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Triangular Probability Density Function Dither, How does this random number exaclty work
aristotel
post Dec 31 2003, 04:52
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Hello everybody,

THis is my first post on this site. NIce to find a forum for this field which I am interested in and studying.

So here is the problem...

I need to write in C, a program that will dither and truncate a 16 bit stereo file to a 14 bit stereo file. It is for an assignment for university basically. I more or less have the idea of how it works after having read several books and websites.

However here is the problem/question.

To go from 16 bit to 14 bit and add dither before truncating it is necessary to add 3 bits of noise to the 16 bit original signal.

3 bits can have the maximum value of 8. In audio Terms -4 to +4. Correct so far?

Now if i generate a random number between 0 and 8, I can't just add that number to the 16 bit stream right? Becuase I need to add a +4 to -4 range number. It that correct? and if it is, how can I generate a random number between +4 and -4 in C?

int a = rand() % 8;

this would give a random value between 0 and 8. BUt how do i set a lower and upper limit for the random number to be generated?

Well, at this point this is all i will ask. I have a feeling this is somehting really simple and for some reason I have been stuck on it for some time now. huh.gif

Thank you in advance for reading it and hopefully replying.

In the meantime, Happy New Year everybody! cool.gif


PS: Oops..i just realised it was moved from general audio to Scientific..Sorry..i am new ..i thought this was a simple question and thats why i put it in General audio.

This post has been edited by aristotel: Dec 31 2003, 05:02
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Nika
post Jun 16 2005, 14:50
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Sorry, guys, I've only just seen the thread and haven't read all the way through it. The bit depth of the dither is not "2 bits" but rather "2 quantization steps" (of the remaining quanta). 2 bits implies the options of 00, 01, 10, and 11. 2 quanta implies 00, 01 and 10. The dither must be of triangular probability within this range. The way to generate the dither is to generate one bit's worth of random values twice, so:

Random value between 0000 (bits 13 through 16) and 0100. Do this twice and add them together.

You now have TPDF dither of 2 quanta in amplitude (not 2 bits). The result will be some value between 0000 and 1000 with the greatest likelihood that the number will be 0100.

To the person that asked, this is precisely the amount and type of dither needed in order to completely remove quantization distortion (or rather turn it into noise). This has been mathematically proven and you can find these proofs in the writings of Lipshitz and Vanderkooy.

I hope this helps?

