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Author Topic: Digital Resoloution and bit depth  (Read 7154 times)

Wiz.

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Digital Resoloution and bit depth
« on: February 10, 2005, 05:26:41 pm »

I have been having a long discussion with someone regards bit depth and George, if you have the time I would like your input.


You have a 16 bit and 24 bit file.

in the area of 0db to -6db of each file, how many steps of resoloution are available.

Is there more available steps of resoloution in the 24 bit file vs the 16 bit file, or are they the same.

I understand how dynamic range equates.


Its just that I think there are more steps of resoloution in a 24 bit file, between 0 and -6db, compared to 16 bit, and he thinks the are the same, only the dynamic range is increased, and the extra resoloution available all lies below -96db.



thanks in advance

Peter Knight
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Nika Aldrich

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Re: Digital Resoloution and bit depth
« Reply #1 on: February 10, 2005, 05:33:35 pm »

Dear god.


Smile


I have to go to a meeting.  I'll chime in when I get back later tonight.

Nika
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Wiz.

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Re: Digital Resoloution and bit depth
« Reply #2 on: February 10, 2005, 05:50:57 pm »

will do

thanks


Peter
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howlback

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Re: Digital Resoloution and bit depth
« Reply #3 on: February 10, 2005, 09:25:10 pm »

Wiz. wrote on Thu, 10 February 2005 17:26

I have been having a long discussion with someone regards bit depth and George, if you have the time I would like your input.


You have a 16 bit and 24 bit file.

in the area of 0db to -6db of each file, how many steps of resoloution are available.

Is there more available steps of resoloution in the 24 bit file vs the 16 bit file, or are they the same.

I understand how dynamic range equates.


Its just that I think there are more steps of resoloution in a 24 bit file, between 0 and -6db, compared to 16 bit, and he thinks the are the same, only the dynamic range is increased, and the extra resoloution available all lies below -96db.



thanks in advance

Peter Knight


Hi Peter,

Each bit in a Linear PCM system is EVENLY spaced throughout the amplitude range.  This is probably the kind of digital system you are talking about (although your converters may do something else...).  So, there are more steps available in a 24 bit system, regardless of the amplitude of the signal.  The error resolution of a system is equal to one half the least significant bit (LSB).  More bits = smaller error.

The important question to ask is whether that matters.  There are at least 2 major concepts to keep in mind.  Quantization error, and quantization distortion.  

Error occurs when the noise caused by quantization is not correlated with the input signal.  Perceptually, this is like low level white noise, noise that you probably can't hear for high amplitude signals.  

As signal level decreases, the quantization error increases, eventually it becomes audible because it is correlated with the input signal; this is quantization distortion.  Adding dither (random noise) to the INPUT signal randomizes the quantization distortion (and error for that matter), practically eliminating its perceptual effect.  In this respect it doesn't matter whether you are using 16 bits properly dithered, or 24 bits.  

I have a feeling your question is actually more complicated.  You probably are wondering what bit depth to use when recording.  There is no simple answer to that question.  But if you like 24 bit recording, its probably not only due to its lower quantization error.

There are other issues too regarding the conversion process, but maybe that gets you on your way to answering the question.
Nika can spank me if he doesn't like what I say.  I'm certain he's sick of writing about this, and that's why he is praying to God for somebody else to post something.  

Best,

KW
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George Massenburg

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Re: Digital Resoloution and bit depth
« Reply #4 on: February 10, 2005, 09:50:05 pm »

Wiz. wrote on Thu, 10 February 2005 16:26

I have been having a long discussion with someone regards bit depth and George, if you have the time I would like your input.


You have a 16 bit and 24 bit file.

in the area of 0db to -6db of each file, how many steps of resoloution are available.

Is there more available steps of resoloution in the 24 bit file vs the 16 bit file, or are they the same.

I understand how dynamic range equates.

Its just that I think there are more steps of resoloution in a 24 bit file, between 0 and -6db, compared to 16 bit, and he thinks the are the same, only the dynamic range is increased, and the extra resoloution available all lies below -96db.

thanks in advance

Peter Knight


Peter,

The exasperated reponsees are because of the very basic nature of your question.  More or less like walking into a college Literature classroom and asking, "What kind of stuff did Shakespeare write, anyway?"

