Dither and Salesianum School: Difference between pages

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{{Infobox School

:''The dictionary definition of "dither" is "a state of indecision" or "to be nervously irresolute in acting or doing." This article is about dither as a technical term in digital signal processing.''

| name = Salesianum

| image = [[Image:Salesianum seal.jpg|175px]]

| motto = ''Tenui Nec Dimittam''

| established = 1903

| type = [[Catholic school|Catholic]]

| principal = [[Priest|Father]] William T. McCandless, [[Oblates of St. Francis de Sales|OSFS]]

| faculty =

| enrollment = approx. 1,100

| free_label =

| free_text =

| free_label2 =

| free_text2 =

| ___location = 1801 N. Broom St.<br />Wilmington, DE 19802-2891

| information =

| website = http://www.salesianum.org/

}}

'''Salesianum School''' is an independent [[Catholic]] [[secondary school]] for boys, located in [[Wilmington, Delaware]]. Salesianum is Latin for "House of Sales" referring to [[St. Francis de Sales]]. Founded in [[1903]], the school is operated by the [[Oblates of St. Francis de Sales]]. The current enrollment is just above 1,100 students, from [[Delaware]], [[Maryland]], [[New Jersey]] and [[Pennsylvania]]. The school has two sister schools, [[Padua Academy]] and [[Ursuline Academy (Wilmington, Delaware)|Ursuline Academy]], close by in the city.

Dither is form of noise added to digital data for the purpose of minimizing quantization error. It most often surfaces in the field of digital audio, but is utilized and many different fields where digital processing and analysis is used - especially waveform analysis. This includes digital audio, digital video, digital photography, seismology, RADAR, weather prediction systems and much more.

Salesianum School educates and develops the whole person based on the spirituality of [[St. Francis de Sales]] whose [[philosophy]] can be summarized in "Live Jesus." The school's official motto is "Tenui Nec Dimittam," meaning "I have taken hold (of the faith) and will not let go." Each day and most classes begin with the reciting of Salesianum's version of the Catholic [[prayer]], The Direction of Intention. The Salesianum version reads: "My God, give me the grace to perform this action with you through love for you. In advance, I offer to you all the good that I may do and accept all the difficulties that I may meet therein." The prayer is followed by the statement "St. Francis de Sales, pray for us."

The premise is that quantization and re-quantization of digital data yields error. If that error is repeating and ''correlated'' to the signal then the result is repeating, cyclical and mathematically determinable error to the signal. In some fields, especially where the receptor is sensitive to such artifacts, cyclical errors yield undesirable artifacts. In these fields we use dither to results in less determinable artifacts. The field of audio is a primary example of this - the human ear functions much like a Fourier Transform, wherein it hears individual frequencies. The ear is therefore very sensitive to ''distortion,'' or additional frequency content that "colors" the sound differently. The ear is far less sensitive to random noise at all frequencies, however, so dither is used in digital audio to turn correlated quantization error into uncorrelated quantization error, or noise.

Salesianum's tuition for the 2006-2007 school year is $8,990.00.

==Dither in everyday life==

Salesianum School was the first [[Racial integration|integrated]] school in the state of [[Delaware]], and recently was awarded for this with a historical marker.<ref>{{cite web | author=Kenney, Edward L. | title=First to break the color line | publisher=[[Gannett]] | year=February 27, 2006 | work=[[Delaware News-Journal|The News Journal]] | url=http://www.delawareonline.com/apps/pbcs.dll/article?AID=/20060227/NEWS03/602270326 | accessdate=April 6 | accessyear=2006}}</ref>

Any time you shake a cookie sheet to get the tater tots to slowly slide off of the sheet you are "dithering" the cooking sheet - adding dither to allow for a smoother, more predictable behavior.

The goal of Salesianum is, and has always been, to welcome boys into their halls and have them leave as "Salesian gentlemen".

In traditional popcorn making techniques people would often put popcorn in a pan and shake the pan in order to keep the heat even throughout the kernels. This, also, is an example of adding "dither" in everyday life.

