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Guide to Unix/Explanations/Compact Discs

Ripping CD audio
This copies the audio from a CD track to a file. With some drives (one without analog connections to the sound card) this is the only way to correctly play a file.

Granting permission to the user
First you should have read-and-write permission to the CD device. (You could become root to rip the CD, but then you would have to "chown" the file back to you.)

First look at your CD devices nodes. On *BSD, they are at /dev/cd* and /dev/rcd*. If they look like this: $ ls -l /dev/cd* brw-r----- 1 root  operator    3,   0 Nov  1 16:26 /dev/cd0a brw-r----- 1 root  operator    3,   2 Nov  1 16:26 /dev/cd0c brw-r----- 1 root  operator    3,  16 Nov  1 16:26 /dev/cd1a brw-r----- 1 root  operator    3,  18 Nov  1 16:26 /dev/cd1c

Here, root needs to grant read and write permission to the user. We decide to add the users to group "wheel". Once they are in, we change the group of the devices and grant read and write permission to the group: $ sudo chgrp wheel /dev/cd* /dev/rcd* $ sudo chmod g+gw /dev/cd* /dev/rcd* $ ls -l /dev/cd* brw-rw---- 1 root  wheel    3,   0 Nov  1 16:26 /dev/cd0a brw-rw---- 1 root  wheel    3,   2 Nov  1 16:26 /dev/cd0c brw-rw---- 1 root  wheel    3,  16 Nov  1 16:26 /dev/cd1a brw-rw---- 1 root  wheel    3,  18 Nov  1 16:26 /dev/cd1c

Ripping tracks
We must insert a CD before ripping the track.

Here, for example, we rip track 2 and store it in song.wav. Our ".wav" suffix is because that is the default format of cdparanoia. With a CD in: $ cdparanoia 2 song37.wav

Eject a disc
Many systems provide an eject command. $ eject cd0

Burn a disk
Scenario: put the contents of a directory called backup to CD.

Here we do the actual burn (and eject) as root. The user needs to have "sudo" access, but not any special access to the CD device node.

Create a disk image of the CD. We will call it burn.iso. $ mkisofs -o burn.iso -r -hfs backup $ chmod a-w burn.iso
 * -R is ISO6990 Rock Ridge support
 * -r is Rock Ridge but with all files to root (usable on computers with different users)
 * -hfs indicates a hybrid ISO9660/HFS disk

Mount it to check for validity. (NetBSD/OpenBSD) $ sudo vnconfig /dev/svnd0c burn.iso $ sudo mount -r -t cd9660 /dev/svnd0a /mnt $ diff /mnt backup $ echo $? 0 $ sudo umount /mnt $ sudo vnconfig -u /dev/svnd0c

The filesystem is good though file is misleading: $ file burn.iso burn.iso: x86 boot sector, extended partition table

Insert a blank disk.

This is a test burn to demonstrate cdrecord -v. $ sudo cdrecord -v -dummy dev=/dev/cd0c burn.iso cdrecord: No write mode specified. cdrecord: Assuming -tao mode. cdrecord: Future versions of cdrecord may have different drive dependent defaults. cdrecord: Continuing in 5 seconds... Cdrecord-Clone 2.01 (--) Copyright (C) 1995-2004 Jörg Schilling TOC Type: 1 = CD-ROM scsidev: '/dev/cd0c' devname: '/dev/cd0c' scsibus: -2 target: -2 lun: -2 Using libscg version 'schily-0.8'. SCSI buffer size: 61440 atapi: 0 Device type   : Removable CD-ROM Version       : 0 Response Format: 2 Capabilities  : Vendor_info   : 'MATSHITA' Identifikation : 'CD-RW CW-8123  ' Revision      : 'CA0T' Device seems to be: Generic mmc2 DVD-ROM. Current: 0x0009 Profile: 0x0010 Profile: 0x0008 Profile: 0x0009 (current) Profile: 0x000A Using generic SCSI-3/mmc  CD-R/CD-RW driver (mmc_cdr). Driver flags  : MMC-2 SWABAUDIO BURNFREE Supported modes: TAO PACKET SAO SAO/R96P SAO/R96R RAW/R16 RAW/R96P RAW/R96R Drive buf size : 1731072 = 1690 KB FIFO size     : 4194304 = 4096 KB Track 01: data   114 MB Total size:      130 MB (12:58.58) = 58394 sectors Lout start:     131 MB (13:00/44) = 58394 sectors Current Secsize: 2048 ATIP info from disk: Indicated writing power: 5 Is not unrestricted Is not erasable Disk sub type: Medium Type B, low Beta category (B-) (4) ATIP start of lead in: -11834 (97:24/16) ATIP start of lead out: 359849 (79:59/74) Disk type:   Short strategy type (Phthalocyanine or similar) Manuf. index: 24 Manufacturer: Sony Corporation Blocks total: 359849 Blocks current: 359849 Blocks remaining: 301455 Starting to write CD/DVD at speed 24 in dummy TAO mode for single session. Last chance to quit, starting dummy write   0 seconds. Operation starts. Waiting for reader process to fill input buffer ... input buffer ready. BURN-Free is ON. Turning BURN-Free off Starting new track at sector: 0 Track 01: 114 of  114 MB written (fifo 100%) [buf  98%]   8.2x. Track 01: Total bytes read/written: 119586816/119586816 (58392 sectors). Writing time:  102.275s Average write speed  7.6x. Min drive buffer fill was 98% Fixating... WARNING: Some drives don't like fixation in dummy mode. Fixating time:  34.457s cdrecord: fifo had 1947 puts and 1947 gets. cdrecord: fifo was 0 times empty and 1860 times full, min fill was 80%. $ echo $? 0

An actual burn: $ sudo cdrecord dev=/dev/cd0c burn.iso Password: cdrecord: No write mode specified. cdrecord: Assuming -tao mode. cdrecord: Future versions of cdrecord may have different drive dependent defaults. cdrecord: Continuing in 5 seconds... Cdrecord-Clone 2.01 (--) Copyright (C) 1995-2004 Jörg Schilling scsidev: '/dev/cd0c' devname: '/dev/cd0c' scsibus: -2 target: -2 lun: -2 Using libscg version 'schily-0.8'. Device type   : Removable CD-ROM Version       : 0 Response Format: 2 Capabilities  : Vendor_info   : 'MATSHITA' Identifikation : 'CD-RW CW-8123  ' Revision      : 'CA0T' Device seems to be: Generic mmc2 DVD-ROM. Using generic SCSI-3/mmc  CD-R/CD-RW driver (mmc_cdr). Driver flags  : MMC-2 SWABAUDIO BURNFREE Supported modes: TAO PACKET SAO SAO/R96P SAO/R96R RAW/R16 RAW/R96P RAW/R96R Starting to write CD/DVD at speed 24 in real TAO mode for single session. Last chance to quit, starting real write   0 seconds. Operation starts. Track 01: Total bytes read/written: 119586816/119586816 (58392 sectors). $ echo $? 0

We should eject the finished disk now. The OS or drive might not know that the disk now has a filesystem on it. $ sudo eject cd0

If we reinsert the disk then we can mount/unmount it: $ sudo mount /dev/cd0a /mnt $ sudo umount /mnt

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


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User:MGSpiller

as on Wikipedia & Wictionary

title: User:MGSpiller


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Guide to Schools/Alphabetical/Carlbrook School

=Carlbrook School=

Contact Information
'''PO Box 755, Halifax, VA 24558

==Key Staff

Administrative head
John Henson, Dean of Administration _

Admission Contact
Grant Price, Dean of Admissions

Head of Academics
Dr. Chris Soto, Dean of Academics

Head of counseling or therapauetics
'''Jonathan Gurney, Dean of Advising'

Grades and Ages
Carlbrook School provides coeducational instruction for grades 9-12.

Size of School
100 Students

Description of Physical Plant
Carlbrook School sits on 200 Acres of beautiful, open land in southside Virginia.

Athletics
Intramural Soccer and Softball are offered at Carlbrook School.

Extra-Curricular Activities other than Athletics
Carlbrook School offers extensive programming for students interested in the visual arts. Particular emphasis is placed on ceramics.

Students also have the opportunity to participate in the performance arts, including theatre and dance.


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Talk:Japanese/Reader/第三夜

Untitled
Some thoughts: - Marsian / talk 04:39, 1 November 2005 (UTC)
 * 1) 慥 is one of obsolete kanjis. Actually, I couldn't read it ;) The same story in Aozora Bunko avoid using the kanji. But since I'm not sure the purpose of this page...
 * 六つ: I thought the reading of the word is むっつ. But according to 大辞林(Daijirin), both むつ and むっつ are used. Perhaps むつ is relatively formal whereas むっつ is casual.
 * 負う: Altough probably this is read おぶう(おぶって) in this case, we read 負う as おう these days. Daijirin separates 負う(おう) and 負ぶう(おぶう).

Nice work! 65.241.152.139 01:05, 2 November 2005 (UTC)

title: Talk:Japanese/Reader/第三夜


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User talk:Tohru

はじめまして．助数詞での修正ありがとうございます．もしかしたらもうご存じかもしれませんが，Yahoo groups を利用した MLがあります．よろしかったらご参加下さい． - Marsian / talk 04:49, 1 November 2005 (UTC)

title: User talk:Tohru


text: User talk:203.198.179.98

title: User talk:203.198.179.98


text: User talk:Gabio

title: User talk:Gabio


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User talk:169.237.5.139

Please stop adding nonsense to Wikibooks. It is considered vandalism. If you would like to experiment, use the sandbox. Thank you.

title: User talk:169.237.5.139


text:
User talk:70.57.228.158

Please stop adding nonsense to Wikibooks. It is considered vandalism. If you would like to experiment, use the sandbox. Thank you.

title: User talk:70.57.228.158


text:
User talk:67.81.73.117

Please stop adding nonsense to Wikibooks. It is considered vandalism. If you would like to experiment, use the sandbox. Thank you.

title: User talk:67.81.73.117


text:
User talk:69.216.53.76

Please stop adding nonsense to Wikibooks. It is considered vandalism. If you would like to experiment, use the sandbox. Thank you.

title: User talk:69.216.53.76


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Mac OS X Tiger/User Accounts

=Introduction= One feature you're almost guaranteed to find in a UNIX-based operating system is a system of user accounts. This feature is designed for computers that are used by more than one person.

