian Navy until 2004. The missile had GRAU indices of 3M65, 3M20, and 3R65. It was carried on board Typhoon-class submarines.

An intercontinental missile, the R-39 had a three-stage solid-fuel boost design with a liquid-fuel post-boost unit carrying up to ten multiple independently targetable reentry vehicle warheads. Like other SLBMs the initial launch was powered by a gas generator in the bottom of the firing tube. During the missile's passage through the water additional motors produce a gaseous wall around the missile, reducing hydrodynamic resistance. The launch system was designated "D-19".

Development
Development work began at NII Mashinostroyeniya in 1971 and the design gained official approval in 1973. Initial test flights from 1979 found problems in the solid-fuel boost engines, over half of the early flights failed. Later tests aboard a modified Typhoon-class submarine were more successful and deployment began in May 1983, with 20 missiles in each submarine. At full deployment, 120 missiles were deployed with 1,200 total warheads.

Under the terms of the START I and START II treaties, from 1996 a number of R-39 missiles were destroyed. Throughout the 1990s, Typhoon class submarines and the R-39 missiles they carried were gradually withdrawn from service. All the missiles were decommissioned by 2004 and all the Typhoon class submarines have been retired, except for one which is used as a test platform for the RSM-56 Bulava.

A successor design, R-39M Grom (Гром, Thunder)/RSM-52V/SS-N-28 for D-19UTTKh launch system, suffered a succession of testing failures and was cancelled.

Former operators

 * Russian Navy
 * Soviet Navy
 * Soviet Navy
 * Soviet Navy

title: R-39 Rif


text:
Talk:Penalty area

"It is rectangular and extends 16.5 metres (54 ft) to each side of the goal" <- i'm not sure about this. other sources say the total width of the area is actually around 40 meters, for example, the 'association football pitch' wiki page. does anyone know for sure what the actual official width of the area is, if there is any strict rule on this? Bazkie botsauto (talk) 18:04, 13 December 2011 (UTC)

Merger
The article appears to relate to one small section of a larger article and could easily be merged in to the main article.--Lucy-marie (talk) 15:58, 10 January 2008 (UTC)
 * This proposed merger was rejected in August 2007 (see Talk:Football pitch). For the record I oppose such a merger, the penalty area is significant and important enough to justify a sub-article.  The Rambling Man (talk) 11:17, 11 January 2008 (UTC)
 * Support As a previous proposer of the merge I stand by my argument - too little content for it's own article, unlikely to be expanded,and all this content can easily be merged into Football pitch. There's actually very little that needs merging - only the 1901 comment (though it's unsourced), and a mention about its role in goal kicks and defensive free kicks; everything else looks to be in Football pitch already. Paulbrock (talk) 12:43, 11 January 2008 (UTC)
 * oppose notable in its own right. The article could do with some significant expanding; an overhead photo and a plan diagram would be a good start. --Dweller (talk) 13:39, 11 January 2008 (UTC)

Picture
The picture used in the "function" section should be replaced. You can barely see the lines on that picture, all I could see without zooming in was a green picture (at least on mobile) 2804:7F2:5A4:CA2F:B8DE:D471:3A1F:2CBC (talk) 22:26, 3 March 2022 (UTC)

Is the line itself inside or outside the penalty box?
I believe it is the case that a ball that overlaps the penalty box line (even a little) is considered inside the penalty box. If so or if not, please modify the article accordingly. — Q uantling (talk | contribs) 21:26, 21 June 2023 (UTC)
 * I've edited the article. If you have an applicable reference, it would be much appreciated.  — Q uantling (talk | contribs) 14:01, 22 June 2023 (UTC)

title: Talk:Penalty area


text:
LBCAST

LBCAST (lateral buried charge accumulator and sensing transistor array) is a type of photo sensor which the manufacturer claims is simpler and thus smaller and faster than CMOS sensors. It was developed over ten years by Nikon, in parallel with other manufacturer's development of CMOS, and resulted in shipping product in 2003.

Both CMOS and LBCAST technologies branched from researchers discussions of "amplifying sensors" as a way to develop an imaging sensor with lower power requirements than the already-existing CCD sensor technology, for use in portable devices such as DSLR cameras.

