text:
Past LSAT Explained/PrepTest 45

The December 2004 LSAT Form 1LSS51 On most test forms, the experimental section appeared in Section 3. Ratings of this administration placed its difficulty on par with other recent exams.

Logical Reasoning One scored Arguments section had 25 questions, and the other had 26. Test takers rated the Arguments sections as harder than usual. Most said the 25-question section was harder than the 26-question section, largely due to the mix of question types. The 26-question section had a more typical distribution of question tasks, and the 25-question section had a relatively large number of tough flaw and principle questions. Overall, there were fewer inference questions than usual.

Reading Comprehension Instead of the usual breakdown of topics - science, law, social science, and arts/humanities, the December RC section had one law, one science, and two social science/policy passages. Though the passage distribution was atypical, the questions tasks and answer choices were comparable to those on other recent exams. Examinees varied in their assessment of passage difficulty, but many said the law passage had the most difficult questions. The first passage had eight questions and advocated changes to the provision of relief after natural disasters. The second passage had six questions, and the author responded to those who criticize the relevance of the Hippocratic Oath in contemporary medicine. The third passage had five questions, and it described how new research into the DNA of the fungi in lichen has led to new insight into the evolutionary path of lichens. Eight questions accompanied the last passage, which dealt with provisions in the Canadian constitution that protect aboriginal rights.

Question 01
IDENTIFY

This is a conclusion question.

READ The author criticizes economists' argument about consumption as a measure of economic well-being.

 * economics
 * well-being

ANALYZE The Conclusion + Evidence

CHOOSE

(A) Correct.

(B) Incorrect. This is a stretch and outside the scope.

(C) Incorrect. This is not true.

(D) Incorrect. This statement can be inferred from the second sentence but it is not what the author is leading us to.

(E) Incorrect. Maybe, but the author does not make this argument. He only discredits the economists obsession.

The following is a parallel question.

The obsession of the generals with manpower as a measure of military strength has prevented us from understanding the true nature of military power. Having a huge number of poorly trained and unequipped soldiers contribute little to the military power and the need to feed them can be a drain to national resources.

The author arguing that

(A) military strength cannot be defined solely in terms of manpower

(B) military power can be measured without considering manpower

(C) valid measures of military power cannot be formulated

(D) a large army of poorly equipped soldiers is a drain to the nation

(E) Things that contribute to the military power can provide an adequate quantitative measure of economic well-being

Question 02
IDENTIFY

This is a weaken question.
 * chlorofluorocarbons
 * ozone layer
 * supernova
 * solar radiation
 * ultraviolet

READ

The commentator discusses ozone layer depletion and an argument that we don't have to worry.

ANALYZE The author's view is that our ancestors was alright even though they were subject to something worse. So we should be OK. This argument presupposes that our ancestors and we are somewhat similar. The weakness is to attack this crucial point.

CHOOSE

(A) Incorrect.

(B) Incorrect.

(C) Correct.

(D) Incorrect.

(E) Correct.

Politician: Many people argue that the news release of the senator's misconduct into the media is distablizing the government and thus hurts the national interest. But 30 years ago a similar political scandal involving the president erupted in the country with no significant effect on our country's political stability. Because the president's scandal was far more serious than the secretary's today, there is no reason to think that the current news is affecting the country significantly.

Which one of the following, if true, would most seriously weaken the politician's argument?

(A) Scandals involving the government officials tend to occur less often than those involving the celebrities.

(B) Loss of popularity among people continue to damage the president's prestige.

(C) People 30 years ago had much greater trust and faith in the government officials than we do now.

(D) The reputation damaged by scandals recovers at a slow rate, barring any chance for reelection.

(E) The country changed from a dictatorship to a democracy during the period the president was in power 30 years ago.

Question 03
A reason the physicist cannot give an expert opinion on the damage of the ozone layer is that she does not have necessary background knowledge in atmospheric science. On the other hand, a reason the biologist cannot is that he does not quite have the training in using the measurement tools. So, the task must be assigned to the chemist, the only scientist in the city other than the sciologist and biologist.

The argument depends on assuming which one of the following?

(A) The physicist has the proper training in using the measurement tools. (B) The expert opinion cannot be given by anyone other than a scientist in the city. (C) The biologist could have give an expert opinion if (D) (E)

Question 04
IDENTIFY

This is a /Method of Argument/ question.

 * baby boom

Question 05
Removed from scoring.

Question 08
trust mutual respect relationship marriage friendship

Dioxins, which cannot be synthesized except in the paper mills, is found in all fish noted for reproductive abnormalities whether they are from fresh water or ocean. However, the abnormalities in fresh water fish, such as loss of fins and inability to swim quickly, emerge only when the fish is infected with a LSAC virus which make them suspectible to dioxins to penetrate their body. Therefore, if fresh water fish have an abnormality, they must have infected with the virus at some point letting dioxins enter their body.

If the statements above are true, then which one of the following must also be true?

(A) A fresh water fish with no contact with a LSAC virus will not suffer from reproductive abnormality. (B) In the context of all reproductive abnormalities, paper mills resuppose dioxins. (C) (D) (E)

Question 09

 * All's well that snds well

Question 12
12. The environmentalist have noted bad breath of the people attending the annual LSAC dinner party. One possible cause is garlic rich dishes, which the party is abundant of. However, garlic dishes are unlikely to be the cause, since the most guests do not have bad breath in a few minutes after the party and garlic smell usually stays in the mouth for a long time.

Which one of the following statements, if true, most seriously weakens the argument?

(A) (B) (C) All guests are given a special mint when they leave that neutralizes garlic residue instantly. (D) Some guests still had bad breath after leaving the party. (E)

Section II Reading Comprehension
Passage 1 Disaster Relief

Question 06
Passage 2 Hippocratic Oath

Question 13
This is an attitude question.

Question 19
Passage 4 Law
 * aboriginal rights

Question 21
This is a purpose question.

Section III Analytical Reasoning
This section was easier than usual. Game 1 order in which a woman scheduled five meetings and a workout (Easiest)

Question 05
Game 2 six people played in four chess matches of two players each (medium)

Question 16
Game 3 determining which one or more of seven people appeared in an album of photographs (medium) Game 4 Three groups each exported two of five products. (hardest)

Question 01
IDENTIFY This is a conclusion question.

READ

The author is defending Mayor McKinney.

ANALYZE

CHOOSE (A) (B) (C) (D) (E)

 * property tax

The government's action to require all the shoe factories to clean up the water in the nearby wetland has often been criticized on the grounds that it hurts the shoe industry, but that is not a fair evaluation. The government action in fact benefits the industry in the long run. The cleaner wetland will promote tourism in the area bringing many people to shop at the local shoe stores which helps the industry to sell many more shoes.

Which one of the following most accurately expresses the main conclusion of the argument?

(A) It is impossible to tell whether the government is more committed to the interests of the industry than to the environmental cause. (B) The government has often been criticized for hurting the local industry. (C) The requirement to clean up the water will add costs to making shoes. (D) The criticism that the government action hurts the manufacturing industry is unwarranted. (E) The government's effort has increased tourists to the area and raised the income of the residents.

Question 02
IDENTIFY

This is a principle question.

READ

ANALYZE

CHOOSE

Question 18
Arbitration enables the parties to avoid the time and cost associated with going to trial. This always permits more flexibility and strongly encourages dialogue between the parties since arbitration facilitates negotiation and bargaining. Arbitration also permits the court to focus on more urgent cases without being overwhelmed by the senseless cases.

The statement above most strongly support which one of the following?

(A) Having no arbitration in the legal system is not maximally flexible. (B) (C) (D) (E) The people who take advantage of arbitration always avoid the cost of going to trial.

Question 21
ettiquette

/Principle/

Question 26
Ronald Dworkin, Taking Rights Seriously. Copyright 1977 by Pantheon Books.

James H. March, ed., The Canadian Encyclopedia. Copyright 1988 by Hurtig Publishers Ltd.

Christopher B. Ogden, "What Kinds of Help?" Copyright 1993 by Time Inc.

Edmund D. Pellegrino, MD, "Ethics: Rethinking the Hippocratic Oath." Copyright 1996 by the American Medical Association.

Norman Solomon, Hidden Agenda. Copyright 1995 by San Francisco Bay Guardian Co., Inc.

Carol Kaesuk Yoon, "Pariahs of the Fungal World, Lichens Finally Get Some Respect." Copyright June 13, 1995 by The New York Times.

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title: Past LSAT Explained/PrepTest 45


text:
Past LSAT Explained/PrepTest 46

June 2005 Form 6LSN68

Section I Reading Comprehension
This section is more difficult than the other recent exams. many said the humanities and law passages had the most difficult questions. They rated the section as more difficult than those on other recent exams. The first passage had seven questions and critiqued economists’ definitions of prosperity. The second passage had eight questions, and it analyzed the structure and symbols in a book about the Japanese Canadian's experience during World War II. The third passage had six questions, and it dealt with the evolutionary factors that may explain why modern pronghorns can run extremely fast, even though they don’t need great speed to elude predators. Six questions accompanied the last passage, which dealt with legal theory regarding whether punishments for criminals were just.

Passage 1 Social Science Critique of Economists' definitions of prosperity
 * ozone layer
 * prosperity
 * timber industry

Question 01
Main Idea

Question 04
Method of Argument

Question 05
Primary Purpose

Question 07
Primary Purpose Passage 2 Humanity (difficult) analyzed the structure and symbols in a book about the Japanese Canadian's experience during World War II
 * Joy Kogawa
 * Obasan
 * Japanese American
 * Japanese Internment
 * rite of passage
 * Christianity

Question 15
Passage 3 Natural Science Evolutionary factors that may explain why modern pronghorns can run extremely fast, even though they don't need great speed to elude predators
 * pronghorn
 * antelope
 * relict behavior
 * herd
 * cheetah
 * hyenas

Question 21
Passage 4 Law (Difficult) Legal theory regarding whether punishments for criminals were just
 * burglary
 * assault
 * legal theory
 * anabolic steroid

Question 01

 * inflammation

Question 02
William Shakespeare Francis Bacon

Must be True Question

Must be true questions require that the test taker select an answer choice that is proven by the information presented in the stimulus.