Why Accounts?
Picture this: a family of four shares one iMac. Fourteen-year-old Andrew imports his collection of punk rock CD's into the computer's iTunes library. All of a sudden, the music is on every other family member's iPod. Seven-year-old Alice wants to have a Barbie desktop picture, but the other family members would rather not. All of Andrew's friends are mixed in with the father Mark's business contacts in Address Book.

In other words, total chaos.

Accounts to the rescue! Each user with an account gets their very own private:

 * "Home Folder" for storing personal documents and other files.
 * Preferences and settings for Mac OS X and individual applications.
 * iTunes library, iPhoto library, Address Book, iCal Calendar, Safari Bookmarks, iChat buddies, etc.

Deciding How You Will Use Accounts
An account is kind of like an entire "version" of the computer. Our family of four could create an account for each child. Andrew gets his own music collection and contacts. Alice gets her Barbie desktop picture. And everyone is happy. Unfortunately, the system of accounts can be a double-edged sword. Let's say that the two parents create separate accounts. Which account will keep the family photos? Which will keep the parents' shared music collection? Things can start to get complicated.

Don't be afraid to get creative with your system of accounts. In this case, the perfect solution is to create a fifth account: "Family". This account is in charge of the family address book, family music library, family photos, etc. With five accounts for the four users of the iMac, nobody gets in anyone else's hair, and yet everyone can access the files they want to.

Your solution may be different than the hypothetical family above. Come up with several different possibilities and weigh their advantages and disadvantages. Consider limits that need to be placed on users, what data needs to be easily accessible to all users, and the varying privacy needs of each user. Try to get it right the first time; creating accounts is easy, but modifying accounts is more difficult.

Types of Accounts

 * Standard
 * This should be your daily use account.
 * Administrator (Super User)
 * The person who manages the computer should have this account *in addition* to their own standard account.
 * Root
 * Most people will never need to access this type of account, but certain high-level management tasks require this level of access.

=Adding an Account= The central control panel for the Account system is the Accounts pane of System Preferences. This pane lets you add, modify, and remove user accounts. To adjust the more serious settings in this pane, you'll need to unlock it with an administrator password. Only an administrator can mess with the account system.

The sidebar on the left lists the accounts on your Mac. Your account is at the top, and everyone else's appears underneath. To add an account, click the plus button underneath this sidebar. A sheet appears, prompting you for some information to set up the account:

 * Name - Type in a name for the account.
 * Short Name - If the user is ever prompted for their name and password, then they can use this name instead. Keep the short name simple and in all lowercase letters. For instance, John Doe's short name should be "john".
 * Password - Depending on how sensitive information in this account is, you may wish to create a password. In a family setting, passwords are usually unnecessary for most accounts, and this field can be left blank.

=Setting Up an Account=

=Fast User Switching= Fast User Switching is a feature Apple "borrowed" from Windows that lets two users stay logged in at the same time. Keep in mind that having multiple users simultaneously logged in with applications running will require a large amount of memory.

title: Mac OS X Tiger/User Accounts


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A-level Mathematics/OCR/M3/Circular Motion

General Equations of Motion
Consider a particle moving in a circle with radius $$r$$ and centre at the origin O.

Let $$\mathbf{r}$$ denote the displacement of the particle. Using the angular displacement $$\theta$$ (as measured from the positive $$x$$-axis) as a parameter, we have

$$\mathbf{r}= r \left[ \begin{matrix}\cos \theta\\ \sin \theta \end{matrix} \right]$$.

To obtain the velocity $$\dot\mathbf{r}$$ of the particle, we differentiate $$\mathbf{r}$$ wrt time $$t$$. Applying the chain rule, we have

To determine the acceleration $$\ddot\mathbf{r}$$ of the particle, we differentiate $$\dot\mathbf{r}$$ wrt $$t$$ and get

Summary
To simplify our expressions, we introduce the unit vectors $$\hat{\mathbf{r}}=\left[ \begin{matrix} \cos \theta\\ \sin \theta \end{matrix} \right]$$, and $$\hat{\mathbf{n}}=\left[ \begin{matrix} -\sin \theta\\ \cos \theta \end{matrix} \right]$$. Observe that $$\hat{\mathbf{r}}$$ is perpendicular to $$\hat{\mathbf{n}}$$ since $$\hat{\mathbf{r}} \cdot \hat{\mathbf{n}} = 0$$.

From the above derivations, we arrive at the following:

We note the following:
 * The velocity is always perpendicular to the displacement of the particle.
 * The acceleration consists of a radial component directed towards the centre of the circle, and a transverse component parallel to the velocity.

Special Case: Uniform Circular Motion
If the particle moves at a constant speed in a circle, then we say that it observes uniform circular motion. For this special case, we set the angular acceleration $$\ddot{\theta}=0$$, and replace the angular velocity $$\dot{\theta}$$ with the constant angular speed $$\omega$$. Our equations of motion reduce to the following:

We note the following:
 * The velocity is always perpendicular to the displacement of the particle. Further, the speed of the particle is simply $$v=r\omega$$.
 * The acceleration is always directed towards the centre of the circle. Its magnitude is given by $$a=r\omega^2=\frac{v^2}{r}$$.

Uniform Horizontal Circular Motion
The following diagrams describe one example of horizontal circular motion. If the particle is moving at a constant speed, then we say that it is performing uniform horizontal circular motion. To obtain the equations of motion, we apply Newton's Second Law to the resolved forces acting on the particle in the horizontal and vertical directions.

Let us assume that the particle is moving at a constant speed around a circle of radius $$r$$.

First, we consider the resolved forces acting on the particle in the vertical direction. Since there is no acceleration, Newton's Second Law produces:

Next, we consider the resolved forces acting on the particle in the horizontal direction. Since the particle is performing circular motion, its acceleration towards the centre of the circle is given by $$a=r\omega^2$$. Thus, by Newton's Second Law, we have:

Vertical Circular Motion
The following diagrams describe one example of vertical circular motion. As before, we obtain the equations of motion by applying Newton's Second Law to the resolved forces acting on the particle in the horizontal and vertical directions. In addition, we can also use the Law of Conservation of Energy to help us relate the speed of the particle to its height.

The motion of a moving car round a circular path is being propagated by the centripetal force acting on the car which is directed towards the center of the circular path.

when we look critically into the Newton's Third Law of motion, it states that in every action, there must be a reaction which is equal to it but opposite in direction. as the car is being held on the circular path by the frictional (Centripetal) force, the car in return exerts and outward pull against the direction of the Fcentri, which is called the centrifugal force.


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Engineering Acoustics/Bass Reflex Enclosure Design

Introduction
Bass-reflex enclosures improve the low-frequency response of loudspeaker systems. Bass-reflex enclosures are also called "vented-box design" or "ported-cabinet design". A bass-reflex enclosure includes a vent or port between the cabinet and the ambient environment. This type of design, as one may observe by looking at contemporary loudspeaker products, is still widely used today. Although the construction of bass-reflex enclosures is fairly simple, their design is not simple, and requires proper tuning. This reference focuses on the technical details of bass-reflex design. General loudspeaker information can be found here.

Effects of the Port on the Enclosure Response
Before discussing the bass-reflex enclosure, it is important to be familiar with the simpler sealed enclosure system performance. As the name suggests, the sealed enclosure system attaches the loudspeaker to a sealed enclosure (except for a small air leak included to equalize the ambient pressure inside). Ideally, the enclosure would act as an acoustical compliance element, as the air inside the enclosure is compressed and rarified. Often, however, an acoustic material is added inside the box to reduce standing waves, dissipate heat, and other reasons. This adds a resistive element to the acoustical lumped-element model. A non-ideal model of the effect of the enclosure actually adds an acoustical mass element to complete a series lumped-element circuit given in Figure 1. For more on sealed enclosure design, see the Sealed Box Subwoofer Design page.

''Figure 1. Sealed enclosure acoustic circuit.''

In the case of a bass-reflex enclosure, a port is added to the construction. Typically, the port is cylindrical and is flanged on the end pointing outside the enclosure. In a bass-reflex enclosure, the amount of acoustic material used is usually much less than in the sealed enclosure case, often none at all. This allows air to flow freely through the port. Instead, the larger losses come from the air leakage in the enclosure. With this setup, a lumped-element acoustical circuit has the following form.

''Figure 2. Bass-reflex enclosure acoustic circuit.''

In this figure, $$Z_{RAD}$$ represents the radiation impedance of the outside environment on the loudspeaker diaphragm. The loading on the rear of the diaphragm has changed when compared to the sealed enclosure case. If one visualizes the movement of air within the enclosure, some of the air is compressed and rarified by the compliance of the enclosure, some leaks out of the enclosure, and some flows out of the port. This explains the parallel combination of $$M_{AP}$$, $$C_{AB}$$, and $$R_{AL}$$. A truly realistic model would incorporate a radiation impedance of the port in series with $$M_{AP}$$, but for now it is ignored. Finally, $$M_{AB}$$, the acoustical mass of the enclosure, is included as discussed in the sealed enclosure case. The formulas which calculate the enclosure parameters are listed in Appendix B.