Nika
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Posts in this topic
- aristotel   Triangular Probability Density Function Dither   Dec 31 2003, 04:52
- - kjoonlee   Hi, I'm quite a newbie, so I can't offer ...   Dec 31 2003, 05:16
- - tigre   AFAIK rectangular dither is equal to random noise ...   Dec 31 2003, 11:23
- - aristotel   Hey..thanks for your replies. I have come up with...   Dec 31 2003, 16:49
- - Jasper   It seems correct, but wouldn't you just need t...   Jan 1 2004, 11:49
- - aristotel   Hey Jasper..thanks for your post. The decision to...   Jan 1 2004, 16:57
- - cabbagerat   You might want to consider the fact that with most...   Jan 2 2004, 06:57
- - Jasper   If you are looking for good random number generato...   Jan 2 2004, 12:02
- - aristotel   Hello, Jasper..the way I understood it was that if...   Jan 3 2004, 20:15
- - Jasper   Actually the information from those two bits of no...   Jan 4 2004, 11:28
- - tigre   There must be a mathematical way to determine how ...   Jan 4 2004, 12:20
- - Ariakis   http://www.hydrogenaudio.org/forums/index....indpo...   Jan 4 2004, 12:33
- - Diocletian   QUOTE (tigre @ Jan 4 2004, 12:20 PM)There mus...   Jan 4 2004, 12:56
- - tigre   totally = not mesurable. e.g. distortion: If you ...   Jan 4 2004, 13:06
- - aristotel   Hello everybody...lots of replies i see...lots of ...   Jan 4 2004, 19:16
- - tigre   QUOTE (aristotel @ Jan 4 2004, 08:16 PM)It ta...   Jan 4 2004, 19:58
- - 2Bdecided   I've only just seen this thread. At the risk ...   Jan 5 2004, 16:07
- - KikeG   QUOTE (tigre @ Jan 4 2004, 12:20 PM)There mus...   Jan 6 2004, 16:49
- - aristotel   QUOTE (tigre @ Jan 4 2004, 10:58 AM)Do proces...   Jan 6 2004, 18:21
- - aristotel   Hello 2bDecided..your post is helpful and thank yo...   Jan 6 2004, 19:04
- - aristotel   QUOTE (KikeG @ Jan 6 2004, 07:49 AM)if I...   Jan 6 2004, 19:16
- - aristotel   QUOTE (aristotel @ Jan 4 2004, 10:16 AM)Howev...   Jan 6 2004, 19:20
- - 2Bdecided   QUOTE (aristotel @ Jan 6 2004, 06:04 PM)Hello...   Jan 7 2004, 13:46
|- - goli   Hi everybody, I just visited this page and i was ...   May 29 2005, 19:02
|- - 2Bdecided   QUOTE (goli @ May 29 2005, 06:02 PM)Hi everyb...   Jun 16 2005, 11:37
|- - Nika   QUOTE (goli @ May 29 2005, 12:02 PM)Hi everyb...   Jun 16 2005, 14:55
- - aristotel   QUOTE (2Bdecided @ Jan 7 2004, 04:46 AM)Hope ...   Jan 9 2004, 03:22
- - Ariakis   Just a note on what David said about a triangular ...   Jan 9 2004, 09:04
- - Jasper   Actually I think you'd want something symmetri...   Jan 9 2004, 13:06
- - 2Bdecided   QUOTE (Ariakis @ Jan 9 2004, 08:04 AM)Just a ...   Jan 9 2004, 13:29
- - spoon   To quote shibatch "Dithered 8bit files contai...   Jun 15 2005, 10:11
- - KikeG   That depends largely on the sample rate.   Jun 15 2005, 13:13
- - Nika   Sorry, guys, I've only just seen the thread an...   Jun 16 2005, 14:50
|- - madshi   QUOTE (Nika @ Jun 16 2005, 14:50) Sorry, ...   Aug 27 2007, 15:47
|- - SebastianG   QUOTE (madshi @ Aug 27 2007, 16:47) Sorry...   Aug 27 2007, 17:53
|- - madshi   QUOTE (SebastianG @ Aug 27 2007, 17:53) T...   Aug 28 2007, 08:23
|- - SebastianG   QUOTE (madshi @ Aug 28 2007, 09:23) (1) a...   Aug 28 2007, 09:13
|- - madshi   QUOTE (SebastianG @ Aug 28 2007, 09:13) T...   Aug 28 2007, 09:23
|- - SebastianG   QUOTE (madshi @ Aug 28 2007, 10:23) QUOTE...   Aug 28 2007, 14:10
|- - madshi   QUOTE (SebastianG @ Aug 28 2007, 14:10) B...   Aug 28 2007, 14:50
|- - SebastianG   QUOTE (madshi @ Aug 28 2007, 15:50) P.S: ...   Aug 28 2007, 14:59
|- - madshi   QUOTE (SebastianG @ Aug 28 2007, 14:59) E...   Aug 28 2007, 16:23
|- - SebastianG   QUOTE (madshi @ Aug 28 2007, 17:23) QUOTE...   Sep 28 2007, 10:51
|- - madshi   QUOTE (SebastianG @ Sep 28 2007, 10:51) Y...   Sep 28 2007, 21:58
- - Nick.C   Is it not simply: new_value = round(old_value/(2^...   Aug 27 2007, 17:01
- - Nick.C   Surely, to round you will have to use FP maths? .....   Aug 28 2007, 08:31
|- - madshi   QUOTE (Nick.C @ Aug 28 2007, 08:31) Surel...   Aug 28 2007, 09:02
- - 2Bdecided   It's probably worth mentioning a simple trick ...   Aug 28 2007, 14:18
|- - Nick.C   QUOTE (2Bdecided @ Aug 28 2007, 14:18) Do...   Aug 28 2007, 14:33
|- - kwwong   QUOTE (2Bdecided @ Aug 28 2007, 08:18) It...   Sep 4 2007, 02:59
|- - SebastianG   QUOTE (2Bdecided @ Aug 28 2007, 15:18) It...   Sep 5 2007, 10:27
- - jlohl   QUOTE What is the effect of a non-white random sou...   Sep 6 2007, 11:02
- - ilo   TPDF dither should have a peak amplitude twice tha...   Sep 27 2007, 22:57
|- - madshi   @ilo, that sounds quite interesting, but honestly...   Sep 28 2007, 09:12
|- - ilo   @ madshi: I think the stuff already posted will d...   Sep 28 2007, 14:16
- - Nick.C   It should be 0..16 as that is (0.0 .. 1.0) x 2^4. ...   Sep 28 2007, 22:11
|- - madshi   QUOTE (Nick.C @ Sep 28 2007, 22:11) Sorry...   Sep 28 2007, 22:18
- - Nick.C   If you're really wanting to use integers, why ...   Sep 28 2007, 22:21
- - madshi   QUOTE (Nick.C @ Sep 28 2007, 22:21) If yo...   Sep 28 2007, 22:29


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