The stimulus to this question does not contain a conclusion, it is fact set. Most question that contain only fact sets are Must be True question stems or Resolve the Paradox question stems.

The correct answer to this question is answer choice (C): Shakespeare wrote neither the love poetry nor the dramas attributed to him.

Many test takers select answer choice (E): Shakespeare may have written the love poetry but did not write the dramas attributed to him.

This answer choice is incorrect because it is not a logical consequence of the facts presented. At no point in the argument did the Literary historian discuss weather the works were written by various artist. Remember in Must Be True questions all the information necessary to answer the question resides in the stimulus and the details are what the test makers aim to test. Test takers can not generalize or go beyond the scope of the information presented in the stimulus.

List of Modifier words in play: could have, but, could only, did not, much

Question 03
genetic test

Question 05
Art Patrons

Strengthen Question

Strengthen questions ask you to support the argument in any way possible. This type of answer has great range, the answer choice that strengthens the argument weather it be by 1% or 100% is correct.

The use of the words "most support" and the sufficient indicator word "if" allow test takers to correctly identify this question as a Strengthen question.

Strengthen question are considered amongst the most difficult questions types because of their great range of answer choices.

The stimuli for strengthen and weaken questions tend to be similar, both often contain faulty reasoning.

Conclusion of the argument: art in the next century will rarely express social and political doctrines that are perceived to be subversive of that social order. Premise: Artist in the next century will be supported largely by private patrons. Premise: These patrons will be supporters of social order - whatever it may be at the time-

Correct Answer choice (A): Art Patrons tend not to support artists whose art expresses social and political views that are in opposition to their own.

In strengthen questions it is important to focus on the conclusion. Strengthen question will always contain an argument.

Answer choice (A) is correct because it eliminates a possible problem with the facts presented. If Patrons did tend to support artist whose art expresses social and political views in opposition of their own then there would be a problem in the reasoning of the argument and would thus weaken instead of strengthen the argument. Incorrect Answer choice (D): Artist ten to become more critical of contemporary social and political arrangements after they are freed of their dependency on private patrons.

Incorrect Answer choice (D) is incorrect because it is out of the scope of the argument. This answer choice supports an issue that is tangential to the argument

Question 06
Artificial Turf/Natural Grass

Resolve the Paradox Question

Resolve the Paradox questions: Resolve the paradox questions do not typically contain a conclusion or an argument. The correct answer will address both sides of the paradox. The correct answer will either explain how both sides came into being or provide new information that allows both occurrences to coexist. The stimulus contains a contradiction by the use of the following words:

However, nevertheless, but, in contrast, yet, although, paradoxically, surprisingly...

Answer choice (B) is the correct answer.

Question 10
Air Traffic Nuclear Power and Physicians

Assumption question:

An assumption is an unstated premise. It is a piece of information that the conclusion rest upon. Conclusion Valid --> Assumption true. For many students assumptions questions are the most difficult Logical reasoning question type? The correct answer in an assumption question is a statement the author must believe in order for the argument to be correct.

Answer choice (A) is correct: There is no indispensable aspect of residency training that requires resident physicians to work exceptionally long hours.

Note an assumption can be consider a minimalistic answer and assumption question can not contain extraneous information. Answer choice (A) is a defender answer choice. The defender role protects the argument by ruling out other scenarios that weaken the argument.

Answer choice (C) is incorrect: The more hours one works in a week, the less satisfactorily one performs one's work. This answer choice is incorrect because it is out of the scope of the argument. The argument states that air traffic controllers and nuclear power plant operators are not allowed to work exceptionally long hours. No where does it state the relationship between work hours and performance.

Question 11
Self-deprecating humor

Weaken Question

Weaken question and strengthen question tend to have holes in the argument. In weaken question the stimulus is suspect and the answer choices are taken as fact.

The correct answer is (A): bases a conclusion about how one group will respond to self-deprecation on information about how a different group responds to it.

This argument contains an improper comparison. The first sentence states career advice for employees and the last sentence describes a study of employers who use self deprecating humor in front of their employees. The comparison is not valid.

Question 12
Researcher: Inducing Deep Sleep

Strengthen question

Focus on the conclusion, similar to weaken question. Cause and effect principals.

Correct answer choice is (E): Raising body temperature slightly by taking a warm bath just before bedtime will likely result in increased deep-sleep

Strengthen questions can either strengthen the argument by 1% to 100%. Answer choice (E) is correct because it strengthens the conclusion of the argument. Remember all strengthen questions will contain a conclusion. The conclusion to this argument is in the final sentence. Exercising in the afternoon tends to raise body temperature slightly until after bedtime, and this extra heat induces deeper sleep.

Answer choice (E) shows that when the cause occurs the effect occurs, when body temperature increases before bedtime (cause) individuals get experience deeper sleep (the effect).

Answer choice (C) is incorrect because it is out of the scope of the argument. In no place of the argument did the Researcher discuss which are the best methods of inducing deep sleep. Note that reading this answer choice quickly and not reading all the answer choices can cause test takers to incorrectly select (C) as the correct answer choice.

Question 14
Roger Bacon vs Authorities

Flaw in the reasoning

The information in the stimulus is regarded as fact and the answer choices are under suspicion. Good test takers should be able to find the flaw in the reasoning before reading the answer choices.

The correct answer choice is (E): Criticizes Bacon's character in order to question his scientific findings

This is a source argument question, the argument attacks the person or source or source instead of the argument they advance.

Question 16
Visually impaired computers

strengthen question:

Focus on the conclusion. What ever strengthens the argument by 1 to 100% is correct. Beware of shell game, opposite, out of scope or strengthening a sub conclusion answers.

The correct answer is (B): Relatively easy-to-use computer systems that can read information aloud, display it in large type, or produce a braille version of it are widely available.

The conclusion of the argument is in the last sentence: Thus, visually impaired people can now access information from computers more easily than they can from most traditional sources.

The correct answer choice (B) proves that the information presented in the argument is correct and accurate.

Question 17
Legislator vs Analyst

Method of reasoning question

Stimulus is fact, answers choices are under suspicion. Method of reasoning questions are simply abstract must be true questions. It is important to read closely in these questions, generalization can be very harmful. The details are all the test taker have to test.

Correct answer (E) implying that the legislator has drawn a conclusion about cause and effect without considering how often the alleged effect has occurred in the absence of the alleged cause.

The terms clearly shows introduced the cause and effect relationship.

The correct answer showed that although the effects occurred the cause did not, this disproves the causal conclusion.

Question 18
Quantum mechanics may complete physical theory

Parallel Reasoning Questions:

Parallel reasoning questions have been known to be quite time consuming. If a parallel reasoning question contains flawed reasoning it will be stated in the question stem, if the question stems does not discuss flawed reasoning then the stimulus does not contain flaws.

Parallel reasoning questions are the most abstract type of question on the LSAT.

Correct answer choice is (C): Your sister is a very good chess player but she has never won a chess tournament; therefore, she will not win this chess tournament.

Question 19
Musical Intervals with 6 month old babies

Strengthen Question

An effective method of attacking a strengthen question is to look for weaknesses in the argument. Address a weakness in an argument will strengthen that argument.

Remember to focus on the conclusion and to stay within the scope of the argument.

The correct answer is (B): None of the babies in the experiment had previous exposure to music from any culture.

Answer choice (A) is incorrect because it is out of the scope of the argument.

Question 26
the experimental section appeared in Section 2. Ratings of this administration placed its difficulty on par with other recent exams.

Princeton Review students rated the difficulty of this section as similar to games sections that have appeared on exams within the past year.

The first game involved determining the order in which six animals appeared on six signposts.

In the second game, four cassette tapes each held songs on their front and back sides. There were four types of songs that could appear.

The third game involved determining in which order five cities experienced storms and what type of precipitation fell on each city.

In the last game, six committee members had to be assigned to three subcommittees with three members each.

Test takers rated the first and third games as easier and the second and fourth games as harder. Our students found that their familiarity with the games and experience with making deductions helped them set up the games and work the questions efficiently.

Joel Feinberg, The Moral Limits of the Criminal Law. ©1988 by Oxford University Press. Times.
 * Cheng Lok Chua, “Witnessing the Japanese Canadian Experience inWorldWar II: Processual Structure,
 * Symbolism, and Irony in Joy Kogawa’s Obasan.” ©1992 by Temple University.
 * Myrna I. Lewis, “What’s So Bad about Feeling Good? How Psychotherapy Can HelpYou Find Peace of Mind.” ©1993 by the American Association of Retired Persons.
 * William Bryant Logan, “What Is Prosperity?” ©1995 by POINT.
 * James Shreeve, “Music of the Hemispheres.” © October 1996 by Discover.
 * Carol Kaesuk Yoon, “Pronghorn’s Speed May Be Legacy of Past Predators.” ©1996 by The New York

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

title: Past LSAT Explained/PrepTest 46


text:
Past LSAT Explained/PrepTest 47

The experimental section appeared in Section 2. Ratings of this administration placed its difficulty on par with other recent exams.

Question 01
IDENTIFY

This is a Flaw question.
 * police patrol

READ

This is an LSAT's perennial favorite. This is a typical causation problem. A causes B not B causes A. Having many crimes causes the number of the police to rise. Maybe the police reinforcement has occurred only recently to have any effect on crime.

ANALYZE

This is the first question and a repeat from previous LSAT tests. You need to be able to do this around half a minute.