It is important to note the parallel combination of $$M_{AP}$$ and $$C_{AB}$$. This forms a Helmholtz resonator (click here for more information). Physically, the port functions as the “neck” of the resonator and the enclosure functions as the “cavity.” In this case, the resonator is driven from the piston directly on the cavity instead of the typical Helmholtz case where it is driven at the “neck.”  However, the same resonant behavior still occurs at the enclosure resonance frequency, $$f_{B}$$. At this frequency, the impedance seen by the loudspeaker diaphragm is large (see Figure 3 below). Thus, the load on the loudspeaker reduces the velocity flowing through its mechanical parameters, causing an anti-resonance condition where the displacement of the diaphragm is a minimum. Instead, the majority of the volume velocity is actually emitted by the port itself instead of the loudspeaker. When this impedance is reflected to the electrical circuit, it is proportional to $$1/Z$$, thus a minimum in the impedance seen by the voice coil is small. Figure 3 shows a plot of the impedance seen at the terminals of the loudspeaker. In this example, $$f_B$$ was found to be about 40 Hz, which corresponds to the null in the voice-coil impedance.

''Figure 3. Impedances seen by the loudspeaker diaphragm and voice coil.''

Quantitative Analysis of Port on Enclosure
The performance of the loudspeaker is first measured by its velocity response, which can be found directly from the equivalent circuit of the system. As the goal of most loudspeaker designs is to improve the bass response (leaving high-frequency production to a tweeter), low frequency approximations will be made as much as possible to simplify the analysis. First, the inductance of the voice coil, $$\it{L_E}$$, can be ignored as long as $$\omega \ll R_E/L_E$$. In a typical loudspeaker, $$\it{L_E}$$ is of the order of 1 mH, while $$\it{R_E}$$ is typically 8$$\Omega$$, thus an upper frequency limit is approximately 1 kHz for this approximation, which is certainly high enough for the frequency range of interest.

Another approximation involves the radiation impedance, $$\it{Z_{RAD}}$$. It can be shown [1] that this value is given by the following equation (in acoustical ohms):

$$Z_{RAD} = \frac{\rho_0c}{\pi a^2}\left[\left(1 - \frac{J_1(2ka)}{ka}\right) + j\frac{H_1(2ka)}{ka}\right]$$

Where $$J_1(x)$$ and $$H_1(x)$$ are types of Bessel functions. For small values of ka,

Hence, the low-frequency impedance on the loudspeaker is represented with an acoustic mass $$M_{A1}$$ [1]. For a simple analysis, $$R_E$$, $$M_{MD}$$, $$C_{MS}$$, and $$R_{MS}$$ (the transducer parameters, or Thiele-Small parameters) are converted to their acoustical equivalents. All conversions for all parameters are given in Appendix A. Then, the series masses, $$M_{AD}$$, $$M_{A1}$$, and $$M_{AB}$$, are lumped together to create $$M_{AC}$$. This new circuit is shown below.

''Figure 4. Low-Frequency Equivalent Acoustic Circuit''

Unlike sealed enclosure analysis, there are multiple sources of volume velocity that radiate to the outside environment. Hence, the diaphragm volume velocity, $$U_D$$, is not analyzed but rather $$U_0 = U_D + U_P + U_L$$. This essentially draws a “bubble” around the enclosure and treats the system as a source with volume velocity $$U_0$$. This “lumped” approach will only be valid for low frequencies, but previous approximations have already limited the analysis to such frequencies anyway. It can be seen from the circuit that the volume velocity flowing into the enclosure, $$U_B = -U_0$$, compresses the air inside the enclosure. Thus, the circuit model of Figure 3 is valid and the relationship relating input voltage, $$V_{IN}$$ to $$U_0$$ may be computed.

In order to make the equations easier to understand, several parameters are combined to form other parameter names. First, $$\omega_B$$ and $$\omega_S$$, the enclosure and loudspeaker resonance frequencies, respectively, are:

Based on the nature of the derivation, it is convenient to define the parameters $$\omega_0$$ and h, the Helmholtz tuning ratio:

A parameter known as the compliance ratio or volume ratio, $$\alpha$$, is given by:

$$\alpha = \frac{C_{AS}}{C_{AB}} = \frac{V_{AS}}{V_{AB}}$$

Other parameters are combined to form what are known as quality factors:

This notation allows for a simpler expression for the resulting transfer function [1]:

$$\frac{U_0}{V_{IN}} = G(s) = \frac{(s^3/\omega_0^4)}{(s/\omega_0)^4+a_3(s/\omega_0)^3+a_2(s/\omega_0)^2+a_1(s/\omega_0)+1}$$

where

Development of Low-Frequency Pressure Response
It can be shown [2] that for $$ka < 1/2$$, a loudspeaker behaves as a spherical source. Here, a represents the radius of the loudspeaker. For a 15” diameter loudspeaker in air, this low frequency limit is about 150 Hz. For smaller loudspeakers, this limit increases. This limit dominates the limit which ignores $$L_E$$, and is consistent with the limit that models $$Z_{RAD}$$ by $$M_{A1}$$.

Within this limit, the loudspeaker emits a volume velocity $$U_0$$, as determined in the previous section. For a simple spherical source with volume velocity $$U_0$$, the far-field pressure is given by [1]:

$$p(r) \simeq j\omega\rho_0 U_0 \frac{e^{-jkr}}{4\pi r}$$

It is possible to simply let $$r = 1$$ for this analysis without loss of generality because distance is only a function of the surroundings, not the loudspeaker. Also, because the transfer function magnitude is of primary interest, the exponential term, which has a unity magnitude, is omitted. Hence, the pressure response of the system is given by [1]:

$$\frac{p}{V_{IN}} = \frac{\rho_0s}{4\pi}\frac{U_0}{V_{IN}} = \frac{\rho_0Bl}{4\pi S_DR_EM_AS}H(s)$$

Where $$H(s) = sG(s)$$. In the following sections, design methods will focus on $$|H(s)|^2$$ rather than $$H(s)$$, which is given by:

This also implicitly ignores the constants in front of $$|H(s)|$$ since they simply scale the response and do not affect the shape of the frequency response curve.

Alignments
A popular way to determine the ideal parameters has been through the use of alignments. The concept of alignments is based upon well investigated electrical filter theory. Filter development is a method of selecting the poles (and possibly zeros) of a transfer function to meet a particular design criterion. The criteria are the desired properties of a magnitude-squared transfer function, which in this case is $$|H(s)|^2$$. From any of the design criteria, the poles (and possibly zeros) of $$|H(s)|^2$$ are found, which can then be used to calculate the numerator and denominator. This is the “optimal” transfer function, which has coefficients that are matched to the parameters of $$|H(s)|^2$$ to compute the appropriate values that will yield a design that meets the criteria.

There are many different types of filter designs, each which have trade-offs associated with them. However, this design approach is limited because of the structure of $$|H(s)|^2$$. In particular, it has the structure of a fourth-order high-pass filter with all zeros at s = 0. Therefore, only those filter design methods which produce a low-pass filter with only poles will be acceptable methods to use. From the traditional set of algorithms, only Butterworth and Chebyshev low-pass filters have only poles. In addition, another type of filter called a quasi-Butterworth filter can also be used, which has similar properties to a Butterworth filter. These three algorithms are fairly simple, thus they are the most popular. When these low-pass filters are converted to high-pass filters, the $$s \rightarrow 1/s$$ transformation produces $$s^8$$ in the numerator.

More details regarding filter theory and these relationships can be found in numerous resources, including [5].

Butterworth Alignment
The Butterworth algorithm is designed to have a maximally flat pass band. Since the slope of a function corresponds to its derivatives, a flat function will have derivatives equal to zero. Since as flat of a pass band as possible is optimal, the ideal function will have as many derivatives equal to zero as possible at s = 0. Of course, if all derivatives were equal to zero, then the function would be a constant, which performs no filtering.

Often, it is better to examine what is called the loss function. Loss is the reciprocal of gain, thus

$$|\hat{H}(s)|^2 = \frac{1}{|H(s)|^2}$$

The loss function can be used to achieve the desired properties, then the desired gain function is recovered from the loss function.

Now, applying the desired Butterworth property of maximal pass-band flatness, the loss function is simply a polynomial with derivatives equal to zero at s = 0. At the same time, the original polynomial must be of degree eight (yielding a fourth-order function). However, derivatives one through seven can be equal to zero if [3]

$$|\hat{H}(\Omega)|^2 = 1 + \Omega^8 \Rightarrow |H(\Omega)|^2 = \frac{1}{1 + \Omega^8}$$

With the high-pass transformation $$\Omega \rightarrow 1/\Omega$$,

$$|H(\Omega)|^2 = \frac{\Omega^8}{\Omega^8 + 1}$$

It is convenient to define $$\Omega = \omega/\omega_{3dB}$$, since $$\Omega = 1 \Rightarrow |H(s)|^2 = 0.5$$ or -3 dB. This definition allows the matching of coefficients for the $$|H(s)|^2$$ describing the loudspeaker response when $$\omega_{3dB} = \omega_0$$. From this matching, the following design equations are obtained [1]:

Quasi-Butterworth Alignment
The quasi-Butterworth alignments do not have as well-defined of an algorithm when compared to the Butterworth alignment. The name “quasi-Butterworth” comes from the fact that the transfer functions for these responses appear similar to the Butterworth ones, with (in general) the addition of terms in the denominator. This will be illustrated below. While there are many types of quasi-Butterworth alignments, the simplest and most popular is the 3rd order alignment (QB3). The comparison of the QB3 magnitude-squared response against the 4th order Butterworth is shown below.