Theoretically (and that word is important because it's not directly measurable) there are 2^24 = 16777216 steps between 0FS (full scale) and the threshold of the first step (which turns out to be kind of a philosophical question in and of itself).  so, because -6.0206dB is half of the maximum amplitude, there are 8388608 steps between 0 and -6.0206dB.  In a 16 bit system (all of the previous caveats apply) there are 32768 steps.

George

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Nika Aldrich

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Re: Digital Resoloution and bit depth
« Reply #5 on: February 10, 2005, 10:42:05 pm »

Wiz. wrote on Thu, 10 February 2005 17:26

I understand how dynamic range equates.


I'm not so sure this is the case.  I think it might be best if you tell us what you know, or how you see it first and then we'll probably be more effective at finding an effective way of responding - a way that gives you all the information you need to know if order to settle this dispute with your cohort.

Let's try these questions on for size.  See what you can do about answering them as comprehensively as possible and then we'll know more about how to proceed:

1.  Why does each bit give us 6dB of dynamic range?

2.  What kind of effect occurs to the waveform when we have to round to the closest quantization step?

3.  Are Signal to Noise Ratio and Dynamic Range the same?  Why or why not?

4.  In a 16 bit system what is the SNR?  If SNR and DR are different, what is the DR of a 16 bit system?

5.  If I have a 16 bit system that covers the range from 0V to 1V and I make it a 17 bit system, what happened to the size of the range that this converter covers?

I hope this will help.

Nika
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Wiz.

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Re: Digital Resoloution and bit depth
« Reply #6 on: February 11, 2005, 12:19:12 am »

Thanks to everyone for replying...


Oh goody a test...Cool



1. Why does each bit give us 6dB of dynamic range?


dB = 20 x Log (V1/V2)

( i didnt pull that equation from memory, i knew of its existence)



2. What kind of effect occurs to the waveform when we have to round to the closest quantization step?


I dont really know.


3. Are Signal to Noise Ratio and Dynamic Range the same? Why or why not?


I dont think so, Dynamic range i think is theoretical, SNR is actual.

4. In a 16 bit system what is the SNR? If SNR and DR are different, what is the DR of a 16 bit system?

Well, the dynamic range is 96db, i dont know what the SNR is.


5. If I have a 16 bit system that covers the range from 0V to 1V and I make it a 17 bit system, what happened to the size of the range that this converter covers?

well, it still overs  0 to 1V. Just with more steps.




I hope this will help.

Nika


Me too


Look, i probably got everything above wrong...Cool

And i guess, I might be asking this question, in a forum, where this stuff is probably, well, to put it badly, beneath you all, if thats the case i am sorry...I was just trying to get a clearer answer. I have been reading and reading and reading and reading.



This is how I understand it to work.

16 bit, gives a dynamic range of 96 db, for the reason I explained above.( i know its not EXACTLY 6db, close enough)

24 bit gives a dynamic range of 144db.


11111111  in binary, 8 bit word, equals in Decimal 256

this is where the bit depth/resoloution comes from, 8 bits gives 256 possible steps, 16 bit gives 65, 535 steps etc etc....


See the way I look at it, and its probably wrong, is that at the time of sample (say 44.1khz) the ADC, takes a snapshot, and determines the level of what it sees, to the resoloution of the bit depth created.

So, it looks and sees a signal , between 0 and -6db, and uses 16 bits to represent that level, in a 16 bit file, and 24 bits to represent that level in a 24 bit file.

In my mind there are more steps available, between 0 and -6db, in a 24 bit file, than there are in a 16 bit file, but my friend disagrees, to his mind, all the extra steps are below -96 db, and there is exactly the same amount of resoloution available to that 0 to -6db window, whether it is 16 bit or 24 bit.

Its almost like we see resoloution the exact opposite of each other. That I see more steps available at 0db than i do at -144db, where he sees the opposite.

I apologise , If i cant be clear enough.

But my basic question remains.


with a 24 bit file, is there more resoloution (steps available,possible values)  to document a signal, between 0 and -6db, than there are in a 16 bit file


thanks for all your time and effort


Peter Knight
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Nika Aldrich

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Re: Digital Resoloution and bit depth
« Reply #7 on: February 11, 2005, 12:35:54 am »

Wiz,

Sorting this out between you and your friend is not as important in the long run as making sure that you understand what is going on with this stuff.  So we're going to take it slow and easy.  For starters:

Quote:

5. If I have a 16 bit system that covers the range from 0V to 1V and I make it a 17 bit system, what happened to the size of the range that this converter covers?

well, it still overs  0 to 1V. Just with more steps.