CHOOSE

(A) Incorrect. No emotional appeal here. If there was, the passage will look like this:

While it might be expected that those neigborhoods most heavily patrolled by police have the least crime, they in fact have the most. Just look at the brutal and heinous murder of children by ruthless Dr. El Saat. With his freightening look and psychopathic behaviors, his dark presence instills fear to all. Therefore, the presence of police does not decrease crime in a neighborhood.

(B) Incorrect. We are only concerned with a particular neighborhood in question. We don't have to worry about whether the same criminals commit something else outside our jurisdiction- none of our business period. For this choice to be correct, it has to be like given that answer (D) does not appear:

While it might be expected that those neigborhoods most heavily patrolled by police have few criminals, the statistical evidence overwhelmingly supports the claim that such neighborhoods have the most. This shows that the presence of police does not decrease the number of criminals in the neighborhood.

(C) Incorrect.

While it might be expected that those neigborhoods most heavily patrolled by police the least crime, the frontpage of LSAC Times recently reported a theft of the LSAT material by a group of pre-law students. Since stealing the LSAT is the most heinous crime of all, this shows that the presence of police does not decrease crime in the neighborhood.

(D) Correct.

(E) Incorrect. Wordy choice but wrong.

Question 02
IDENTIFY This is a Weaken question. Premise: There have been increased international efforts to protect habitats of endangered species.
 * endangered species

Premise: Rate that species goes extinct still rising.

Conclusion: Efforts to protect endangered species have been wasted.

Choose the answer that WEAKENS the argument:

A) It doesn't matter if they can preserve habitats any better now, their PAST efforts could still have been wasted.

B) CORRECT This shows that despite the extinction rate, their efforts were not entirely wasted.

C) Confirms the rate, does not impact argument.

D) The argument does not mention economic benefit.

E) Like A, it doesn't matter what they may do in the future. The argument is about what has been done in the past.

Question 03

 * psychology
 * academic department

Question 04
DISAGREE QUESTION

Aaron: Judge's statements were irresponsible.

Belinda: They were natural and truthful.

A) Aaron's opinion, Belinda doesn't address this.

B) CORRECT The explicitly mention opposing viewpoints.

C) Tricky, but Aaron never states that he condones the lawyer's actions, just that he disagrees with the judge's statement.

D) This is not addressed by either.

E) This is not a point of contention.

Question 05
Principle consists of two parts:

1. People believe only real things can evoke emotions.

2. Sometimes they have real emotions to things they know are not real.

The correct answer choice will have both parts.

A) CORRECT 1: Fred didn't expect to be scared. 2: He was actually scared, even though he knew it was fake.

B) No emotions discussed.

C) It wasn't real, but Raheem didn't know. Doesn't satisfy either part.

D) This may be representative of part 2, but definitely missing part 1.

E) No emotions discussed.

Question 06

 * earthquake
 * seismic shock

Question 07
insurance bicycle

Question 08
fortune telling psychic extrasensory perception (ESP)

Question 09
Premise: Historians have 2 criticisms

Premise: First, uncritical of status quo

Premise: Second, self-indulgent with own dreams.

Premise: Moviemakers gave audience what they desired.

Conclusion: Second can't be true.

This question asks us to find the assumption that would be sufficient to make the argument true.

A) Does not make the second criticism not true.

B) Only discusses the reasonableness of criticism 1

C) Only discusses criticism 1

D) Totally unrelated to criticism 2.

E) CORRECT This explains why criticism 2 is unfounded.

Question 10

 * volunteerism

A) Editorial does not claim there is no causality, just that it "may not" be true.

B) No specific example is cited.

C) This claim was not in the argument.

D) CORRECT The author suggests another interpretation.

E) Author did not attempt to prove anything.

Question 11

 * cash-flow

Question 12

 * origin of life

Question 14

 * dialect

Question 15

 * brand

Question 18

 * atmospheric science
 * troposhere
 * ultraviolet
 * stratosphere

Question 19

 * oral polio vaccine
 * inactivated polio vacine

Question 20

 * day care

Question 22

 * pesticide

Question 23

 * neuroscientist
 * creativity

Question 24

 * manual

Question 25

 * demography

Question 26

 * education

Section II Reading Comprehension
Reading Comprehension - 26 questions the humanities and science passages had the most difficult questions.

The first passage had described New York African-American ministers’ leadership role in a protest during the early 1960s.

The author of the second passage argued that China’s Cultural Revolution, which attempted to restrict expression that defied centrally defined values, paradoxically inspired divergent artistic movements.

The third passage contrasted approaches to family law and contended that mediation was superior to court proceedings.

The last passage discussed new evidence about the relationship between a pathogen and its host; it concluded that a pathogen that it is easily transmitted or can survive outside the body can kill its host and still reproduce successfully.

Question 26
the difficulty of this section as similar to games sections that have appeared on exams within the past year. They felt it was slightly harder than the June 2005 Games section, but quite manageable. The first game involved determining the order in which seven elements were placed. In the second game, you had to determine whether each of seven switches was in the On or Off position, according to a set of complex conditional rules. The third game involved figuring out which one or more of four music genres were sold at each of five stores. In the last game, six employees, three of whom were supervisors, had to be assigned to a Monday-to-Friday work schedule. Two people worked each day, and at least one had to be a supervisor. Test takers rated the first and fourth games as easier and the second and third games as harder.

 * "Court-Connected Family Mediation Programs in Canada." May by Alberta Law Reform Institute.
 * Paul W. Ewald, "The Evolution of Virulence." Copyright May 1993 by Scientific American, Inc.
 * Clarence Taylor, The Black Churches of Brooklyn. Copyright 1994 by Columbia University Press.
 * Li Xianting, "Major Trends in the Development of Contemporary Chinese Art." tr. Valerie C. Doran. Copyright 1993 by Hanart T Z Gallery.

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title: Past LSAT Explained/PrepTest 47


text:
Past LSAT Explained/PrepTest 48

October 2001 Form 1LSS51 On most test forms, the experimental section appeared in Section 3. Ratings of this administration placed its difficulty slightly below that of other recent exams.

Games (Analytical Reasoning) - 22 questions the difficulty of this section as easier than Games sections that have appeared on exams within the past year.

In the first game, a student in a dorm room had five appliances, but they could not all be used at once. The conditions listed appliances that could not be plugged in at the same time, and test takers had to determine how many and which appliances were used in various scenarios.

The second game involved determining the order in which a farmer plowed each of his eight fields.

The third game asked test takers to determine which one or more of three appliance types five workers were able to repair.

In the last game, three folk bands and three rock bands each had to be scheduled for one of six time slots on two concert stages. The complexity of the setup and conditions made this the most challenging game. Overall, test takers rated the first and second games as easier and the third and fourth games as harder.

Question 01
The question asks to identify a statement that will weaken the argument. The conclusion stated that lie-detectors that can detect the physiological reaction are a "sure" way of determining when someone is lying. One way to weaken this conclusion is to break the relationship. Answer D shows just that physiological reaction is not necessarily a result of lying.

Question 02
This question asks us to identify a flaw in the argument. The publishing executive states that the company needs to sell at least 100,000 books to make a profit. And his conclusion is that because the best selling of the 12 books is unlikely to sell over 100,000 copies, the company will not make a profit. The flaw is obvious. We are not concerned of the number of copies sold for ONE book, but instead, a total of ALL books from the company. Answer D identifies just that.

Section II Reading Comprehension
Examinees varied in their assessments of passage difficulty, but many said the humanities and science passages had the easiest questions.

The first passage described prehistoric cave paintings and speculated about their purpose.

The second passage discussed the work of contemporary poet Louise Gluck. While some critics have argued that Gluck should write from a distinctively female perspective, Gluck contends that great poetry deals with universal subjects.

The third passage reviewed native Canadians’ efforts to win property rights by getting the courts to recognize communal ownership as a viable legal concept.

The fourth passage examined how embryonic polarity differs among species—a somewhat surprising feature because other developmental processes are more similar across species.

Question 26
Natalie Angier, "[http://query.nytimes.com/gst/fullpage.html?res=9905EFDC1339F932A15752C1A963958260 Heads or Tails?" How Embroyos Get It Right.]" Copyright by The New York Times.

Catherine Bell, "Aboriginal Claims to Cultural Property in Canada: A Comparative Legal Analysis of the Repatriation Debate." Copyright 1992 by the American Indian Law Review.

Louise Gluck, Proofs & Theories: Essays on Poetry. Copyright by Louise Gluck.

"Why Bad Hair Days May Not Matter." Copyright 1996 by Sussex Publishers Inc.

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title: Past LSAT Explained/PrepTest 48


text:
Past LSAT Explained/PrepTest 49

Summary As always, test forms for the June 2006 LSAT included an experimental (unscored) section. On most test forms, the experimental section appeared in Section 2. Be aware, however, that LSAC often administers a few selected forms with identical scored sections, but with their experimental sections in a different location. Ratings of this administration placed its difficulty slightly above that of other recent exams. Princeton Review students report being pleased with their overall performance. Games - 22 questions Princeton Review students rated the difficulty of this section as on par with Games sections that have appeared on exams within the past year. In the first game, you had to determine the order in which six foreign language films were shown at a film festival. Twelve films were available, two each in six languages. The second game concerned five types of mail that were delivered to one of three people. The third game asked test takers to determine which of seven courses were offered during a summer term. In the last game, eight computer chips had to be ranked in order from fastest to slowest. Our students found that their familiarity with the games and experience with making deductions helped them set up the games and work the questions efficiently.

Scored Arguments - 25 questions in each section One scored Arguments section had 26 questions, and the other had 25. Test takers rated the 26-question section as harder than the 25-question section. The 26-question section included an unusually large number of long and densely-worded arguments and answer choices, and it had several challenging questions. Test takers cited careful use of process of elimination (POE) as the most helpful technique. Overall, Princeton Review students found the techniques they had learned in class worked well on the exam. They reported that their ability to spot language shifts, recognize common flaws, and diagram conditional statements were the most useful tools for analyzing arguments. Broad experience with past exams was invaluable to test takers, and smart pacing choices were required to get the best possible results.