Notice that the case $$B = 0$$ is the Butterworth alignment. The reason that this QB alignment is called 3rd order is due to the fact that as B increases, the slope approaches 3 dec/dec instead of 4 dec/dec, as in 4th order Butterworth. This phenomenon can be seen in Figure 5.

Figure 5: 3rd-Order Quasi-Butterworth Response for $$0.1 \leq B \leq 3$$

Equating the system response $$|H(s)|^2$$ with $$|H_{QB3}(s)|^2$$, the equations guiding the design can be found [1]:

Chebyshev Alignment
The Chebyshev algorithm is an alternative to the Butterworth algorithm. For the Chebyshev response, the maximally-flat passband restriction is abandoned. Now, a ripple, or fluctuation is allowed in the pass band. This allows a steeper transition or roll-off to occur. In this type of application, the low-frequency response of the loudspeaker can be extended beyond what can be achieved by Butterworth-type filters. An example plot of a Chebyshev high-pass response with 0.5 dB of ripple against a Butterworth high-pass response for the same $$\omega_{3dB}$$ is shown below.

Figure 6: Chebyshev vs. Butterworth High-Pass Response.

The Chebyshev response is defined by [4]:

$$|\hat{H}(j\Omega)|^2 = 1 + \epsilon^2C^2_n(\Omega)$$

$$C_n(\Omega)$$ is called the Chebyshev polynomial and is defined by [4]:

Fortunately, Chebyshev polynomials satisfy a simple recursion formula [4]:

For more information on Chebyshev polynomials, see the Wolfram Mathworld: Chebyshev Polynomials page.

When applying the high-pass transformation to the 4th order form of $$|\hat{H}(j\Omega)|^2$$, the desired response has the form [1]:

$$|H(j\Omega)|^2 = \frac{1+\epsilon^2}{1+\epsilon^2C^2_4(1/\Omega)}$$

The parameter $$\epsilon$$ determines the ripple. In particular, the magnitude of the ripple is $$10\rm{log}[1+\epsilon^2]$$ dB and can be chosen by the designer, similar to B in the quasi-Butterworth case. Using the recursion formula for $$C_n(x)$$,

$$C_4\left(\frac{1}{\Omega}\right) = 8\left(\frac{1}{\Omega}\right)^4 - 8\left(\frac{1}{\Omega}\right)^2 + 1$$

Applying this equation to $$|H(j\Omega)|^2$$ [1],

Thus, the design equations become [1]:

Choosing the Correct Alignment
With all the equations that have already been presented, the question naturally arises, “Which one should I choose?” Notice that the coefficients $$a_1$$, $$a_2$$, and $$a_3$$ are not simply related to the parameters of the system response. Certain combinations of parameters may indeed invalidate one or more of the alignments because they cannot realize the necessary coefficients. With this in mind, general guidelines have been developed to guide the selection of the appropriate alignment. This is very useful if one is designing an enclosure to suit a particular transducer that cannot be changed.

The general guideline for the Butterworth alignment focuses on $$Q_L$$ and $$Q_{TS}$$. Since the three coefficients $$a_1$$, $$a_2$$, and $$a_3$$ are a function of $$Q_L$$, $$Q_{TS}$$, h, and $$\alpha$$, fixing one of these parameters yields three equations that uniquely determine the other three. In the case where a particular transducer is already given, $$Q_{TS}$$ is essentially fixed. If the desired parameters of the enclosure are already known, then $$Q_L$$ is a better starting point.

In the case that the rigid requirements of the Butterworth alignment cannot be satisfied, the quasi-Butterworth alignment is often applied when $$Q_{TS}$$ is not large enough.. The addition of another parameter, B, allows more flexibility in the design.

For $$Q_{TS}$$ values that are too large for the Butterworth alignment, the Chebyshev alignment is typically chosen. However, the steep transition of the Chebyshev alignment may also be utilized to attempt to extend the bass response of the loudspeaker in the case where the transducer properties can be changed.

In addition to these three popular alignments, research continues in the area of developing new algorithms that can manipulate the low-frequency response of the bass-reflex enclosure. For example, a 5th order quasi-Butterworth alignment has been developed [6]; its advantages include improved low frequency extension, and much reduced driver excursion at low frequencies and typically bi-amping or tri-amping, while its disadvatages include somewhat difficult mathematics and electronic complication (electronic crossovers are typically required). Another example [7] applies root-locus techniques to achieve results. In the modern age of high-powered computing, other researchers have focused their efforts in creating computerized optimization algorithms that can be modified to achieve a flatter response with sharp roll-off or introduce quasi-ripples which provide a boost in sub-bass frequencies [8].

Back to Engineering Acoustics

Appendix B: Enclosure Parameter Formulas
Figure 7: Important dimensions of bass-reflex enclosure.

Based on these dimensions [1],


text:
Cookbook talk:Salt

Please look at the last sentence of this text. "I think", in my opinion, shouldn't go in a "neutral tone" encyclopaedic text. (bagica@bitdefender.com)

I totally agree with the above poster, does "I think" really belong in an online encyclopedia? (some random guy)

Common salt
On a pure chemistry basis, the term "salt" really refers to a whole family of compounds. "Common salt" would be better. —The preceding unsigned comment was added by 60.228.25.50 (talk • contribs) 2007-04-16T16:09:05.

 * Maybe so, but in culinary use, salt is sodium chloride unless otherwise specified (e.g. horn salt, natron - a red link, perhaps you'd like to fill it in?) Webaware talk 09:04, 16 April 2007 (UTC)

Wikidata
Are you absolutely sure this page should link in Wikidata to sodium chloride (Q2314), defined as chemical compound, and not to table salt (Q11254), defined as sodium chloride (NaCl) used as a food ingredient and nutrient? This here is, after all, a cookbook, not a chemistry book. --Ehitaja (discuss • contribs) 20:08, 28 August 2020 (UTC)

Salt is not a chemical compound.
It's a spice Cuber2020 (discuss • contribs) 09:51, 21 June 2022 (UTC)

title: Cookbook talk:Salt


text:
Reaktor/Tutorials/Rounding a number

Suppose you have a floating point number, for example the output of a mouse area, and you want to round this number to the lower integer bound. One way to do this is to Modulo/Divide the number by 1.

Input -> Modulo.A  Modulo.Div -> RoundedNumber 1    -> Modulo.B

It is often useful to add a StepFilter on the output if you only want to trigger on changing values.

In Core, you can round a number by building a macro with a float input and an integer output. If you want to round to the upper number, you can add 1 first. If you want to round to the upper number for fractional values bigger than 0.5, add 0.5 first.

title: Reaktor/Tutorials/Rounding a number


text:
Reaktor/Tutorials/Converting Gate to Edge

Converting a gate signal, for example a midi gate or the mouse button output of a mouse area, to a trigger signal can be used to trigger an envelope, to store a value into a snap value, etc...

This can be achieved using a stepfilter with a threshold of 0.

GateValue -> StpFlt.In StpFlt.Out -> TriggerSignal StpFlt.Tol

Another way to achieve this is to use a Separator combined with a stepfilter. This can be useful to separate the two-levels of the gate signal into separate signals.

GateValue -> Separator.In  Separator.Hi -> HighValueTrigger Separator.Thld Separator.Lo -> LowValueTrigger


text: Template:Georgia Water/Infobox People

title: Template:Georgia Water/Infobox People


text:
Signals and Systems/Frequency Domain Analysis

Frequency Analysis
Noise, like any other signal, can be analyzed using the Fourier Transform and frequency-domain techniques. Some of the basic techniques used on noise (some of which are particular to random signals) are discussed in this section.

Gaussian white noise, one of the most common types of noise used in analysis, has a "flat spectrum". That is, the amplitude of the noise is the same at all frequencies.

Power Spectral Density (PSD) of Gaussian White Noise
White noise has a level magnitude spectrum, and if we square it, it will also have a level Power Spectral Density (PSD) function. The value of this power magnitude is known by the variable N0. We will use this quantity later.

Wiener Khintchine Einstein Theorem
Using the duality property of the Fourier Transform, the Wiener-Khintchine-Einstein Theorem gives us an easy way to find the PSD for a given signal.

if we have a signal f(t), with autocorrelation Rff, then we can find the PSD, Sxx by the following function:

 * $$S_{xx} = \mathcal{F}(R_{ff})$$

Where the previous method for obtaining the PSD was to take the Fourier transform of the signal f(t), and then squaring it.

Bandwidth
The bandwidth of a random function.

Windowing
Many random signals are infinite signals, in that they don't have a beginning or an end. To this effect, the only way to really analyze the random signal is take a small chunk of the random signal, called a sample.

Let us say that we have a long random signal, and we only want to analyze a sample. So we take the part that we want, and destroy the part that we don't want. Effectively, what we have done is to multiply the signal with a rectangular pulse. Therefore, the frequency spectrum of our sampled signal will contain frequency components of the noise and the rectangular pulse. It turns out that multiplying a signal by a rectangular pulse is rarely the best way to sample a random signal. It also turns out that there are a number of other windows that can be used instead, to get a good sample of noise, while at the same time introducing very few extraneous frequency components.

Remember duality? multiplication in the time domain (multiplying by your windowing function) becomes convolution in the frequency domain. Effectively, we've taken a very simple problem (getting a sample of information), and created a very difficult problem, the deconvolution of the resultant frequency spectrum. There are a number of different windows that we can use.


text:
Signals and Systems/Filter Terminology

Terminology
When it comes to filters, there is a large amount of terminology that we need to discuss first, so the rest of the chapters in this section will make sense.