From the Nikon Website:

 * "In July 2003, Nikon introduced LBCAST- a completely new type of image sensor, different from CCD and CMOS, that is a high-speed, power-efficient, low-noise device to be installed in Nikon's flagship camera, the D2Hs."

 * "... Compared with conventional sensors, it saves more power and achieves less dark noise. (Dark noise is a phenomenon in which randomly spaced bright pixels appear in images due to the heat from the image device during shooting). Also, LBCAST increases image processing speed and improves sensitivity, contrast and color reproduction."

Comparison between LBCAST and CMOS photo sensors
The main differences between LBCAST and CMOS-based sensors appear to be those given below:

 * LBCAST divides the photosites to be read out into two channels by colour, red and blue photosites—making up 50% of the total number of photosites between them, as in CMOS and CCD colour sensors—accumulate using one read-channel, while green photosites—which make up the other 50% of total pixels, as in CMOS and CCD—accumulate in a dedicated channel.

 * This division is to speed reading, and the separation of green pixels, to which the human eye is most sensitive, reduces noise artifacts which might otherwise be introduced by residual electrical charge in the accumulation circuitry, acquired previously from reading a pixel of a different colour.

 * Red and blue are significantly less important in human sight, and so presumably a decision was made not to keep separate read channels for the two colours, in order to simplify the circuit design for practical use -- at least in the described version of LBCAST technology.

 * Each photosite in LBCAST uses a single JFET transistor in place of two MOSFET transistors used for the separate tasks of photosite read-out selection and signal amplification, in CMOS technology. In total, CMOS uses four transistors per photosite, where LBCAST manages with three.
 * Charge to be (re-)distributed between components in the sensor during use are channeled via the LBCAST lower layers, where CMOS channels this charge over the surface layer. This difference is also claimed to reduce the presence of noise artifacts.
 * The simpler circuitry required translates into more space for light to be received, since wiring and opaque masking takes less space.
 * The simpler circuitry required translates into fewer layers of material in the silicon chip meaning that tangential light requires less correction in order to traverse to the depth at which the photons result in signal, simplifying the need for lensing at each pixel or photosite, and therefore theoretically, attaining greater image uniformity.

Uses of LBCAST sensors
As at end 2006, the Nikon D2H and the D2Hs were the only publicly available cameras known to carry the sensor. Nikon has opted to use CCDs sourced from Sony in most of their low and mid range cameras and used a CMOS sensor in the flagship D2Xs/D2x. The LBCAST sensor in the D2Hs has remained at 4.1MP.

With the advent of the D3, D700 and D300 cameras in 2007 and 2008, all featuring CMOS sensor technology, it is unknown whether LBCAST plays a part in the design of the CMOS sensor of either, since Nikon's implementation of LBCAST is an adaptation of CMOS, and it is therefore technically correct to refer to the known instances of LBCAST as CMOS, Nikon has not been forthcoming to requests for specific information on the D3 sensor and Nikon have claimed in the past that LBCAST would be further developed.

Criticisms of LBCAST sensors
The following weaknesses have been cited as affecting the Nikon D2H, although whether these issues have origins specific to LBCAST, and whether LBCAST necessitates these problems, is not known.

 * Colour cast—generally (and by definition) colour correction is a fundamental requirement of imaging in any medium where incident light quality is variable, including unaided human vision, and so this possibly a software issue.
 * Infra-red pollution—incident infra-red light is usually filtered on image sensors, using a specific thin film dedicated to this task (but which may serve an additional purpose in protecting the relatively much more expensive sensor component from contamination and damage), and so this issue, if truly the result of ir pollution, may be a problem which is independent of the LBCAST technology of the sensor.
 * Low resolution—it is not known whether the relatively low resolution of the D2H and D2Hs in comparison with other professional cameras of the day is a technological limitation of LBCAST, a business management or marketing decision, or whether it has other causes such as gradual ramping-up of manufacturing capability of a new technology by Nikon, who did not appear previously to have the capacity to have novel sensors manufactured to their specification. It is known that there is a market for high-speed, power efficient cameras where higher resolution is not required, for example newspaper journalism.

title: LBCAST