Scored Reading Comprehension - 28 questions The reading comprehension section offered the usual breakdown of topics—science, law, social science, and arts/humanities. Examinees found the law passage easiest and the science passage hardest. The first passage dealt with the use of computer-assisted crime reenactments in the courtroom. The author discussed the benefits, described potential problems, and suggested ways to prevent those problems. The second passage argued that because African artists alter their styles to suit consumers from other ethnic groups and regions, scholars can’t reliably draw conclusions about an object’s origins based on fine style distinctions. The third passage argued that though the historical evidence is limited, source records clearly indicate that ancient Greek and Roman societies had female physicians. The author supported this contention by citing examples of Classical writers who referred to female physicians in a matter-of-fact way. The fourth passage explained why maize’s method of photosynthesis makes it such a productive crop. Overall, this section demanded the skills of mapping the passage well, paraphrasing its contents, searching for specific evidence in support of answers, and eliminating choices judiciously.

Question 26
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title: Past LSAT Explained/PrepTest 49


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Past LSAT Explained/PrepTest 50

The September 2006 LSAT Form 6LSN70

Section I Reading Comprehension
The experimental section appeared in Section 2. Ratings of this administration placed its difficulty slightly above that of other recent exams. Scored Reading Comprehension - 28 questions Examinees found the arts passage easiest and the science passage hardest.

On the whole, Test takers found this to be a difficult section because of the number of questions, difficulty of the questions, and complexity of the passages.

Passage 1 The first passage discussed Mexican-American writers and argued that their writing displays a fusion of language and theme unique to their experiences.

Passage 2 The second passage reviewed changes in bankruptcy law, noting a shift in emphasis from punishment to restitution. The author viewed the change as beneficial because those who declare bankruptcy can better repay their debtors. Passage 3 The third passage addressed the malleability of cultural identity. It used historical examples to illustrate how one culture can engulf another and cause identity shifts. Passage 4 The last passage dealt with chaos theory, specifically the idea that you can predict a future state but not how something will get to that state. It described recent work in the field that challenges the reproducibility of scientific results and has the potential to undermine some of science’s core tenets.

Section II Logical Reasoning
Most examinees found one of the sections harder than the other, though the difference in difficulty was less pronounced than on some other recent exams.

Section III Analytical Reasoning
Games - 22 questions Princeton Review students rated the difficulty of this section as easier than Games sections that have appeared on exams within the past year.

In the first game, you had to determine at which of four airports six flights, ordered 1 to 6, landed.

The second game involved selecting a panel of five people from a group of three parents, three students, and four teachers.

The third game asked test takers to determine in which of five years three students graduated and in which of those years they purchased cars.

In the last game, a child eating alphabet soup decided to eat from one to three of six remaining letters in three spoonfuls. You had to determine which letters were in each spoonful.

Question 24
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title: Past LSAT Explained/PrepTest 50


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Past LSAT Explained/PrepTest 51

The December 2006 LSAT Form The experimental section appeared in Section 1.

Section I Logical Reasoning
22 questions Princeton Review rated the difficulty of this section as similar to that of Games sections that have appeared on exams within the past year.

The first game concerned the colors of a clown’s jacket and overalls. Two arrangements were possible: Either the jacket had three colors and the overalls one color, or the jacket had a single color and the overalls two colors.

The second game involved ranking six hotel suites in order from most to least expensive.

The third game asked test takers to determine in what order seven songs were placed on a CD and whether each song was new or classic.

In the last game, you had to determine the order of delivery for eight parcels based on clues that specified the relative order of the elements.

Section II Reading Comprehension
This section was easier than those on other recent exams.

Passage 1 Humanity (easiest) Topic: The difficulties critics have classifying Mphahlele’s works
 * Ezekiel Mphahlele

Passage 2 Natural Science (medium) Topic: Reviewing Theories and Evidence related to Late Heavy Bombardment (LHB), a period approximately 4 billion years ago during which the Moon, Earth, Mercury, Venus, and Mars were subjected to many impacts from space
 * Late Heavy Bombardment

Passage 3 Social Science (medium) Topic: communication specialists’ views on how foreign television programming influences cultures

Passage 4 Law hardest Topic: The use of artificial intelligence programs in the practice of law
 * Artificial intelligence

Question 01
A clown will select a costume consisting of two pieces and no others: a jacket and overalls. One piece of the costume will be entirely one color, and the other piece will be plaid. Selection is subject to the following regulations:

If the jacket is plaid, then there must be exactly three colors in it. If the overalls are plaid, then there must be exactly two colors in them. The jacket and overalls must have exactly one color in common. Green, red and violet are the only colors that can be in the jacket. Red, violet, and yellow are the only colors that can be in the overalls.

We can diagram all of the possibilites:

Plaid Jacket               Plaid Overalls G R  V            R/V  Y

Solid Jacket               Solid Overalls G/R/V                      R/V/Y

Question 06
Six hotel suites--F, G, H, J, K, L--are ranked from most expensive (first) to least expensive (sixth). There are no ties. The ranking must be consistent with the following conditions:

H is more expensive than L. If G is more expensive than H, then neither K nor L is more expensive than J. If H is more expensive than G, then neither J nor L is more expensive than K. F is more expensive than G, or else F is more expensive than H, but not both.

This convoluted question consists of two scenarios based on the following constraints defining which room is the most expensive (Most expensive always to the left):

H > L if G > H then J > K if G > H then J > L if H > G then K > J if H > G then K > L F > G / F > H F is never greater than G and H (F is always between G and H)

The constraints can be diagrammed into two diagrams as follows (Where those letters further to the left are more expensive than the letters to the right connected either with a "-" or a "/" or a "\". The ellipses denote that it cannot be determined from the constraints what comes after a particular letter, and letters on different lines who are not connected can also not be said to be more or less expensive than one another unless they are directly connected through either one or a series of lines from left to right.):

1)

...G - F - H - L... /         ...J - K...

2) ...H - F - G...   \     L...    / ...K - J...

Thus when we examine all of the choices in question six against the two diagrams, we find that the only possible answer is:

B. (H, K, F, J, G, L)

Question 07
Using the diagram from Question 6 above...

If G is the second most expensive suite, then which one of the following could be true?

The question states that G is the second most expensive suite. Looking at our two diagrams, we can see that only in the first diagram can G be the second-most expensive suite (remember expense is left to right, more expensive to less). That being said, we can quickly compare each of the answers to the first diagram. The only possibility is

C. (K is more expensive than F)

because while our lines denote that K must be less expensive than J, we do not know anything about the relation of the second line of the diagram to the first except that J is less expensive than L. This allows J to fall anywhere on the continuum so long as it does not fall to the right of L. While K must come after J, there is no problem with J and K falling to the left of F in the first diagram.

Question 08
Using the diagram from question 6...

Which one of the following CANNOT be the most expensive suite?

This question could be answered independently from the diagrams based only on the final constraint. "F is more expensive than G, or else (in the event that it is less expensive than G) F is more expensive than H, but not both.

We can take this to mean that F is always situated between G and H in some fashion, meaning that it will never be the most expensive suite in any situation.

A. (F)

Question 09
Using the diagram from question 6...

If L is more expensive than F, then which of the following could be true?

Only in diagram 2 can L be more expensive then F because in the first diagram L must be less expensive than H which is less expensive than F. Therefore, we are to use our second diagram to answer this question.

Because J is not in any way directly connected to L (which now falls between H and F), it is entirely possible for G and J to be interchangeable as the least expensive suite. Therefore, it is entirely possible for G to be more expensive than J.

D. (G is more expensive than J)

Question 10
Using the diagram from question 6...

If H is more expensive than J and less expensive than K, then which one of the following could be true?

Only in diagram two is it possible for H to be simultaneously more expensive than J and less expensive than K, because K can move indefinitely to the left, and J can move indefinitely to the right. Therefore, we are to use our second diagram.

Knowing that K is more expensive (farther to the left) than H, we can plausibly form the chains KHJLFG or KHLJFG. Only the first 4 letters are relevant to the question, and given the question's constraint, we can see that it is possible to get the answer

D. (J is more expensive than L)

Question 13
The answer to this question requires all the clues.

You know every rock song must have new composition track before it (rule 5). Therefore, track 5 must be a new composition because, as stated in rule 4, track 6 is a rock classic.

You also can conclude track 7 is a new composition because it would be impossible for track 7 to be a rock classic. For track 7 to be a rock classic, track 6 must be a new composition (rule 5). Because track 6 is a rock classic and not a new composition (rule 4), track 7 is a new composition.

So! So far, we know tracks 5 and 7 are new compositions and track 6 is a rock classic.

We know that VXZ (in some order) must be tracks 5-7 (rules 1-3). According to rule 6, Z is a rock classic. Therefore, both V and X must be new compositions.

Lucky X is choice D.

Question 26
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title: Past LSAT Explained/PrepTest 51


text:
Growing Edible Sprouts

The Basics of Growing Edible Sprouts

 * 1) Introduction - A Clean and Healthy Crop
 * 2) /Seeds/
 * 3) /Water and Air/
 * 4) Removing Hulls and Hard Seed
 * 5) /Storage/

Growing Sprouts

 * 1) Growing Sprouts in Jars
 * 2) Growing Sprouts in Trays
 * 3) Growing Sprouts in Buckets
 * 4) Growing Large Batches of Commercial Sprouts

Regulations and Research

 * 1) /Seed Testing/
 * 2) /FDA Guidelines/
 * 3) Recent Scientific Research

Appendices

 * 1) Seed Yield and Growing Time
 * 2) Nutritional Information
 * 3) /Recipes/
 * 4) /Bibliography/

title: Growing Edible Sprouts


text:
New Zealand History/The Treaty of Waitangi

‹ Back to Missionaries Dispatched to New Zealand

The Treaty of Waitangi
The Treaty of Waitangi was an agreement between the British and about 540 Maori chiefs, in which the Maori people gave their sovereignty to the British Crown. Today, it is seen as the founding document of New Zealand.