 * Order (Filter Order) : The order of a filter is an integer number, that defines how complex the filter is. In common filters, the order of the filter is the number of "stages" of the filter. Higher order filters perform better, but they have a higher delay, and they cost more.

 * Pass Band : In a general sense, the passband is the frequency range of the filter that allows information to pass. The passband is usually defined in the specifications of the filter. For instance, we could define that we want our passband to extend from 0 to 1000 Hz, and we want the amplitude in the entire passband to be higher than -1 db.

 * Transition Band : The transition band is the area of the filter between the passband and the stopband. Higher-order filters have a thinner transition band

 * Stop Band : The stop band of a filter is the frequency range where the signal is attenuated. Stop band performance is often defined in the specification for the filter. For instance, we might say that we want to attenuate all frequencies above 5000 Hz, and we want to attenuate them all by -40 db or more

 * Cut-off Frequency: The cut-off frequency of a filter is the frequency at which the filter "breaks", and changes (between pass band and transition band, or transition band and passband, for instance). The cut-off of a filter always has an attenuation of -3db. The -3 db point is the frequency that is cut in power by exactly 1/2.

Lowpass
Lowpass filters allow low frequency components to pass through, while attenuating high frequency components.

Lowpass filters are some of the most important and most common filters, and much of our analysis is going to be focused on them. Also, transformations exist that can be used to convert the mathematical model of a lowpass filter into a model of a highpass, bandpass, or bandstop filter. This means that we typically design lowpass filters and then transform them into the appropriate type.

Highpass
Highpass filters allow high frequency components to pass through, while attenuating low frequency components.

Bandpass
A bandpass filter allows a single band of frequency information to pass the filter, but will attenuate all frequencies above the band and below the band.

A good example of a bandpass filter is an FM radio tuner. In order to focus on one radio station, a filter must be used to attenuate the stations at both higher and lower frequencies.

Bandstop
A bandstop filter will allow high frequencies and low frequencies to pass through the filter, but will attenuate all frequencies that lay within a certain band.

Gain/Delay equalizers
Filters that cannot be classified into one of the above categories, are called gain or delay equalizers. They are mainly used to equalize the gain/phase in certain parts of the frequency spectrum as needed. More discussion on these kinds of advanced topics will be in Signal Processing.

title: Signals and Systems/Filter Terminology


text:
Principles of Sociology/Transsexuality

Information drawn exclusively from How Sex Changed by Joanne Meyerowitz

''Individuals with ambiguous sex/gender/sexuality identities have always been present in human societies – they are a genetically assured occurrence and thus we must strive to create at least semi-normalized roles for them. Also, many cultures are not as uncomfortable with sexual/gender ambiguity as Americans are today. There are many examples from the historical/ anthropological record of different cultures tolerating and embracing these people as specially endowed by the creator with specific roles to play in society. But how do we determine today who is male, who is female, and why do we care? Can humans actually change or alter sex, and if so, does this mean that ideas about sex may be much less self-evident than we conventionally treat it.''

The Latin etymology (root) of the prefix “ trans ” (as to clarify meanings and not confuse ourselves) exemplifies ideas such as across, beyond, through, so as to change or transfer material or meanings...

Some early attempts to sort out ideas of sex/gender used these organizational schemes, which may be helpful:

Primary features – genitals and internal reproductive organs

Secondary features – breasts, body hair, and other physical changes occurring after puberty

Tertiary features – sexual drives and desires towards one particular sex, or both

Quaternary features – socially gendered behaviors – preferences, mannerisms, cloths, occupation

Why should we care about the tiny segment of the population that is considered transsexual/transgendered?

• Extrapolated medical statistics suggest that the total number of people with ambiguous genitalia is comparable to the number of Jews worldwide or about 12 million

• Transgenderism is at the cutting edge of the debate on the meaning of sex, sexuality, and gender – some political/cultural/social cornerstones of our society based on traditionally static behavior

• Is sex/gender/sexuality more a biological given of male vs. female or always involving some mix of the two?

• It isn't just about the hundreds of thousands “out” transsexuals in America today, but exactly what their plight, their attempts re-negotiate sex/gender, and society's responses can teach us… (nature/nurture debate)

• Social and biological researchers are so interested in transsexuals for much the same reasons that they are similarly interested in twin studies (mirror twins especially) – they are rare and get at base human processes

• To understand the “normal” processes of human sex/gender/sexuality development and differentiation, they look for a gross deviation from the norm and attempt to relate it back to answering the core questions

• Transsexuals necessarily deliberate management of gender illuminates processes in “normally” gendered acts

• The term transgender Includes transvestite (cross-dressers), intersexed persons (hermaphrodites), transsexuals, drag queens, “gender benders”, and often butch lesbians and effeminate gay men as well

• These people have serious problems negotiating social life where there sexual and gendered identity does not fall into a very narrowly defined set of characteristics (often still binary)

• Thus, they are at risk for a multitude of personal problems over the life course due to anomie (normlessness)

• They may have trouble being accepted in their family, in interpersonal relationships, in schools, in intimate relationships, and are often discriminated against in professional occupations and legal appeals for civil rights

• Their health is also more precarious due to higher rates of STDs, AIDS, violence, and illicit drug use

Historical Ideas and Trends regarding Transsexuality

• Unlike much of today's medical advances, patients with a “ fierce and demanding drive” to alter their biological sex (“I feel like I've been trapped in a man's/woman's body my whole life), not doctors or pharmaceutical R&D, were the driving force behind the demand for sex-change technologies

• Transsexuals who wanted sex change but didn't have enough money or didn't live in a time when such medical procedures were performed often turned in desperation to “quacks” or did it themselves (at home!)

• Transsexuals suffered great abuse at the hands of disgusted police officers, judges, and psychologists

• The first highly publicized cases in America popped up in the 1950s, but were almost all male-to-female

• There was an WWII GI from the Bronx, NYC named Christine Jorgensen who traveled to Copenhagen , Denmark in 1952 for two major surgeries to alter her genitals and have massive estrogen therapy

• “He” came home as a conventionally beautiful “blonde bombshell” whose newfound celebrity got her an regular act at a flashy Manhattan nightclub for the a decade plus, then later autobiography and movie deals

• The idea that biological sex cannot be wholly constituted by chromosomes, hormones, and genitalia about sex has been increasingly redefined more as a matter of personal choice, psychological disposition

• Quite a few nations including politically moderate England and Australia have allowed transsexuals to change their biological sex on their birth certificates and thus given greater leeway with civil rights

• However, transsexuals are often seen as the greatest subversionist threat to the traditional the gender order

• In fact, there continue to be serious disagreements between transsexuals and the gay community at large and various feminist organizations who sometimes think their agendas might not be mutually beneficial

• Change will be hard to come by, keep in mind that we still cannot talk about someone in the English language without using appropriate gender pronouns (he, she, her, his) and/or great semantic discomfort

Statistics point to disproportionately more male-to-female (MTF) than female-to-male (FTM) sex changes, why?

• This would seem to be especially counterintuitive - why would men want to become part of what is socially considered the weaker sex? No reproductive potential, lower pay, more risk of violence from men, etc.

• An “embryonic hypothesis” = female is the base sex for early human embryo development – for babies to become fully male, there must be a additionally significant dose of testosterone involved later in development - if the dose is only marginally large enough, there may always be the tendency to revert to base female

• Older sexologists believed that since male homosexuality seems more common that female homosexuality, extremely effeminate homosexual males' desire for “real” (i.e., heterosexual) men manifests into a desire to become a “quasi-real” woman. To them, “I've been trapped in a man's body my whole life” is just a story.

• Men are socially more powerful and thus have the power (and masculine drive for control) to actually get up the “courage” (pun = balls) and the money (and possibly job stability) required for the surgery

• Men also have been known to be more exhibitionist and also use their sex change as a way to parlay themselves into deviant theatrical/talent show drag queen venues

• Also, MTF transsexuals have received far more publicity in the popular press in the last 50 years than their FTM counterparts, so perhaps this increased visibility has led to more male viewer with similar inclinations taking the plunge into transsexual behaviors

title: Principles of Sociology/Transsexuality


text:
Principles of Sociology/Education

Subtopics

Principles of Sociology/Social Science in Higher Education

This American Life presents... "Two Steps Back"... Ten years ago, when he was still a reporter for NPR's All Things Considered, host Ira Glass did a year-long series on a Chicago public school where things were getting better. Test scores were rising. Students were motivated. Last year, changes at the school dismantled some of the programs that had made for the school's success. And one of the best teachers in the school is thinking about quitting. We devote the whole hour to this story, about the rise and fall of school reform. Prologue. When Ira heard that Cathy La Luz, the best public school teacher he'd met during all his years of education reporting, was considering leaving her job, he went to see her in her classroom. (6 minutes) Act One. 1994. Washington Irving Elementary School became a model of school reform in Chicago a decade ago. The school did it without adding a ton more money. It wasn't a magnet school or charter school. Their strategy: get the kids to enjoy reading and writing; get them glasses if they need them; give teachers control of their classrooms. Scores climbed. Teachers like Cathy were happy. Students actually liked coming to school. We hear excerpts from Ira's 1994 All Things Considered series about the school. (21 minutes) Act Two. 2004. We continue with the story of Irving Elementary, and hear what's happened to make Cathy La Luz think about quitting. In just nine months, the reforms that had made the school a model began to unravel. Well-meaning directives from the central school board undermined what the school was trying to do. And the new principal didn't quite understand why the teachers were balking at seemingly small things, like writing up lesson plans. The climate in the school changes. The principal is oblivious. The head of the Chicago schools, Arne Duncan, says he'll look into the problems. Cathy's skeptical. (28 minutes)

title: Principles of Sociology/Education


text:
Principles of Sociology/Social Science in Higher Education

Based on John Scanzoni's 2005 book "Universities as if Students Mattered: Social Science on the Creative Edge"

Some Questions You Should Ponder:

1. Given what we think we know about likely future social, technological and economic trends, if we were to create a college or university from scratch today to reflect those changes, what would it look like?