That's the one you got right.  Now think for a second - why does the dynamic range improve if I just take the region and cut it into more and more pieces?  How does that help our dynamic range?  Why do these smaller quantization steps manifest themselves as lowering the noise?

I'm going to have to answer it from there in the morning, but think on that one for a bit and see what you can come up with.

Cheers!
Nika
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Duardo

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Re: Digital Resoloution and bit depth
« Reply #8 on: February 11, 2005, 12:45:23 am »

Quote:

Its just that I think there are more steps of resoloution in a 24 bit file, between 0 and -6db, compared to 16 bit, and he thinks the are the same, only the dynamic range is increased, and the extra resoloution available all lies below -96db.


For a gross oversimplification...you're both right.  There are more "steps", evenly spaced, in a 24-bit system...but even though they're evenly spaced, they only manifest themselves as more detailed "resolution" below -96 dBFS.

-Duardo
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jfrigo

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Re: Digital Resoloution and bit depth
« Reply #9 on: February 11, 2005, 12:50:22 am »

George et al,

I think he's asking in a practical sense if the top 96dB sound better in the 24 bit system than the 16 bit system; in other words, do you gain more than just increased dynamic range and lower noise when recording?

The simplest answer in a practical rather than theoretical sense is that the top 96dB (a few dB of dither notwithstanding) is not somehow better in 24 bit compared to a properly implimeneted 16 bit system. The audible way the error in a 16 bit system manifests itself is as noise. A 16 bit recording is noisier than a 24 bit recording and you lose the ability to capture some of the quieter signals, but 16 bits is perfectly capable of accurate reproduction within its dynamic limits.

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steve parker

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Re: Digital Resoloution and bit depth
« Reply #10 on: February 11, 2005, 07:03:45 am »

Peter,

you are about to learn some surprising and satisfying things. . .
and you are absolutely in the right place.
some of the people here will give the clearest explanations you will find anywhere.

happy learnin'

steve parker.
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Nika Aldrich

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Re: Digital Resoloution and bit depth
« Reply #11 on: February 11, 2005, 11:12:14 am »

OK, I'll see what I can do, here.  

Let's start simple.  Let's talk about a sampling system with a range from 0V to 4V and four quantization steps.  Each step is 1V, yes?  That means that if I put a signal into it, each time I take a sample I am going to have an error, and that error is going to be +/-.5V, yes?  Each time I take a sample it is going to have to round up or round down, and the amount it is going to round is going to be no greater than half the amplitude of a quantization step.

What I have just done is ADDED a signal to my original waveform.  By rounding the signal I have, by default, added some harmonic content to the waveform.  I could subtract my original signal from the sampled version of it and this would yield the specific waveform that I added.  You can do this on graph paper - overlay the original waveform on top of the sampled version of it and look at the areas where you have error.  That error is a waveform unto itself.  We can extract the error from this and analyze it separately, as a separate waveform.  It IS, after all, a separate waveform.  It is the waveform that you added to the original waveform by means of sampling.

Now, let's look at that error waveform.  What is it?  What is its amplitude?  Well since we didn't round any more than .5V in either direction we know that the error waveform can't have an amplitude of greater than -.5 to +.5, so it has a total amplitude of 1V, yes?  As for its frequency content, that gets a bit tricky, but for the sake of this discussion we're going to say that its frequency content is noise.  We can think that the likelihood of any particular sample in this error-waveform being at any particular given amplitude is pretty random, since it is just the error remaining from the sampling process.  In truth that has some qualifiers, but run with me.  So since all of the sample points on this error-waveform are random we'll say that this waveform is simple noise.

What we have determined, and what we can now say is that the result of sampling is that we have added random noise to our waveform at an amplitude of 1V.  Since 1V is 1/4 the amplitude of the maximum signal you can put into this system (4V) we could compare the amplitude of this noise to full scale and realize that its amplitude is 12dB lower than any full-scale waveform you could put into the system.  Therefore, 4 quantization steps gives you 12dB of dynamic range - noise is added 12dB below the maximum peak.  