An Overview of the Treaty
Prior to 1840, the British Government was at first uninterested in annexing the country, but with New Zealand settlers becoming lawless and reports of the French planning to take control of the country, the British finally decided to act. Once the treaty had been authorised by British authorities, the English draft of the treaty was translated overnight by the missionary Henry Williams and his son, Edward, into Maori on the 4th of February 1840.

The treaty was then debated by about 500 Maori over the course of a day and a night, with Lieutenant-Governor William Hobson, who had been appointed the task of securing British control over New Zealand, stressing the benefits to the Maoris of British sovereignty. Once the chiefs were reassured that their status and authority would be strengthened, about 40 chiefs signed the treaty at Waitangi on the 6th of February 1840. After this, the document was taken all over the country, and about 500 more chiefs signed.

The English Version and the Maori Version are as follows:

The English Version of the Treaty
The actual draft for translation into Maori and dated 4th February 1840 was as follows: Her Majesty Victoria, Queen of England in Her gracious consideration of the chiefs and the people of New Zealand, and Her desire to preserve to them their lands and to maintain peace and order amongst them, has been pleased to appoint an officer to treat with them for the cession of the Sovereignty of their country and of the islands adjacent, to the Queen. Seeing that many of Her Majesty's subjects have already settled in the country and are constantly arriving, and it is desirable for their protection as well as the protection of the natives, to establish a government amongst them. Her Majesty has accordingly been pleased to appoint Mr. William Hobson, a captain in the Royal Navy to be Governor of such parts of New Zealand as may now or hereafter be ceded to Her Majesty and proposes to the chiefs of the Confederation of United Tribes of New Zealand and the other chiefs to agree to the following articles. Article first The chiefs of the Confederation of the United Tribes and the other chiefs who have not joined the confederation, cede to the Queen of England for ever the entire Sovereignty of their country. Article second The Queen of England confirms and guarantees to the chiefs and the tribes and to all the people of New Zealand, the possession of their lands, dwellings and all their property. But the chiefs of the Confederation of United Tribes and the other chiefs grant to the Queen, the exclusive rights of purchasing such lands as the proprietors thereof may be disposed to sell at such prices as may be agreed upon between them and the person appointed by the Queen to purchase from them. Article third In return for the cession of their Sovereignty to the Queen, the people of New Zealand shall be protected by the Queen of England and the rights and privileges of British subjects will be granted to them. Signed, William Hobson Consul and Lieut. Governor. Now we the chiefs of the Confederation of United Tribes of New Zealand assembled at Waitangi, and we the other tribes of New Zealand, having understood the meaning of these articles, accept them and agree to them all. In witness whereof our names or marks are affixed. Done at Waitangi on the 6th of February, 1840.

The Maori Version of the Treaty
KO WIKITORIA te Kuini o Ingarani i tana mahara atawai ki nga Rangatira me nga Hapu o Nu Tirani i tana hiahia hoki kia tohungia ki a ratou o ratou rangatiratanga me to ratou wenua, a kia mau tonu hoki te Rongo ki a ratou me te Atanoho hoki kua wakaaro ia he mea tika kia tukua mai tetahi Rangatira – hei kai wakarite ki nga Tangata maori o Nu Tirani – kia wakaaetia e nga Rangatira Maori te Kawanatanga o te Kuini ki nga wahikatoa o te wenua nei me nga motu – na te mea hoki he tokomaha ke nga tangata o tona Iwi Kua noho ki tenei wenua, a e haere mai nei.

Na ko te Kuini e hiahia ana kia wakaritea te Kawanatanga kia kaua ai nga kino e puta mai ki te tangata Maori ki te Pakeha e noho ture kore ana.

Na kua pai te Kuini kia tukua a hau a Wiremu Hopihona he Kapitana i te Roiara Nawi hei Kawana mo nga wahi katoa o Nu Tirani e tukua aianei amua atu ki te Kuini, e mea atu ana ia ki nga Rangatira o te wakaminenga o nga hapu o Nu Tirani me era Rangatira atu enei ture ka korerotia nei.

Ko te tuatahi Ko nga Rangatira o te wakaminenga me nga Rangatira katoa hoki ki hai i uru ki taua wakaminenga ka tuku rawa atu ki te Kuini o Ingarani ake tonu atu – te Kawanatanga katoa o o ratou wenua.

Ko te tuarua Ko te Kuini o Ingarani ka wakarite ka wakaae ki nga Rangitira ki nga hapu – ki nga tangata katoa o Nu Tirani te tino rangatiratanga o o ratou wenua o ratou kainga me o ratou taonga katoa. Otiia ko nga Rangatira o te wakaminenga me nga Rangatira katoa atu ka tuku ki te Kuini te hokonga o era wahi wenua e pai ai te tangata nona te Wenua – ki te ritenga o te utu e wakaritea ai e ratou ko te kai hoko e meatia nei e te Kuini hei kai hoko mona.

Ko te tuatoro Hei wakaritenga mai hoki tenei mo te wakaaetanga ki te Kawanatanga o te Kuini – Ka tiakina e te Kuini o Ingarani nga tangata maori katoa o Nu Tirani ka tukua ki a ratou nga tikanga katoa rite tahi ki ana mea ki nga tangata o Ingarani.

-William Hobson, Consul and Lieutenant-Governor.

Na ko matou ko nga Rangatira o te Wakaminenga o nga hapu o Nu Tirani ka huihui nei ki Waitangi ko matou hoki ko nga Rangatira o Nu Tirani ka kite nei i te ritenga o enei kupu, ka tangohia ka wakaaetia katoatia e matou, koia ka tohungia ai o matou ingoa o matou tohu.

Ka meatia tenei ki Waitangi i te ono o nga ra o Pepueri i te tau kotahi mano, e waru rau e wa te kau o to tatou Ariki.

A Literal Translation of the Maori Text
Here's Victoria, Queen of England, in her gracious remembrance towards the chiefs and tribes of New Zealand, and in her desire that the chieftainships and their lands should be secured to them and that obedience also should be held by them, and the peaceful state also; has considered it as a just thing, to send here some chief to be a person to arrange with the native men of New Zealand, that the Governorship of the Queen may be assented to by the native chiefs in all places of the land, and of the islands. Because too many together are the men of her tribe who have sat down in this land and are coming hither.

Now it is the Queen who desires that the Governorship may be arranged that evils may not come to the native men, to the white who dwells lawless. There! Now the Queen has been good that I should be sent, William Hobson, a captain of the Royal Navy, a Governor for all the places in New Zealand that are yielded now or hereafter to the Queen. She says to the Chiefs of the Assemblage (Confederation) of the tribes of New Zealand, and other chiefs besides, these laws which shall be spoken now.

Here's the first: Here's the chief of the Assemblage, and all the chiefs also who have not joined the Assemblage mentioned, cede to the utmost to the Queen of England for ever continually to the utmost the whole Governorship of their lands.

Here's the second: Here's the Queen of England arranges and confirms to the chiefs, to all the men of New Zealand the entire chieftainship of their lands, their villages, and all their property.

But here's the chiefs of the Assemblage, and all the chiefs besides, yield to the Queen the buying of those places of land where the man whose land it is shall be good to the arrangement of the payment which the buyer shall arrange to them, who is told by the Queen to buy for her.

Here's the third: This, too, is an arrangement in return for the assent of the Governorship of the Queen. The Queen of England will protect all the native men of New Zealand. She yields to them all the rights, one and the same as her doings to the men of England.

-William Hobson, Consul and Lieutenant-Governor.

Now here's we: Here's the chiefs of the Assemblage of the tribes of New Zealand who are congregated at Waitangi. Here's we too. Here's the chiefs of New Zealand, who see the meaning of these words, we accept, we entirely agree to all. Truly we do mark our names and marks.

This is done at Waitangi on the six of the days of February, in the year one thousand eight hundred and four tens of our Lord.

A Comparison of the English and Maori Versions
The final draft of the treaty was done by William Hobson and James Busby Although the English and Maori versions of the treaty are mostly the same, there are some subtle differences.

In the First Article, the English Version stated that the chiefs should give all rights and powers of sovereignty to the Queen. In the Maori Version it states that Maori give up government to the Queen. There is no direct translation for sovereignty in Maori, because the Maoris had individual tribes instead of an overall ruler.

In the Second Article, the English Version stated that the Crown had the sole right of purchase to Maori land. It is not certain if the Maori Version conveyed this message properly.

Forward to European Colonisation of New Zealand ›


text: User:Peteturtle~enwikibooks/lockedpage

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text: User:SB Johnny/sandbox 8

title: User:SB Johnny/sandbox 8


text:
Talk:Sound Synthesis Theory/Modulation Synthesis

The Amplitude Modulation diagram of C(t) x M(t) is wrong; the graph of M(t) does not correspond properly to the graph of C(t) x M(t). Must fix in the future. - Damien Karras 12:47, 12 September 2007 (UTC)

Figure 8.4 does not seem to show AM. It is RM since the modulator is bipolar.


text:
Sound Synthesis Theory/Physical Modelling

=Physical Modelling Synthesis=

Introduction
Physical Modelling synthesis is not confined to a particular technique, but rather represents a family of approaches to synthesis. Physical modelling systems attempt to model the propagation of sound energy in a system, typically starting with a mathematical model or algorithm that is often recursive. Physical modelling techniques often start by attempting to replicate the basic structure of an acoustic instrument and hence mimic the sound it makes when 'excited'. This excitation normally comes in the form of an initial impulse, typically a short burst of noise.