2. How much do you know about the workings of your primary educational institution?

3. How did we get to the point where many, if not most students spend years in higher education not because they love learning, but because they feel intense social pressure to do so in order to be a “success”?

4. How much do you learn in school that you couldn't learn more effectively through hands-on experience?

5. Which group do you think is better at tolerating boredom and following rules: students or professors?

Underdeveloped Educational Processes

• Most college courses are based on the ingestion-regurgitation (IR) method, that is, the experts (professors and texts) provide the students with information and students are then judged by how proficiently they reproduce this info in various evaluation contexts (essays, multiple guess, etc.)

• Research has shown that when utilizing this method, students remember perhaps a quarter of this information when retested in the near future. Not only does this represent mediocre educational performance, but it provides a very monotonous context for learning in general.

• Furthermore, this method of teaching was originally designed for colleges whose mission it was to “stock the students” minds with the widest possible base of knowledge. This represents the old ways of “culturing” the children of aristocrats, not the application-based learning valued today.

• Though students and professors alike may be interested in doing things to “make life better” for others, there is not yet a system in place for allowing them to do much in concert to achieve these ambitions. There still remain stark divisions between teaching, research, and “doing good works.”

• The skills of analysis, evaluation, and synthesis have always been the hallmarks of good education, but are more so now that job insecurity demands more broad-based learning capacity

Conflicting Research and Teaching Objectives

• The “best” universities in the country are judged by research success, not teaching excellence.

• The most prized departments in a research university (like ours) are physical sciences that consistently produce the components for technological innovation that can be brought to market.

• Professors advance in their career and achieve tenure (job security) by performing exceptional research work that brings in outside funding. Their teaching activities are but secondary concerns.

• The vast majority of professors have no formal training in educational theory or practice and thus tend to reproduce the status quo in teaching, which has at this point been reified over generations.

• With this model in place, the teaching obligations of most professors (if they can't evade them) are at best a burden on their overall careers, so their classes are normally organized with as many labor-saving mechanisms as possible. This ends up looking very mechanized (powerpoint) and IR focused. The emphasis remains on instruction efficiency and not how students actually learn best.

Accountability and Entrepreneurship in Higher Education

• State governments have begun to tire of funding such large numbers of university institutions and their students, especially since there are few reliable methods in place to judge the performance of professors and students in the realm of education and preparation for the job market.

• In Florida, the majority of undergraduate students enrolled in state universities are funded by state scholarships, meaning that that the university system runs not off citizens directly paying tuition for their kids, but from money gained from property taxes (the rich) and lottery profits (the poor).

• States have begun to try to reduce this burden by encouraging more professors to demonstrate performance by fund their own research initiatives – changing their overall professional designation from that of hired hands for the state to independently contractors i.e. entrepreneurs

• The state hopes that the innovations developed from increased university research will spur economic activity within the state, thus generating larger tax revenues that justify their job pay

• These changes devalue teaching further due to the greater pressure on professors to “produce”

• Some have promoted the growing trend of cyber-credentialing or distance-learning as an option to cut down on overhead for educating a vast number of students. This is mostly an extension of the same efficiency paradigm. The use of high technology does not guarantee high quality education.

How the Social Sciences Fell Behind

• Social science in the US was originally begun as an attempt to mirror what the natural sciences had done in improving human well being through technological advancement. The University of Chicago sought to develop social innovations that would help the immense problems stemming from poverty in a largely immigrant city around the turn of the century.

• Many social scientists of the day were more interested in reform than science. Some blamed the poor for character flaws that caused their situation. Others believed that the public didn't know enough about bad living conditions, and that once they were “enlightened”, things would change.

• However, their efforts eventually offended many of the powerful men profiting from these poor conditions. Eventually, social science was forced back from this obligation to the betterment of humanity and into a more detached role as an analyst/commentator on the state of the social world.

• Today, while arts and humanities (history, philosophy, English, etc.) departments are under greatest threat from the new entrepreneur model, the social sciences too face significant challenges because both politicians and the public understand that the hard sciences have been the ones most often fulfilling their mandate to produce innovations that improve human lives.

• Furthermore, unlike natural scientists, who often collaborate on interdisciplinary research projects with faculty from other departments within the university, academics from the social sciences have more frequently remained mired in their respective disciplinary obscurity.

The Coming Credentialing Crisis

• The sheer number of college degrees handed out around the country has been increasing at breakneck speed for a few decades now. It is inevitable that as more individuals acquire such degrees, the less valuable each one becomes. Grade inflation had sped this process further along.

• Employers need ways to effectively distinguish amongst qualified (credentialed) job candidates. This task cannot be adequately accomplished through assessing GPA and standardized test scores.

• At present, employers base much of their hiring on the ranked prestige of specific educational institutions. However, these rankings are based mostly on research, not teaching.

• Many hiring decisions are based on the prestige of the educational institution that students attend, regardless of what quality of education they received there. With the cost of a college degree rising nationwide, these decisions will mostly reflect the socio economic standing of individuals.

• While they will for some time at least rely on these more unreliable and antiquated methods, the job market of today often requires that candidates present evidence their actual skills and abilities.

A Way Out and Over

• Make research based learning the standard – skills can only be reliably cultivated in one way – make students pose a question and then help them launch into the process of trying to answer it – we learn by thinking hard about what actions we are taking to try resolve a specific problem

• This Discovery Based Learning (DBL) is superior to Learning by Telling and Testing (LTT) and for this reason has been utilized in graduate education for some time now – the only problem is that it currently seems too expensive in large-scale undergraduate education.

• A different approach that takes seriously both accountability to students and performance of the social sciences' historical mandate to help humanity take possession of society could integrate the two by forming goal-oriented teams to tackle specific problems in the context of higher education.

• Specific modules would be formed within colleges and universities to develop and test innovative strategies to address social problems or shortcomings worthy of public attention. They would be led by professors and graduate students that specialize in these issues and have developed skills necessary to help undergraduates acquire knowledge and skills necessary to fully participate.

• An action research model would help utilize both the expertise of the professor and the interested effort of undergraduates to collaborate with folks in the local community to research tough social problems and produce meaningful and empowering social innovations to help the situation.

Potential Challenges to a New Model

* The system of tenure is still based mostly on research productivity. Although tenure is an outdated concept, is very attractive for professors' job security and will be resistant to this new model. * Could introductory classes be designed to reflect the DBL model or are they totally outmoded? * How could the worth of professors as “coaches” in DBL teams be assessed outside the productivity of a specific action research project? * How could portions of the population over the age of 25 be integrated for continuing education?


text:
Principles of Sociology/Race and Ethnicity

Subtopics:

Principles of Sociology/Roma Issues

This American Life presents... "Lincoln's Second Inaugural"... we begin with perhaps the most moving, poetic inaugural speech in American history, and look at its legacy today. In his second inaugural address, Lincoln wondered aloud why God saw fit to send the slaughter of the Civil War to the United States. His conclusion: that slavery was a kind of original sin for the United States, for both North and South, and all Americans had to do penance for it. Prologue. Ira reads briefly from Lincoln's Second Inaugural address, which describes slavery as America's Original Sin of sorts. Act One. Jack Hitt on the confederate flag over the South Carolina Statehouse. Act Two. Nelson Mandela and Abraham Lincoln. Some stunning parallels between the political strategies of the two leaders, by John Matisonn. Act Three. Good Blacks, Bad Blacks. Writer Malcolm Gladwell reads from a story that he first wrote for the New Yorker magazine, about his cousins, who immigrated to from Jamaican 12 years ago Act Four. Good Whites, Bad Whites. A documentary by Cecilia Vaisman, Christina Egloff, with Jay Allison, about a white woman named Carolyn Wren Shannon who grew up hating blacks in a Catholic neighborhood, and how her attitudes change.


text:
Principles of Sociology/Roma Issues

Race and Ethnicity – The Gypsy (Roma) Phenomena

''Social science research has effectively redefined the significance of race - previously based in biological terms - to that of a social construction contingent on the dynamics of particular societies in particular historical eras. However, the ethnicity component that has always played a large role in racial explanations has been much slower to change. While in public society today, one would have a hard time defending explanations of a specific groups' behavior patterns based on racial disposition, ethnicity, or the shared cultural heritage of a particular group, still serves as a popular and largely unexamined explanatory mechanism. Instead of focusing on the often divisive issues of race and ethnicity ever present when discussing the plight of ethnic minorities in American society, it may be more enlightening to examine the similarities between situations and social context of racial/ethnic minorities in other nations.''