==Athletics==

In the 1940s (as the story goes) the British Naval Air Fleet was having difficulty calibrating their navigation systems - primitive systems with cogs and gears. While the planes were on the ground the systems would not calibrate because the mechanisms would choke and stick. While the planes were in the air they would work much more fluidly because the vibration of the engines caused more fluid motion. The British ended up using engines to calibrate their equipment while on the ground in order to get more accurate results. This was the first known use of intentionally adding "dither" and calling it such.

*Salesianum has won 105 state championship sports titles. In the fall of 2005, it became the first [[Delaware]] school to win the boys state championships in [[Football]], [[Soccer]], and [[Cross country running|Cross Country]] in one year, an achievement known as the "Fall [[Triple Crown]]". They repeated this feat in the fall of 2006. Salesianum also won the Spring Triple Crown in 2005. Recently, Salesianum won the Fall Triple Crown for the second consecutive year, making them, as patrons say, a "dynasty."

*Salesianum's general nickname is "Sallies", while the sports moniker is the "Sals

*In 1994, Salesianum's football team defeated Bethlehem Catholic from [[Bethlehem, PA]] in one of the greatest upsets in school history. Bethlehem Catholic's [[quarterback]], Dan Kendra, was widely regarded as the #1 high school quarterback in the [[U.S.]] and went on to play the position at [[Florida State University]] before tearing his ACL and being moved to fullback.

*Salesianum has twice won the Cross Country, Winter Track, and Spring Track State Championships during one school year, something which no other Delaware school has achieved.

==Trivia==

==Dither in digital audio==

*Salesianum's arch rival is [[St. Mark's High School]].

*Salesianum has won the Triple Crown for the last two years.

== External links ==

The final version of audio that goes onto a [[compact disc]] contains only 16 [[bit]]s, but throughout the audio editing process the digital data grows in bit depth as computation occurs. The more math we do, the larger the samples grow in bit depth - just like adding, multiplying, or dividing decimal numbers. In the end, the digital data must be returned to 16 bits for pressing onto a CD and distributing.

* [http://www.salesianum.org/ Salesianum]

{{Delaware-school-stub}}

There are multiple ways in which one can return the data to 16 bits. They can, for example, simply lop off the excess bits - called ''truncation.'' They can also ''round'' the excess bits to the nearest value. Each of these methods, however, results in predictable and determinable errors in the result. Take, for example, a waveform that consists of the following values:

[[Category:Educational institutions established in 1903]]

1

[[Category:High schools in Delaware]]

2

[[Category:Salesian secondary schools]]

3

[[Category:Wilmington, Delaware]]

4

5

6

7

8

If we reduce our waveform by, say, 20% then we end up with the following values:

.8

1.6

2.4

3.2

4.0

4.8

5.6

6.4

If we truncate these values we end up with the following data:

0

1

2

3

4

4

5

6

If we round these values we end up with the following data:

1

2

2

3

4

5

5

6

Any waveform comprised of the original values, then processed by multiplying each value by .8, would have errors in it in the result, and the errors would be manifested as repeatable. A repeating sine wave quantized to the original sample values, for example, would experience the same error every time its supposed value was "3," in that the truncated result would be off by .4. Any time the supposed value was "5" the error after processing and truncation would be 0. Therefore, the error amount would change repeatedly as the values change. The result is cyclical behavior in the error, which manifests itself as additional frequency content on the waveform. The ear hears this as 'distortion,' or the presence of additional frequency content.

We cannot avoid error resulting in this process. Taking a 2 digit number (4.8) and turning it into a 1 digit number (4 or 5) is going to result in error, and that is unavoidable. What we want to do, however, is create a system wherein that error does not repeat as the values repeat.

A plausible solution would be to take the 2 digit number (say, 4.8) and round it one direction or the other. For example, we could round it to 5 one time and then 4 the next time, etc., etc. This would make the long-term average 4.5 instead of 4, so that over the long-term the value is closer to it's actual value. This, on the other hand, still results in determinable (though more complicated) error. Every other time the value 4.8 comes up the result is an error of .2, and the other times it is -.8. This still results in repeating, quantifiable error.

Another plausible solution would be to take 4.8 and round it so that four times out of five it rounded up to 5, and the other time it rounded to 4. This would average out to exactly 4.8 over the long term. Unfortunately, however, it still results in repeatable and determinable errors, and those errors still manifest themselves as distortion to the ear.

