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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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2Bdecided
post Jan 9 2004, 13:29
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QUOTE (Ariakis @ Jan 9 2004, 08:04 AM)
Just a note on what David said about a triangular generator being a combination of two rectangular generators...

He said that to get 8 bits of triangualr pseudorands, you'd need to combine two rectangular generators with ranges of [0, 255].  This, however, would allow a total range of [0, 510], which is more than 8 bits.

So to get 8 bits of triangular dither, you'd need to combine [0, 127] and [0, 128] rectangular generators to get a [0, 255] triangular generator.  At least, I think.

So, in your case, you'd want 3 bits of noise, which is [0, 7]... so you'd want to combine [0, 3] and [0, 4] rectangular generators, I think.

Someone correct me if I'm wrong, please. =)

Triangular dither must be two bits peak to peak, so I'm affraid you're not right!

Correct triangular dither removes noise modulation - that means that the resulting noise (after truncation) from adding dither will be independent of the level of the original signal.

Rectangular dither doesn't so this properly. If the original signal lies exactly half way between two steps in the least significant bit of the truncated signal, then it can be bumped up or down by 0.5 bits - therefore the resulting noise (noise=final-original) will always have a magnitude of 0.5 bits. Whereas if the original signal is elsewhere, the magnitude of the noise (i.e. the rounding error) will be different, and signal dependent.

Triangular dither solves this by always giving the rounded signal the chance of being the same number of "bits" (or fractions of one bit) away from its original value. Without scanning a picture in, I can't explain this any better.

If you only have 1 bit peak to peak triangular dither (that's called 0.5 bits in Cool Edit for some reason), then it will cause even worse noise modulation than recntangular dither, and won't even remove harmonic distortion.

So it must always be 2 bits peak to peak.

Cheers,
David.
(That's "Dr David Robinson" for your credits aristotel! I nearly did an MSc at York, and I've stayed there a time or two (once at the uni) - I won't hold you to that drink though! - I'm a long way away now.)
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- 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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