Current World Population Dynamics: 13 million Roma worldwide (close to worldwide Jewish population)

- ¾ of the 8 million European Gypsies live in Eastern Europe where they are around 10% of the total pop

- The Roma Diaspora began in India and has now established significant populations all over the world

- These Roma populations do not conform to any one unified group in cultural, political, or ethnic terms

- Roma overall have very high fertility rates compared to the majority populations around them

Social Situation of Roma:

- Roma lag far behind the majority populations around them in terms of all standard of living indicators

- Roma are generally feared and despised by the majority populations around them, irregardless of specific location, mostly because the rules governing their society are generally very misunderstood by outsiders

- Roma speak a Sanskrit based tongue called Romani, which no one outside their ranks really understands

- Their language and cultural belief systems keep them mostly unintegrated in larger societal institutions

Roma history :

- They are believed to be a nomadic lower caste from NW India that specialized in music, animal trading, and metal work that were either captured in warfare or sold as slaves after the Islamic invasions in 1000AD

- From there they were able to migrate throughout the Near East, Northern Africa, and Eastern Europe

- In the kingdoms that comprise present day Romania, they were legally enslaved until the mid 1800s

- One million Gypsies were killed in the Holocaust, but they fared much better than the Jews because their history had made them very unassimilated and adept at evading the authorities

- Most Roma fell under the rule of Eastern European communist governments following the end of WWII, who settled the gypsies on collective farms and in factory towns in a program the called “the great halt”

- After the fall of communism in 1989, there were numerous attacks on Roma communities that amounted to government condoned genocide on a people that had never really been assimilated in these societies

- The communists had instead isolated and deracinated many Roma who now had no sense of coherent culture or community in nations where they were by far the poorest and most hated ethnic groups

Roma Culture and Customs :

- Roma define themselves and other Roma not by group physical attributes, but by knowledge (or lack thereof) of the Romani language and the codes of conduct prescribed by Roma tradition

- Roma culture has a very premodern and traditional division between clean and unclean in all life arenas

- For example, all non Roma are called Gadje, or peasants, and considered very unclean, thus all interactions with gadje outside of economic exploitation bring along fear of contamination

- There are strong gender roles in Roma society – men control secular matters and women control spiritual matters – also, women have the power to pollute men and thus must be controlled by strict behavior codes

- Roma are stratified at three social levels, nation, tribe, and community – there are only a few different nations, many tribes, and many collected communities of unrelated families within the tribes

- There are complex marriage patterns within Roma society that are used to prevent inbreeding while stabilizing networks of power based relationships within and between the tribes

- In Roma families and communities, men have all the decision making power while women are kept subservient and constantly toiling in domestic labor until menopause, after which they become equals

- Roma have very different codes of cleanliness – children often appear very dirty and the yards of their houses are especially cluttered with garbage – but personal hygiene rituals are actually incredibly elaborate

How Roma and their Way of Life Survive :

- Roma are what are termed “middlemen minorities” in sociology – they make a living by catering to the specific needs of the majority population – in European history, Jews most prominently played this role

- Traditional Roma will not socialize or have sexual relations with gadje under normal circumstances

- The Roma have adjusted their “religion” to fit whatever specific region they reside within

- Roma have had certain historical trades that they have specialized in – horse trading, music, copper metallurgy, bear training, fortune telling, small craft manufacture, theatre performance, begging, etc.

- These trades have largely been decimated by the historical process of industrialization, so gypsies have found other ways of making a living including auto trading and repair, off market commerce, and welfare

- Roma cannot make ethically make money from one another, but there is no such ethical code concerning economic relations with gadje, who they see fit to swindle and steal from at any and all times

- Because of these tenuous relationships with gadje, gypsies have never been able to stay in one place very long… so their nomadic lifestyle is a necessity when one cannot sustainably exist in one place for very long

- Roma communities are very close and are responsible for taking care of group economic needs – so that no individual can hold onto known liquid assets for very long and thus must buy cars and furniture instead

- Furthermore, Roma are communitarian, so family honor and well being of the community is paramount

- The laws of conduct within these communities are very specifically delineated so that there is a traditionally endorsed behavior for almost every conceivable situation encountered in life

- Roma culture offers what the outside world cannot provide - belonging - the worst sanction is banishment

Why the Roma are an Important Example to Understand:

- It is imperative that we acknowledge the cultural traits of specific groups are not a natural occurrence, but products of specific interaction dynamics between majority/minority groups that make them most workable

- If one does not understand their historical and present circumstances of a group, they cannot explain their behavior and thus must invent self-serving means to explain their “strange self-defeating behavior”

- Roma have been subject to the same kind of persecution that many ethnic minority groups have faced throughout history – slavery, bonded labor servitude, segregation, discrimination, genocide, stereotyping

- Social and economic displacement courtesy of the dominant society has followed them everywhere – if no one allowed them to settle anywhere under decent conditions, why wouldn't they keep perpetually moving

- Gypsy stereotypes justify the majority/minority power relationships = lazy thieves, dirty and diseased, cannibals, baby snatchers, devil worshipers, spies for foreign powers, assassins, etc.

- Often, minority groups capitalize on stereotypical beliefs to present a certain kind of image to outsiders that could help them profit – exoticized Gypsy fortune tellers present a certain kind of occult mystique

- The degree of difference that Roma communities exemplify is a test of civil society – How can societies cope with truly different groups that are unwilling to assimilate or compromise their values?

'''Europeans keep asking... What to do with the Gypsies…'''

- One might hope that today's societies would have more of a place for Roma culture… their historical opposition to settled agriculture is now moot, Gypsies are notably good at free market commerce, and as a whole, the world has become more accepting of multiculturalism ideals

- Still, the Roma people have big problems – high unemployment, low literacy, low life expectancy

- Gypsies trying to get to Western Europe have not been well received and often their stateless predicament has not been recognized – thus they remain displaced people with no real chance in life

- Roma culture does not blend in well with modernization – they dislike gadje doctors (sometimes they sterilize Roma women), gadje schools (track Roma children into lowest classes), and the gadje legal systems that try to stop their child marriage and dowry systems, nomadic lifestyle, and business ventures

- Furthermore, Roma are unlikely to be able to organize their own institutions or their own de facto territories (like the Kurds perhaps) very well, because their social structure doesn't promote collaboration

- Outside the confines of family and community, Roma leaders counter productively infight for personal aggrandizement, collaborating with gadje officials in the process and further tarnishing the Roma image

- Can “gypsy problems” be redefined from focusing on disparate social problems to a unified ethnic issue?

- In Romania today, gypsies account for about 20% of the total population. They are openly despised and discriminated against. The kinds of human rights violations that define the Romanian peoples relationship with Roma are a major issue, perhaps a core one holding them back from EU integration… can gypsies organize cross nationally to take advantage of this situation and garner some real political clout in the process?

title: Principles of Sociology/Roma Issues


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Principles of Sociology/Gender Stratification

''I am of the opinion that a prime measurement of the goodness of a society must be how much of their population's potential they utilize. In more modern societies, it is thought that task specialization (what Durkheim called organic solidarity) replaced the need for an expansion of the general knowledge base of most members of societies. Nowadays, in the so-called post-modern or information age, it isn't so much knowing how to fix cars and household appliances that is so crucial, but understanding other people's behavior patterns and means of justification that proves useful. We still have a lot of leftover barriers from the days of mechanical solidarity along the lines of race, class, and gender especially. These barriers restrict our development as individuals insomuch as they constrain our choices throughout our lives. Our key task is to discuss how socially gendered systems of meaning are constructed, maintained, and changed.''

Interesting Thoughts and Examples:

Why might sorority row be located where it is today? Conversely, what about fraternity row? (I ask this of my freshman students at the University of Florida and almost none can reason it out... frat row is next to the law school and sorority row is next to the education college)

What do you think the two professions are in which average women's earnings outpace men's?

Gender Polarization refers to the tendency to construct more homogenized, mutually exclusive ideal types of male/female characteristics rather than embracing the naturally occurring diversity within the gender spectrum. This also refers to the ways we initially stereotype the ways we think others relate to the world.

Stratification on the basis of sex/gender channel males and females into very different and often unequal life situations. However, resistance to this system is often mitigated by the process of enculturation, whereby individuals encountering hegemonic gendered discourses and institutions gradually internalize socially acceptable standards of behavior and are rewarded for constructing identities consistent with them.

Androcentrism refers to the idea that our society is male-centered, that is, hegemonic notions of masculinity are what most individuals must live up to in order to access positions of high status and prestige.

Throughout history, men in positions of power have argued that gender stratification is inherent in societies due to biological essentialism (sociobiology). Others have used religious texts as justification. The same lines of argument were long used to oppress all racial/ethnic groups outside of Nordic Europeans, but it seems that with gender, this reasoning has not been so fully discredited and still curries public favor.

• Gendered conservation of energy was used to justify women's exclusion from education and voting because proponents argued that women would use up their “vital energy” on intellectual pursuits, thus leaving insufficient quantities for the optimal development of reproductive faculties.

• Darwin concluded that males of a particular species are always more highly evolved than the females because males' selection relies on more competition with sexual rivals.

• Evidence that men are innately more active and dynamic can be found in the behavior of sperm, while evidence that females are innately passive can be found in the behavior of the egg.

When thinking about how biology influences behavior, as it doubtlessly does, we have three choices:

1. Exaggerate biological dispositions 2. Try to change biological limitations through other innovations (technological, social) 3. Accept biological limitations and adapt within them

We have made significant strides in minimizing #1 and expanding #2, but the third option still seems to be our cultural default. The real flaw in this reasoning lies in the notion that common sense folk knowledge or science as it's currently practiced (tools and ethics) can really apprehend “human nature”, especially gender

Since it seems that more and more we're settling on option #2, we should look at how people attempt to alter the cultural environment and corresponding social systems of meaning corresponding with gender…

We've witnessed in the Western world and in much of the non-Western world a political movement over the last 150 years that has transformed women from an almost totally disenfranchised and disempowered population whose social relevance only extended as far as their father/husband to full fledged equal citizens

Still, gross inequities remain. Most all of these cannot be effectively chalked up to biology. With the opportunities for women seemingly expanded to such a large degree, it seems strange that persistent social patterns that disadvantage women remain. Equally as strange has been men's role change stagnation. Why?