Now, what happens when we double the number of quantization steps?  You cut each "region" in your sampling system in half, yes?  As you correctly stated above, the overall range of 0V to 4V is still valid, but the quantization steps are no longer at 0V, 1V, 2V, etc.  They are now at 0V, .5V, 1V, 1.5V, etc.  Yes?  With the cutting in half of the quantization steps we also cut the error-signal's maximum amplitude in half, yes?  The error-signal can no longer have an amplitude of +/-.5V.  It is now restricted to +/-.25V.  That means its overall amplitude is .5V, which is half of what it was before.  Since reducing a signal by 50% is equivalent to a reduction by 6dB, we have just lowered the error signal (the signal that gets added to our original signal by means of quantizing) by 6dB.  Therefore the dynamic range is no longer 12dB but is instead 18dB.  

And what would happen if we double the number of quantization steps again?  And again?  Each time double the number of quantization steps we lower the noise that gets added to the system by 6dB.  Since adding a bit in a binary system is equivalent to doubling the number of quantization steps, each bit added gives us 6dB of dynamic range.

STOP ME NOW IF YOU'RE NOT FOLLOWING.

OK, you didn't stop me.  Plowing forth:

Let's take a 16 bit system.  That gives us 96dB of dynamic range.  That means that the amount of error that gets added is 96dB down from full scale.  Let's go back to our 4V converter.  That means that the amount of error is about .00006V in total amplitude.  Let us talk about putting a signal into this system for quantization that has a SNR of, say, 12dB.  That means that the signal itself has error - random noise - and the amplitude of the random noise on the signal itself, before we ever put it into the sampling system, is 12dB lower than the peak value.  It's like taking a pure sine wave generator and a noise generator.  Set the pure sine generator to put out a sine wave at about 4V and set the noise generator to generate white noise at 12dB down from that, or 1V.  Sum the two together.  There's your signal.

Now we're going to run this 4V, 12dB SNR signal into our 16 bit sampling system.  As we know, the sampling system is going to add noise to our signal at an amplitude of .00006V.  This little bit of noise, however, is absolutely DWARFED by the fact that there is already 1V of noise present!  Sure, we added noise by quantizing, but how are you ever going to notice that you added .00006V of noise when you already had 1V of noise there?  There is no way that you, as a human, would ever hear the addition of this noise.  You, as a human, DO have the ability to hear things even if noise is present at a higher amplitude.  If I play noise at full scale and a sine wave at 4kHz 25dB lower than full scale you would hear it.  Our ears are sensitive to things below the noise floor - but only to a certain degree - 25dB is the maximum for this.  Even if I decreased the noise coming out of my signal generator, thereby increasing the SNR of the signal going in, such that the SNR was now 60dB - the amplitude of the noise is now .004V - you still wouldn't hear the added noise from the sampling process.  That noise is too far below the amplitude of the already-present noise in the system.  Depending on the signal, etc., I could lower the amplitude of the noise generator much lower still and you STILL wouldn't detect a difference.

Now, if this is the case - if I have a signal whereby the noise added because of sampling at 16 bits was so low that it could not be detected, what would be the benefit of adding more quantization steps?  Again, remember, the adding of quantization steps only lowers the error-signal (noise) in the system.  If I can't detect that noise anyway, what is the benefit of reducing it?

Now, how are we doing on answering your question?

Nika
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PookyNMR

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Re: Digital Resoloution and bit depth
« Reply #12 on: February 11, 2005, 01:59:21 pm »

Nika Aldrich wrote on Fri, 11 February 2005 09:12


if I have a signal whereby the noise added because of sampling at 16 bits was so low that it could not be detected, what would be the benefit of adding more quantization steps?  



So bats can enjoy the music too.  Wink

I think the original question arose from the idea that increased bit depth (to 24 bit) would give more increments (numercial values) for each sample which would prvide for more "resolution" in those last 6 dB (if I even interpret the original question properly).

Nika, do you know of any books that talk about this kind of stuff?  I'd prefer one with lots of pictures...  Smile

Nathan
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David Schober

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Re: Digital Resoloution and bit depth
« Reply #13 on: February 11, 2005, 03:01:19 pm »

Nika,

I just wanna drop in on this dialog and say thanks for your time and patience with all of us in explaining these things.  (sometimes no doubt, over and over)  This thread is a pefect example of the time and effort you take.  We really appreciate it and it's very helpful to all of us.  And it's great to see a forum where people can feel free to ask questions from the simple to complex and esoteric without feeling foolish.