The main advantage of this system is that one can generate convincing acoustic sounds, such as a plucked string or drum hit. Aside from this, other advantages include the ability to tweak parameters (e.g. instrument body density, string length) in order to create specific types of instrument from a generic model. In the extremes, one can specify strange and unrealistic parameters in order to create models of instruments that are impossible to realise physically! Physical modelling systems typically employ delay lines in their structure and this can mean that the output of the system can go out of control and create unwanted feedback.

The Karplus-Strong Algorithm
Alexander Strong and Kevin Karplus developed software and hardware implementations for this algorithm, naming it "Digitar" synthesis.


text:
Talk:Introduction to Astrophysics/Albert Einstein

Einstein discovered relativity?
If Einstein “developed” the theory of relativity from a previous period of scientific history how could he have “discovered” it in the 20th Century? The theory of relativity that Einstein worked on and developed predates Roger Boscovich who extensively wrote about it during the mid 1700s. Moshe-paz 13:41, 12 September 2007 (UTC)


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Signal Processing

This book is about the topic of signal processing, especially the topics of signal analysis and filtering. We will cover advanced filter theories, including adaptive Wiener and Kalman filters, stationary and non-stationary signals, beamforming, and wavelet analysis. This book requires all readers to have a solid foundational understanding of the topics covered in Signals and Systems. Readers should also have a good understanding of advanced calculus, including topics covered in Engineering Analysis.

Table of Contents

 * Introduction

Filtering

 * Fourier Analysis
 * Analog Filters
 * Digital Filters
 * Filter Design

Linear Predictors

 * /Wiener Filters/
 * Linear Prediction
 * Lattice Predictors
 * Steepest Descent Algorithm

Least-Mean-Square Filtering

 * Least-Mean-Square
 * Normalized Least-Squares
 * Recursive Least-Squares
 * Kalman Filtering
 * Square Root Filters

Applications

 * Image editing

Resources

 * Resources
 * Licensing

title: Signal Processing


text:
Template:Signal Processing/Page

 Signal Processing

title: Template:Signal Processing/Page


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Signal Processing/Resources

Books

 * Haykin, Simon, Adaptive Filter Theory, Fourth Edition, Prentice Hall, 2002. ISBN 0130901261

External Resources

 * Lloyd R. Welch, Weiner Filter Theory

Wikibooks

 * Signals and Systems
 * Digital Signal Processing
 * Control Systems

title: Signal Processing/Resources


text:
Connect Four

 * For other reading until then, Sterling Publishing and Hasbro are supposed to release a book soon by James Allen entitled, The Complete Book of Connect Four. In addition, refer to the Additional Resources section.

Theory
The board has 42 spaces: 7 columns (vertical lines) and 6 rows (horizontal lines). When all 42 spaces are empty, it is the first player's (Red) turn to move. It is Red's turn again when there are 40 empty spaces, and again when there are 38 empty spaces. There is a pattern: when the number of empty spaces is even, it is Red's turn to move. Conversely, when there are an odd number of empty spaces, it's Black's turn.

Often there are certain spaces that both players want to occupy and don't want the opponent to occupy. These shall be referred to as "critical" spaces. A wise player will never move under a critical space, but instead wait for the opponent to do so. If both players play this way, no critical space will be playable until one player is forced to move under it due to having no other options (this situation is known as "zugzwang"). Who gets to occupy critical spaces depends, of course, on whose turn it will be when the only playable spaces are those directly below the critical spaces. This depends on the number of empty spaces remaining on the board when the only playable spaces are those directly below the critical spaces. Whether or not that number is even or odd can be predicted based on how many spaces are above the above the critical spaces (whether the critical spaces are on even rows or odd rows*), and how many critical spaces there are. *Note: "odd rows" refers to the 3rd and 5th row up, and excludes the bottom row because its spaces are always playable.

A critical space on an even row has an even number of empty spaces above it. For instance, the 2nd row has four rows above it, therefore any space on the 2nd row has 4 spaces above it. A critical space on an odd row has an odd number of empty spaces above it.

 * If the only critical space is even (on an even row), the number of empty spaces remaining when a player is forced to move underneath the empty space is even. For example, if the critical space is on the 2nd row, there will be 6 empty spaces remaining (one full column) when the move underneath the critical space is forced.  An even number of empty spaces means it is Red's turn, therefore Red must move under the critical space and Black will occupy the critical space.
 * If there are multiple critical spaces and all of them are even, the number of empty spaces remaining when Zugzwang occurs is: (even #) + (even #) = (even #)  and therefore it will be Red's turn when Zugzwang occurs and Black will occupy the critical spaces.
 * If the only critical space is odd (on an odd row), there will an odd # of empty spaces when Zugzwang occurs. Therefore it will be Black's turn, and therefore Red will get the critical space.
 * If there are 2 critical spaces and both are odd, the sum of empty spaces when Zugzwang occurs will be: (odd #) + (odd #) = (even #)   and therefore it will be Red's turn to move, allowing Black to occupy whichever critical space Red move under.  If Black's occupation of that critical space does not end the game, the game will continue until another zugzwang occurs.  In that situation, there will be one critical space on an odd row, which is the same situation as previously described.  Red will therefore occupy the 2nd critical space.  The following generalization can be made: For any even # of odd-row critical spaces, Black will get the 1st, 3rd, etc., and Red will get the 2nd, 4th, etc.
 * If there are 3 critical spaces and all 3 are odd, the sum of empty spaces when Zugzwang occurs is: (odd #) + (odd #) + (odd #) = (odd #)  resulting in Black's turn and therefore Red's occupation of whichever critical space Black chooses to give Red.  If Red's occupation of that critical space does not end the game, the game will continue until the previous situation occurs.  So another generalization can be made: For any odd # of odd-row critical spaces, Red will get the 1st, 3rd, etc., and Black will get the 2nd, 4th, etc.  (Note that each generalization is implied by each other)
 * If there are 2 critical spaces, one being odd and the other being even, the following will result from Zugzwang: (odd #) + (even #) = (odd #)   and therefore Red will get the first (decided by Black) critical space.  Thus only odd-row critical spaces influence the result; even-row critical spaces have no affect because even #'s do not change the evenness/oddness of the sum of the empty spaces remaining.

Theory-based strategy for 7x6 board
Expert players attempt to create a long-term attack that one's opponent will be forced to move under late in the game when the board is nearly filled. There is a rule of thumb that can be used to tell which kinds of attacks are good long-term attacks (leading to victory), and which attacks the opponent will get to block. Red needs one more unshared attack on an odd row than Black in order to win, or an odd number of shared odd-row attacks. Black needs either an even-row attack or a combination of odd-row attacks. If Black is to win via odd-row attacks, Black needs 2 odd-row attacks, each on a different column, and Red must have no odd-row attack on any column separate from Black's 2 columns, and no even threat below either of Black's odd-row attacks. A draw results if Red has an odd-row attack in a separate column from Black's odd-row threats (separate attacks like these will hereby be referred to as “unshared” as earlier). When Black wins, it is usually by an attack on an even row because those attacks are easier to obtain.

If both players play flawlessly, Red wins. Therefore, in short, Red's strategy is to play offense and seek an odd-row attack while preventing Black's odd threats (and even threats below his own odd threats). Black's strategy is primarily to defend Red's odd-row attacks and then to obtain (usually) an even-row attack. The major reason Black is on defense is that if Red has an odd-row attack and Black has an even-row attack, Red wins. Black should be content to earn a draw against Red, because it often means Black outplayed Red since Red has the advantage.

Strategy for any board size, 2D or 3D
Note: Any board size’ strategy can be derived using the method of the "Theory" section. The same generalizations cannot always be made, but using the same method, one will arrive at the correct new generalizations and understand why the bullet-rules below are true.

 * For a list of win/loss results for 2D boards, see John Tromp's webpage*

* While expert players on LittleGolem believe 8x8 to be a second player win, no proof is known.

Note:
 * For 3D "boards", assume a box shape.
 * The bullet-rules below assume attacks that are not immediately playable.
 * A 2D board's area, or a 3D board's volume, will be referred to as its "domain".

Even Height
With these boards, everything is the same is in 7x6 since 7x6 falls in this category. The only difference between 7x6 and other board sizes of this category is the win/loss results, depending on the board size. The strategy section above is summarized below:

For Red to win:
 * 1 more unshared odd-row attack than Black, or
 * the same # of unshared odd-row attacks as Black, plus an odd # of shared ones, or
 * an odd # of odd-row attacks (whether shared or unshared), if Black has no unshared ones

For Black to win:
 * an even-row attack, if Red has no odd-row attacks, or
 * two more unshared odd-row attacks than red, or
 * the same # of unshared odd-row attacks as Red, plus an even # of shared ones, or
 * one more unshared odd-row attack than Red, plus any # of shared ones, or
 * one unshared odd-row attack plus any number of shared ones, if Red has no unshared ones, or
 * an even # of odd-row attacks (whether shared or unshared), if Red has no unshared ones

Even domain, odd height

 * Red: 1 more unshared even-row attack than Black to win, or odd # of shared even-row attacks.
 * Black: odd-row attack or even # of even-row attacks (2 more unshared than Red, or the same # of shared) to win.
 * If Red and Black have the same # of unshared even-row attacks, the game is drawn.
 * If Red has 1 even-row attack and Black has 1 odd-row attack, Red wins.

Remark: The even rows in these types of boards are like 7x6's odd rows.

Note: the situation described in the "Tactics" section applies to (even)by(odd) boards if one reads the section replacing "odd" with "even" and vice versa. ("Red" and "Black" stay the same)

Odd domain

 * Red: odd-row attack or even # of even-row attacks (2 more unshared than Black, or the same # of shared) to win.
 * Black: 1 more unshared even-row attack than Red to win, or odd # of shared even-row attacks.
 * If Red and Black have the same # of unshared even-row attacks, the game is drawn.
 * If Black has 1 even-row attack and Red has 1 odd-row attack, Black wins.