Possible explanations: 1. Entrenched cultural scripts… example = linguistic sexism

• Think of some popular slang to describe intercourse… and what do you find?

• 500 synonyms for prostitute and 1000 sexually derogatory words/phrases to describe women

• 10 times as many slang terms for stupid/superficial women as for similar men

• “girls and guys” not “boys and girls” – women often described as irresponsible, immature, small

• women professionals are often linguistic derivatives of masculine nouns – men get male nurse

• formal distinctions based marriage status are only used for women – Ms. is best perceived

• he, his, and man are still used as our generic descriptors – men and women respond differently

Does language merely represent our past values and prejudices or does it actively reinforce it? Social psychologists have shown that people given a position paper to read enough times will begin to adjust their own attitudes towards that position, regardless of initial disposition, this is how “brainwashing” is done…

2. Workplace androcentrism and power

• women are underpaid and underemployed relative to men – hence the higher poverty

• the more women in a specific profession, the more its prestige declines

• model behavior for success in the professional/corporate workplace is traditionally unfeminine – women must vanquish their femininity lest they be seen as weak or sexually conniving, but then face the stigma of being labeled “manly” - demanding too much and stepping out of their “place”

• the subordination of all other life activities to the service of workplace achievement requires that someone else take care of your other essential life activities for you (food, children, cleaning) – in effect, a wife – however, few men will take a position and look after their wives' affairs

• women know how to work in teams, but not in teams that don't want token players on them.

• Minorities have great difficulties exercising power because they need approval from the majority

• Women must also negotiate disproportionate burdens at home while in fulfilling their female role over the life course – “the double shift”

3. Ineffective tactics of the feminist movement

• Why do you think most American adults don't favor women using collective action to better their social position? Is it because they truly fear gender equity at a visceral level, or because they fear particular representations of feminism? Where are their public relations advisors?

• Like most movements that seem to achieve success in their early days (1960s) – certain subgroups with more extreme agendas (for better or worse) branched off – deflecting public attention off their core mainstream goals (mentioned in book) and socialist and radical versions emerged

• Furthermore, the rhetoric wasn't well tuned from the beginning – in retrospect, why name a movement that advocates equality for men and women feminism – we can see the early justifications, but today most uninformed people interpret the term as a female power grab…

• How do feminist organizations go about attempting to persuade men, the assumed principle opposition to the feminist agenda, of the righteousness of their political vision?

• Feminists have had a lot of trouble reconciling different cultural beliefs as well, especially along religion lines, but along class and racial ones as well

• What is the feminist vision today and what group is responsible for disseminating it to the public at large? How could it be improved to advance the interests of women in America ?

4. Men and Masculinities

• Men haven't been paid nearly as much attention to over the last 50 years or so and their change movements have been even more hokey and ineffective than women's – Christian revival of family values (the “Promise Keepers”) and wilderness retreats to revive the “wild man within” (read Robert Bly's Iron John)

• Men haven't changed their behaviors and attitudes nearly as fast as women – as is usually the case with a group in power responding to a challenge to that power – its only now in the last decade or so that some men have begun to soften their masculine displays, hence the metrosexual emergence

• Why would men in their current mindset relinquish power, especially when they think it comes directly at the expense of their manhood?


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Signals and Systems/Filter Implementations

Filter design mostly bases on a limited set of widely used transfer functions. Optimization methods allow to design other types of filters, but the functions listed here have been studied extensively, and designs for these filters (including circuit designs to implement them) are readily available. The filter functions presented here are of lowpass type, and transformation methods allow to obtain other common filter types such as highpass, bandpass or bandstop.

Butterworth Filters
The Butterworth filter function has been designed to provide a maximally flat amplitude response. This is obtained by the fact that all the derivatives up to the filter order minus one are zero at DC. The amplitude response has no ripple in the passband. It is given by:

 * $$A(j\omega) = |H(j\omega)| = \sqrt{ \frac{1}{1+\omega^{2n}} }$$

It should be noted that whilst the amplitude response is very smooth, the step response shows noticeable overshoots. They are due to the phase response which is not linear or, in other words, to the group delay which is not constant.

The amplitude response plot shows that the slope is 20n dB/decade, where n is the filter order. This is the general case for all-pole lowpass filters. Zeros in the transfer function can accentuate the slope close to their frequency, thus masking this general rule for zero-pole lowpass filters.

The plot also shows that whatever the order of the filter, all the amplitudes cross the same point at $$A(\omega = 1) = \frac {1}\sqrt{2}$$, which corresponds to approximatively -3 db. This -3 db reference is often used to specify the cutoff frequency of other kinds of filters.

Butterworth filters don't have a particularly steep drop-off but, together with Chebyshev type I filters, they are of all-pole kind. This particularity results in reduced hardware (or software, depending on the implementation method), which means that for a similar complexity, higher order Butterworth filters can be implemented, compared to functions with a steeper drop-off such as elliptic filters.

Zeroes of the Butterworth function
The normalized Butterworth function is indirectly defined by:

 * $$H(s) \cdot H(-s) = \frac{1}{1+\omega^{2n}}$$

This functions has zeros regularly placed on the unit circle. Knowing that a stable filter has all of its poles on the left half s-plane, it is clear that the left half poles on the unit circle belong to $$H(s)$$, whilst the right half poles on the right belong to $$H(-s)$$.

The normalized Butterworth function has a cutoff frequency at $$f_c = \omega_c / (2 \pi) = 1/ (2 \pi) [Hz]$$. A different cutoff frequency is achieved by scaling the circle radius to $$\omega_c = 2 \pi f_c$$.

Butterworth Transfer Function
The transfer function of a Butterworth filter is of the form:
 * $$H(s) = \frac{1}{den(s)}$$

It can also be written as a function of the poles:
 * $$H(s) = \frac{k}{\prod_{i=1}^N (s-p_i)}$$

With this, the denominator ploynom is found from the values of the poles.

Chebyshev Filters
In comparison to Butterworth filters, Chebyshev filters have a supplemental parameter: a ripple in amplitude. This ripple, which could be considered as non ideal, has the tremendous advantage to allow a steeper roll-off between passband and stopband.

The ripple can happen in the passband, which is the case for Type I Chebyshev filters, or in the stopband for Type II filters.

Chebyshev Polynomials

Chebyshev Polynomials have the property to remain in the range $$-1 < T_n(x) < 1$$ for an input in the range −1 < x < 1 and then rapidly grow outside this range. This characteristic is a good prerequisite for devising transfer functions with limited oscillations in a given frequency range and steep roll-offs at its borders.

The Chebyshev polynomials of the first kind are defined by the recurrence relation:

\begin{align} T_0(x) & = 1 \\ T_1(x) & = x \\ T_{n+1}(x) & = 2x \cdot T_n(x) - T_{n-1}(x). \end{align} $$

The first Chebyshev polynomials of the first kind are:

 * $$ T_0(x) = 1$$

 * $$ T_1(x) = x$$

 * $$ T_2(x) = 2x^2 - 1$$

 * $$ T_3(x) = 4x^3 - 3x$$

 * $$ T_4(x) = 8x^4 - 8x^2 + 1$$

Chebyshev Type I
Chebyshev type I filters show a ripple in the passband. The amplitude response as a function of angular frequency $$\omega$$ of the nth-order low-pass filter is:

 * $$G_n(\omega) = \left | H_n(j \omega) \right | = \frac{1}{\sqrt{1+\varepsilon^2 T_n^2\left(\frac{\omega}{\omega_0}\right)}}$$

where $$\varepsilon$$ is the ripple factor, $$\omega_0$$ is the cutoff frequency and $$T_n$$ is a Chebyshev polynomial of order $$n$$.

The passband exhibits equiripple behavior, with the ripple determined by the ripple factor $$\varepsilon$$. In the passband, the Chebyshev polynomial alternates between 0 and 1 so the filter gain will alternate between maxima at G = 1 and minima at $$G=1/\sqrt{1+\varepsilon^2}$$. At the cutoff frequency $$\omega_0$$ the gain again has the value $$1/\sqrt{1+\varepsilon^2}$$ but continues to drop into the stop band as the frequency increases. This behavior is shown in the diagram on the right. The common practice of defining the cutoff frequency at −3 dB is usually not applied to Chebyshev filters; instead the cutoff is taken as the point at which the gain falls to the value of the ripple for the final time.

Chebyshev Type II
Chebyshev Type II filters have ripples in the stopband. The amplitude response is:

 * $$G_n(\omega,\omega_0) = \frac{1}{\sqrt{1+ \frac{1} {\varepsilon^2 T_n ^2 \left ( \omega_0 / \omega \right )}}}.$$

In the stopband, the gain will always be smaller than

 * $$\frac{1}{\sqrt{1+ \frac{1}{\varepsilon^2}}}$$

Also known as inverse Chebyshev, this filter function is less common because it does not roll-off as fast as type I, and requires more components. Indeed, the transfer function exhibits not only poles but also zeros.

Elliptic Filters
Elliptic filters, also called Cauer filters, suffer from a ripple effect like Chebyshev filters. However, unlike the type 1 and Type 2 Chebyshev filters, Elliptic filters have ripples in both the passband and the stopband. To counteract this limitation, Elliptic filters have a very aggressive rolloff, which often more than makes up for the ripples.

Comparison
The following image shows a comparison between 5th order Butterworth, Chebyshev and elliptic filter amplitude responses.

Filter Design
Using what we've learned so far about filters, this chapter will discuss filter design, and will show how to make decisions as to the type of filter (Butterworth, Chebyshev, Elliptic), and will help to show how to set parameters to achieve a set of specifications.


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 Embedded Systems

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