Additionally you rarely, if ever, tout your book or say, "Go read my book and get back to me."  You slog on thru these threads, taking time to say what probably is in the book.

I know there are many of us here who would say, "Thanks very much!"

btw....I'm heading over to your site right now and ordering a copy!

Now...back to today's lesson....
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Wiz.

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Re: Digital Resoloution and bit depth
« Reply #14 on: February 11, 2005, 07:06:44 pm »

Firstly

I wish to say a hearty thank you, to everyone who has replied to my, somewhat basic question, for the peeps on THIS board. I am sure there are a heap of lurkers, out there, who like me have a hard time wrapping our heads around this issue, and given the fact there is so much white noise on the net, on this very topic.

so again thank you.

To Nika in particular.

What a fantastic reply. I had to read thru it very slowly, and re read paragraphs over and over, but as I did, the clouds parted and the sun began to shine...Cool


A truly wonderfull explanation.

I particularly like the fact that you didnt just provide the answer, you provided the tools for me to reach the answer for myself, the mark of a GREAT teacher.

I would have taken you ages, to put it in, and I VERY much appreciate it.

I also notice, you have written a book on the subject, i also admire the fact, that you didnt plug your book in anyway, when it would have been very easy to do so, i admire ethics, again the mark of a person of integrity, and maturity.

If there is anyway i could ever help, just ask.

I will continue to lurk here and post if I ever think I can be of assistance.

Once again

thankyou


Peter Knight
aka Wiz
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Nika Aldrich

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Re: Digital Resoloution and bit depth
« Reply #15 on: February 11, 2005, 09:14:33 pm »

Whew!  That explanation worked!  Let us know if you have any more questions.

Nika
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Re: Digital Resoloution and bit depth
« Reply #16 on: February 12, 2005, 01:45:55 am »

Nika Aldrich wrote on Fri, 11 February 2005 11:12

 - if I have a signal whereby the noise added because of sampling at 16 bits was so low that it could not be detected, what would be the benefit of adding more quantization steps?  Again, remember, the adding of quantization steps only lowers the error-signal (noise) in the system.  If I can't detect that noise anyway, what is the benefit of reducing it?



Nika, I like your explanation.

But as you know, music isn't sine tones.  The point of my previous post, was that you can hear the error-signal (noise) you are talking about with some kinds of music in a 16 bit system.  Sometimes low amplitude signals fade below the noise-floor of the system, then reappear again.  Things like cymbals, or the reverb of a room ringing out.  This is what is called quantization distortion.  

Nika, I know you know this, but I am just writing it here for clarity's sake.

The audibility of this quantization distortion is eliminated by using dither.  This dither decorrelates the quantization error from the low amplitude music signal.  It gives us a better representation of the signal to our ear, by randomizing the distortion, making it noise again.  Effectively, dither gives us a perceived dynamic range of 115 dB.  Probably close enough to our ear's theoretical 120 dB dynamic range.

However, we could also avoid quantization distortion by recording in 24 bits.  This would give us 144 dB of dynamic range.  There might be other reasons to record in 20 or 24 bit too.  I think this is what Nika was getting at when he wanted Peter to think about signal to noise ratio.

Other books I've read state that 20 and 24 bit systems  do not dither the input signal.  I wonder if your more recent investigation have found this to be true Nika?

Best Wishes,

Kent
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Re: Digital Resoloution and bit depth
« Reply #17 on: February 12, 2005, 08:16:58 am »

If I'm correct 20 bit convertors and above are self-dithering, due to the inherent input noise (20 bit = 120 dB dynamic range, and I've never seen any AD convertor with less noise).
So there is no necessity to add (digital) noise.

If I'm correct, quantizing distortion was mainly an issue with 16 bit convertors that were not really 16 bit convertors ?
I thought a correctly dithered (true) 16 bit convertor has dynamic range beyond 96 dB, so we'd never be able to hear quantisation distortion ?
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jfrigo

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Re: Digital Resoloution and bit depth
« Reply #18 on: February 12, 2005, 01:55:00 pm »

Yannick Willox wrote on Sat, 12 February 2005 05:16

If I'm correct 20 bit convertors and above are self-dithering, due to the inherent input noise (20 bit = 120 dB dynamic range, and I've never seen any AD convertor with less noise).
So there is no necessity to add (digital) noise.