Remark: The even rows in odd-area boards are like 7x6's odd rows, and Red in odd-area boards is like Black in 7x6 (but the win/loss results vary with size).

Note: the situation described in the "Tactics" section applies to (odd)by(odd) boards if one reads the section replacing "Red" with "Black" and vice versa, and replacing "odd" with "even" and vice versa.

Theory and strategy for selected variants
The theory of the following variants is, as you will see, derived using the same principles as used for regular Connect Four and its board size variations.

2-way gravity (aka "Connect Four Flip")
Section forthcoming: expected to be complete within two weeks.

Edge (4-way/6-way) gravity
Click for explanation of the game rules (on a 2D board). (referred to as "Stack 4x4")

Red moves when the number of empty spaces = even. There are two types of long-term 3-piece attacks: "even zugzwang value" and "odd zugzwang value", whose meanings will be explained. Furthermore, there are 2 ways to make attacks: orthogonally (horizontally or vertically) or diagonally.

An orthogonal attack can create up to 2 critical spaces. If it only forms one, the zugzwang situation will be such that one player will be forced to move to one of 4 spaces—2 spaces in the column where the critical space lies and 2 spaces in the row where it lies. Spaces like these---which, when filled, allow the critical space to be occupied on the next turn---will hereby be referred to as "zugzwang spaces". So orthogonals with one end and discontinuous (unconnected/gapped) form 4 zugzwang spaces and 1 critical space, which means when Zugzwang occurs, 5 empty spaces remain. This sum will be referred to as a "zugzwang value" for convenience. Single critical space orthogonals, as shown, have a zugzwang value of 5--or more importantly, an odd zugzwang value.

An orthogonal can form 2 critical spaces by one of two ways: an open-ended connected line (being at least 3 spaces from either perpendicular edge of the board or 2 spaces from any legal move in the extension of the line), or a discontinuous line with two gaps. In both cases, there are 6 zugzwang spaces. Its zugzwang value (ZV from now on) is 8, hence is even. Note, however, that once the 1st critical space is occupied by one player, the 2nd one is immediately playable by the other. Therefore in some situations, an open-ended orthogonal attack can be thought of as forming 1 critical space with 4 zugzwang spaces, and thus having an odd ZV (the "one" critical space could be on either side of the line, depending on which one the opponent chooses).

Diagonals, whether continuous or not, form 4 zugzwang spaces for each critical space they create. A discontinuous diagonal forms 1 critical space and therefore has an odd ZV (five). A continuous, open-ended diagonal has a ZV of: (2 critical spaces) + 4 + 4 = 10, which is of course even. Notice that this is a combination of 2 odd-ZV attacks. A closed-ended diagonal, for example, has only 1 critical space and 4 zugzwang spaces, and therefore has a ZV of 5 which is odd.

For 3D, box-shaped boards with 6-way gravity, the only thing that changes is that 2 more zugzwang spaces are created by each kind of attack. Adding an even # to another # does not change the evenness/oddness of it. Therefore, the evenness/oddness of the ZV's will be the same, and each player will need the same attacks as in 4-way-gravity.

From these facts, the following conclusions can be drawn.

Boards with even domain

 * Red needs 1 more unshared odd-ZV attack than Black to win, or an odd # of shared odd-ZV attacks.
 * Any attack will accomplish this.
 * Black needs an even-ZV attack to win or an even # of odd-ZV attacks (2 more unshared than Red, or the same # of shared).
 * A 2 critical space orthogonal, a 2-critical-space diagonal, or 2 of any other type of attack will achieve this.
 * If Red and Black each have 1 unshared odd-ZV attack, and Black has no even-ZV attacks, the game is drawn.
 * If Red has an odd-ZV attack and Black has an even-ZV attack, Red wins.

Note: shared attacks are probably rare situations in the edge-gravity variant, but they are possible.

Boards with odd domain

 * Red needs an even-ZV attack to win or an even # of odd-ZV attacks (2 more unshared than Black, or the same # of shared).
 * A 2 critical space orthogonal, a 2-critical-space diagonal, or 2 of any other type of attack will achieve this.
 * Black needs 1 more unshared odd-ZV attack than Red to win, or an odd # of shared odd-ZV attacks.
 * Any attack will accomplish this.
 * If Red and Black each have 1 unshared odd-ZV attack, and Red has no even-ZV attacks, the game is drawn.
 * If Red has an even-ZV attack and Black has an odd-ZV attack, Black wins.

(In other words, what a color needs for boards with odd domain is the opposite of what that color needs for boards of even domain.)

Zero gravity, surface-sticking
Section forthcoming: expected to be complete within two weeks.

No barriers
Subsection to be included in forthcoming section.

With barriers
Subsection to be included in forthcoming section.

Stacking (downward gravity)
Rules: Red's 1st turn is one move. Then every turn after that (including Black's first turn) is 2 moves. Other than that, same rules as standard Connect Four.

In this variant, which rows each player needs depends not on whether they are even or odd, but on which player moves last (and on the board dimensions).

Who moves first depends only on how many turns it takes to fill the entire board. If the # of turns is even, then each player has the same # of turns and therefore Black moves last. If the # of turns is odd, Red gets 1 more turn than Black and therefore Red moves last.

For boards with even domain, the last move is the first and only move of the last turn. On boards with odd domain, the last move is the 2nd move of the last turn. This is important because it determines which zugzwang-values each player needs.

Consider, for example, the 8x8 board. Red moves last and takes the top row; he moves when there is 1 space left. Before that, Black moves and takes the 6th and 7th row; she moves when there are 2 and 3 spaces left. The alternation continues and the following list can be generated:
 * Red moves when there are: 1, 4,5, 8,9, 12,13, 16,17, 20,21... spaces left.

If the board were instead 9x9, Red moves last and takes rows 8 and 9, thus moving when there are 1 and 2 spaces left. This will change the list to:
 * Red moves when there are: 1,2, 5,6, 9,10, 13,14, 17,18, 21,22... spaces left.

To see why this is important, consider some attacks. It has been demonstrated that on an 8x8 board, a 6th-row attack is good for Black. It has a ZV of 5 (4th, 5th, 6th, 7th, and 8th row are empty when Zugzwang occurs) and notice from the list that Red moves when there are 5 empty spaces left. One 6th-row attack would therefore be useless for Red. But what if Red had two 6th-row attacks? The combined ZV would be 10, and notice from the list that Black moves when there are 10 empty spaces left. On Red's turn there would be 9 empty spaces left, and Red would move twice in one column and make Connect Four with one of the 6th-row attacks, so two -6th row attacks are good for Red in 8x8. The complete strategy for the 2-move-turn variant can be solved using this method.

The strategy will now be categorized by board dimensions. But note that the bottom 2 rows are never included in the list of strategic attacks since they are always immediately playable. Strategic rules of thumb only apply to critical spaces that will not be filled until immediately after Zugzwang.

Even domain

 * # of turns = $$(area/2)+1$$
 * Alternate: if the area is a multiple of 4 (meaning, if area/4 = an integer), Red moves last. If not a multiple of 4, Black moves last.
 * Last turn consists of 1 move.
 * Last mover moves when # of empty spaces = (any multiple of 4 + 0 or 1) = {1, 4,5, 8,9, 12,13, 16,17, 20,21, 24,25...}
 * 2nd-to-last mover moves when # of empty spaces = the combination of the sets {2,3} and {any multiple of 4 + (2 or 3)} = {2,3, 6,7, 10,11, 14,15, 18,19, 22,23...}

Even height
Last mover can win with:
 * any even row being the top row or a multiple of 4 rows (2 even rows) down from the top row (note: 4 rows down from the top = 5 rows down, 8 rows down from the top = 9 rows down, and so on).
 * 1 more unshared good odd row than 2nd-to-last mover---good being a multiple of 2 odd rows down from the top row (meaning, the 4th row down or any multiple of 4 rows down from the 4th row down)---or an odd # of shared ones. (If equal # of unshared ones, a draw results.)
 * the combinations of bad attacks listed 2 paragraphs below which result in "+"

2nd-to-last mover can win with:
 * any odd row being the 2nd-to-top row or a multiple of 4 rows (2 odd rows) down from the 2nd-to-top row
 * 1 more unshared good even row than last-mover---good being the 3rd-to-top row or a multiple of 2 even rows down from the 3rd-to-top row---or an odd # of shared ones. (If equal # of unshared ones, a draw results.)
 * an odd # (>1) of bad even rows (3 more unshared than last-mover, or the same # of shared).
 * the combinations of bad attacks listed in the paragraph below which result in "-"

The following situations are solved by adding the ZV's of each attack together and knowing which player benefits from the new ZV that results.
 * Good even-row attack for last-mover (which will be referred to as "+even") + bad even-row attack for last-mover ("-even", aka "good even-row attack for 2nd-to-last mover) = good for 2nd-to-last mover. Summarized: (+even) + (-even) = -
 * (-even) + (-even) = + equivalent to (+odd)
 * (+odd) + (+odd) = - equivalent to (-odd)
 * (+even) + (+odd) = -
 * (+even) + (-odd) = +
 * (+odd) + (-odd) = +
 * (+odd) + (-even) = +

(For the situations above where the 1st attack is + and the 2nd is -, the same results apply whether the last-mover has both of the mentioned attacks (1 good and one bad) or whether the last-mover has the first attack and the 2nd-to-last mover has the second attack (meaning, each player has 1 good attack). For the situations with 2 good attacks or 2 bad attacks, the result assumes that the corresponding player has both of the attacks.)

Result for 7x6 board: Black wins.