This leads to the ''dither'' solution. Rather than predictably rounding up or down in a repeating pattern, what if we rounded up or down in a random pattern? If we came up with a way to randomly toggle our results between 4 and 5 so that 80% of the time it ended up on 5 then we would average 4.8 over the long run but would have random, unrepeating error in the result. This is done through dither.

We calculate a series of random numbers between 0 and .9 (ex: .6, .4, .5, .3, .7, etc.) and we add these random numbers to the results of our equation. Two times out of ten the result will truncate back to 4 (if 0 or .1 are added to 4.8) and the rest of the times it will truncate to 5, but each given situation has a random, but 20% chance of rounding to 4 or 80% chance of rounding to 5. Over the long haul this will result in results that round to 4.8 and a quantization error that is random - or noise. This "noise" result is less offensive to the ear than the determinable distortion that would result otherwise.

===When to add dither===

Dither must be added before any quantization or re-quantization process in order to prevent non-linear behavior (distortion). The results of the process still yield distortion, but the distortion is of the noise so its results are effectively noise. Any bit-reduction process should add dither to the waveform before the reduction is performed.

===Different types of dither===

'''RPDF''' stands for "Rectangular Probability Density Function," equivalent to a role of a die. Any number has the same random probability of surfacing.

'''TPDF''' stands for "Triangular Probability Density Function," equivalent to a role of two dice. The number sums have different probabilities of surfacing:

:1/1 = 2

:1/2 2/1 = 3

:1/3 2/2 3/1 = 4

:1/4 2/3 3/2 4/1 = 5

:1/5 2/4 3/3 4/2 5/1 = 6

:1/6 2/5 3/4 4/3 5/2 6/1 = 7

:2/6 3/5 4/4 5/3 6/2 = 8

:3/6 4/5 5/4 6/3 = 9

:4/6 5/5 6/4 = 10

:5/6 6/5 = 11

:6/6 = 12

7 is far more likely to surface than 2 or 12, and the relationship between these probabilities is said to be "triangular."

'''Gaussian PDF''' is equivalent to a role of infinite dice. The relationship of probabilities of results follows a bell-shaped, or [[Gaussian]] curve. Gaussian PDF dither is closest in proximity to the sound of natural atmospheric noise, tape hiss, etc.

'''Colored Dither''' is sometimes mentioned as dither that has been filtered to be different than white noise. Some dither algorithms use noise that has more energy in the higher frequencies so as to lower the energy in the critical audio band.

'''Noiseshaping''' is not actually dither, but rather a feedback process that has dither within it. It is used for the same purposes.

===Which dither to use===

If the signal being dithered is to undergo any further processing at all then it should be processed with TPDF dither that has an amplitude of two quantization steps (so that the dither values computed range from, say, -1 to +1, or 0 to 2). If colored dither is used at these intermediate processing stages then the frequency content can "bleed" into other, more noticeable frequency ranges and become distractingly audible.

If the signal being dithered is to undergo no further processing - it is being dithered to its final result for distribution - then colored dither or noiseshaping are appropriate, and can effectively lower the audible noise level by putting most of that noise in areas where it is less critical.

==See also==

* [[Digital audio]]

* [[Quantization (signal processing)]]

== External links ==

Much of the research in the field of dither for (at absolute least) the audio industry was done by Lipshitz and Vanderkooy out of the University of Waterloo. Other well-written papers on the subject at a more elementary level are available by:

*Aldrich, Nika. "[http://www.cadenzarecording.com/dither Dither Explained]"

*Katz, Bob. "[http://www.digido.com/portal/pmodule_id=11/pmdmode=fullscreen/pageadder_page_id=27/ The Secrets of Dither]"

Both Nika Aldrich and Bob Katz are esteemed experts in the field of digital audio and have books available as well, each of which are far more comprehensive in their explanations:

*Aldrich, Nika. "[http://www.cadenzarecording.com Digital Audio Explained]"

*Katz, Bob. "[http://www.digido.com/portal/pmodule_id=11/pmdmode=fullscreen/pageadder_page_id=66/?PHPSESSID=62e494f55b80063f2bf090bf60c0253b Mastering Audio]"

[[Category: Audio engineering]]