Odd height
Last mover can win with:

 * any odd row being the top row or a multiple of 4 rows (2 odd rows) down from the top row.
 * 1 more unshared good even row than 2nd-to-last mover---good being the 2nd-to-top row or a multiple of 2 even rows down from the 2nd-to-top row---or an odd # of shared ones. (If equal # of unshared ones, a draw results.)
 * the combinations of bad attacks listed 2 paragraphs below which result in "+"

2nd-to-last mover can win with:

 * any even row being the 2nd-to-top row or a multiple of 4 rows (2 even rows) down from the 2nd-to-top row.
 * 1 more unshared good odd row than last-mover---good being the 3rd-to-top row or a multiple of 2 odd rows down from the 3rd-to-top row---or an odd # of shared ones.
 * an odd # (>1) of bad odd rows (3 more unshared than last-mover, or the same # of shared).
 * the combinations of bad attacks listed in the paragraph below which result in "-"

Other notable situations:

 * (-odd) + (-odd) = + equivalent to (+even)
 * (+even) + (+even) = - equivalent to (-even)
 * (+even) + (+odd) = -
 * (+even) + (-even) = +
 * (+even) + (-odd) = +
 * (+odd) + (-odd) = -
 * (+odd) + (-even) = +

Odd domain

 * # of turns = $$[(area-1)/2]+1$$ = $$(area+1)/2$$
 * Last turn consists of 2 moves.
 * Last mover moves when # of empty spaces = 1,2, (any multiple of 4 + 1 or 2)
 * 2nd-to-last mover moves when # of empty spaces = 3,4, (any multiple of 4 - 0 or 1)

Last mover can win with:

 * any even row being the 2nd-to-top row or any even row a multiple of 4 rows (2 even rows) down from the 2nd-to-top row
 * 1 more unshared good odd row than 2nd-to-last mover---good being the top row or a multiple of 4 rows (2 odd rows) down from the top row---or an odd # of shared ones.
 * an odd # (>1) of bad odd rows (3 more unshared than 2nd-to-last mover, or the same # of shared).
 * the combinations of bad attacks listed 2 paragraphs below which result in "+"

2nd-to-last mover can win with:

 * any odd row being the 3rd-to-top row or any odd row a multiple of 4 rows (2 odd rows) down from the 3rd-to-top row.
 * 1 more unshared good even row than last mover---good being the 4th-to-top row or a multiple of 4 rows (2 even rows) down from the 4th-to-top row---or an odd # of shared ones.
 * the combinations of bad attacks listed in the paragraph below which result in "-"

Other notable situations:

 * (-even) + (-even) = + equivalent to (+even)
 * (+odd) + (+odd) = - equivalent to (-even)
 * (-even) + (-odd) = +
 * (+even) + (-even) = +
 * (+even) + -(odd) = +
 * (+odd) + (-odd) = +

Four-way/6-way gravity
This (non-existent, but possible) variation is a combination of the 4-way/6-way gravity variant and the 2-move turn variant.

Who moves last is relevant. The same 2 (4 condensed to 2) formulas apply for figuring out the # of turns as with the regular 2-move-turn variant:

 * Even domain: # of turns = (#spaces/2)+1
 * Odd domain: # of turns = (#spaces+1)/2

Critical spaces in this variant have higher ZV's than those in 1-move-turn edge gravity. There are three different base ZV's that can be created: 9, 14, and 16.

 * ZV's of 9 are created by any attack that creates just one critical space. ZV's of 18 are created by open-ended connected diagonals, and 2-critical-space discontinuous diagonals whose 2 critical spaces are separated by 2 diagonal spaces.
 * ZV's of 14 are created by 2-critical-space orthogonals.
 * ZV's of 16 are created by 2-critical-space diagonals whose 2 critical spaces are separated by only 1 diagonal space.

The kinds of attacks needed for each player are equivalent to those needed in the regular 2-move-turn variant in the corresponding board sizes.

By "equivalent attacks" the following is meant. Consider two situations: a connected single-ended orthogonal attack on an 8x8 board with 4-way gravity, and a 4th-row attack on an 8x8 board with downward gravity. Both situations have a zugzwang-value of 7, and therefore are equivalent. So on an 8x8 board, the last mover (who would benefit from a 4th-row attack in the regular 2-move variant) would benefit from a connected single-ended orthogonal attack in 4-way gravity 2-move-turn.

In similar fashion (using the principle of equivalence) one derives the following rules:

Even domain
Last mover can win with:
 * 2, 3, or [(2 or 3) + (multiple of 4)] of 9-ZV attacks
 * An odd # of 14-ZV attacks
 * A good attack plus a bad attack.

2nd-to-last mover can win with:
 * 1 or [(0 or 1) + (multiple of 4)] of 9-ZV attacks
 * An even # of 14-ZV attacks
 * A 16-ZV attack
 * Two bad attacks.

Odd domain
Last mover can win with:
 * 3, 4, or [(3 or 4) + (multiple of 4) of 9-ZV attacks
 * An even # of 14-ZV attacks
 * A 16-ZV attack
 * Two bad attacks.

2nd-to-last mover can win with:
 * 1, 2, or [(1 or 2) + (multiple of 4) of 9-ZV attacks
 * An odd # of 14-ZV attacks
 * A good attack plus a bad attack.

Collapsing lines
Section forthcoming: expected to be complete within a few months.
 * Note: I've removed my colleague's submission temporarily, but will incorporate it into this section. "Teachme2play" is an expert and specializes in variants including this one.

Inversed
Section forthcoming: expected to be complete within a few months.

Wrap-around
Section forthcoming: expected to be complete within a few months.

Diagonal stacking
Rules: a piece can be placed diagonally above another piece. The bottom row is always playable.

There is only one type of long-term diagonal attack that can be made: a connected one pointed downward (meaning the critical space is below it). This has a ZV of 3 (resulting from the critical space and the 2 zugzwang-spaces below it).

Single orthogonals, whether connected or gapped, have a ZV of 3. Doubles have a ZV of 6.

In short, all critical spaces have 2 zugzwang-spaces.

Since the turns consist of only one move each, the strategy can be understood in more than one way. One could think in terms of last-mover and 2nd-to-last mover (as with 2-move-turn variants), or simply in terms of Red and Black and the evenness/oddness of the # of empty spaces left (as with regular Connect Four). The latter approach will be taken and the strategic rules are:

Even domain

 * Red needs 1 more unshared critical space than Black, or an odd # of shared ones.
 * Black needs an even # of critical spaces (shared, or 2 more unshared than Red).

Odd domain

 * Red needs an even # of critical spaces (shared, or 2 more unshared than Black).
 * Black needs 1 more unshared critical space than Red, or an odd # of shared ones.

Chess-knight motion, no gravity
Rules: Red's first move can be anywhere, then pieces can be placed a knight-move away from another piece.

No matter how a critical space is made, it will have a ZV of 9. All single-critical-space attacks will have ZV's of 9 and all double-critical-space attacks will have ZV's of 18.

Strategic rules:

Even domain

 * Red needs 1 more unshared critical space than Black, or an odd # of shared ones.
 * Black needs an even # of critical spaces (shared, or 2 more unshared than Red).

Odd domain

 * Red needs an even # of critical spaces (shared, or 2 more unshared than Black).
 * Black needs 1 more unshared critical space than Red, or an odd # of shared ones.

Scoring variant
Section forthcoming: expected to be complete within two weeks.

title: Connect Four


text:
Signal Processing/Introduction

What is Signal Processing?
The field of signal processing is a very important field of study and one that makes possible various other fields such as communications. MP3 music files contain processed, transformed, and compressed music signal data. Speech recognition systems such as dictation software need to analyze and process signal data to identify individual words in a spoken sentence. Neural interface devices, such as various medical prostheses must read the complicated signals of neurons, process those signals to determine the important features, and then convert those features to digital data. Signal processing enables high-speed data communication, even in the presence of interference or noise.

Who is This Book For?
This book is intended for readers at the undergraduate and graduate college levels, specifically those studying electrical engineering or a related field. This book can be used to accompany several semesters of study, depending on how the material is divided and presented.

What are the Prerequisites?
All readers should have significant prior knowledge of Signals and Systems, probability, Linear Algebra, and Calculus. Knowledge of linear algebra topics covered in Engineering Analysis, especially the sections about probability are required. Readers who do not have the necessary mathematics background will be at a severe disadvantage.

What Will This Book Cover?
This book will take a look at the traditional problems and methods of signal processing. We will attempt to cover many analog processing techniques, but we also must cover many advanced digital techniques as well. The Digital Signal Processing book will lay many foundations about digital systems that will be used in this book. The reader is strongly encouraged to either read both these books simultaneously, or to read the beginning sections of Digital Signal Processing first before reading this book. That book will cover many topics that are specific to digital systems, while this book will attempt to cover techniques that are useful for either analog or digital, are hybrid in nature (that they have analog and digital components) or that are traditionally analog but that can be modified for fast digital computation.

This book will attempt to cover the concept of filtering specifically, including adaptive Weiner and Kalman filters. This book will also look at some offshoots of adaptive filter theory, including beamforming. The more advanced sections of this book will look at additional subject, such as nonlinear systems and wavelet analysis.

This book will not cover, and will not attempt to cover, prerequisite information that is already covered in the Signals and Systems book or any of the other prerequisites. This includes, but is not limited to:
 * Integral or differential calculus
 * Differential equations
 * Digital systems and difference equations
 * LTI systems theory
 * Stochastic signals or processes
 * Fourier transform and fourier series

title: Signal Processing/Introduction


text:
Talk:Connect Four

Tell me if the article is clear or if I should add pictures to give visual examples of the concepts explained. Feel free to email me with any questions/comments.Div0ckrehnee 14:32, 12 September 2007 (UTC)

 * Shut up, your low communist

title: Talk:Connect Four