There are a few converters with less noise than -120. The original Lavry AD122 was so named because of its 122dB range, and the newest gold AD has noise at -127dB.

As for self dithering, while the end user wouldn't add "digital noise" (dither) while originally converting at 20bits (unless using a 24 bit converter), you can't always count on ambient or electrical noise to provide self-dithering as you can't be sure it has enough high frequency component to be completely effective.

Kent wrote:
Quote:

But as you know, music isn't sine tones.

But remember, it can be broken down into component sine waves - fundamentals and overtones/harmonics in very complex and constantly varying combinations. Learning how a digital system behaves with individual sine waves is essentially learning how it behaves with complex waveforms like music.

Quote:

However, we could also avoid quantization distortion by recording in 24 bits. This would give us 144 dB of dynamic range.


We don't avoid it, rather it exists below our ability to perceive it. With strings of processors running at 24 bits in DAWs, truncation distortion can conceivably become an audible problem again. Ideally, I prefer even to dither to 24 bits from 48 bit processors (but not all processors & plugs offer the option unfortunately).
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howlback

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Re: Digital Resoloution and bit depth
« Reply #19 on: February 12, 2005, 03:16:44 pm »

Quote:



"Quote:

However, we could also avoid quantization distortion by recording in 24 bits. This would give us 144 dB of dynamic range."


We don't avoid it, rather it exists below our ability to perceive it. With strings of processors running at 24 bits in DAWs, truncation distortion can conceivably become an audible problem again. Ideally, I prefer even to dither to 24 bits from 48 bit processors (but not all processors & plugs offer the option unfortunately).


Thanks for correcting me Jay.  I wrote something false.  You wrote what I meant to say.  

-peace

Kent
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Re: Digital Resoloution and bit depth
« Reply #20 on: February 12, 2005, 03:55:24 pm »

kent walker wrote on Sat, 12 February 2005 12:16


Thanks for correcting me Jay.  I wrote something false.  You wrote what I meant to say.  


I knew what you meant. I just wanted to make sure any lurkers also knew.  Smile
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Nika Aldrich

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Re: Digital Resoloution and bit depth
« Reply #21 on: February 12, 2005, 06:14:02 pm »

kent walker wrote on Sat, 12 February 2005 01:45

But as you know, music isn't sine tones.  The point of my previous post, was that you can hear the error-signal (noise) you are talking about with some kinds of music in a 16 bit system.


That's dangerous territory and needs to be qualified.

Quote:

Sometimes low amplitude signals fade below the noise-floor of the system, then reappear again.  Things like cymbals, or the reverb of a room ringing out.  This is what is called quantization distortion.  


Not necessarily.  It is quantization distortion if there is not enough noise present to decorrelate the quantization error from the valid signal.  I think you touch into some of this in the post below.  Of course, as I said in my post, we were just going to "accept" for the time being that the quantization error is noise.  This is not inherently so.  It is indeed distortion unless noise at an adequate amplitude is present prior to the conversion process.  This delves into the area of "stochastics," an area that we aren't quite ready to go into with respect to the poster who framed the question, but certainly open for dialogue beyond his initial question.

Quote:

Effectively, dither gives us a perceived dynamic range of 115 dB.  Probably close enough to our ear's theoretical 120 dB dynamic range.


Uh?  On a 16 bit signal during recording?  Not actually - the presence of dither only gives us perceived dynamic range of 16 bits, unless colored dither or noise-shaping is used - which it should never be in a recording environment unless the material is going straight to disk.  Those types of dither (or noiseshaping) that are designed specifically to add to the perceived dynamic range cause problems if used in the recording process.

Quote:

Other books I've read state that 20 and 24 bit systems  do not dither the input signal.  I wonder if your more recent investigation have found this to be true Nika?



I'm not sure what you mean?  Are you talking about the converters?  Most 16 bit A/D converters are actually 24 bit converters that dither down to 16 bits internally.

Nika
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Re: Digital Resoloution and bit depth
« Reply #22 on: February 12, 2005, 09:52:07 pm »

Quote:

 
Kent wrote previously:

Effectively, dither gives us a perceived dynamic range of 115 dB. Probably close enough to our ear's theoretical 120 dB dynamic range.


Uh? On a 16 bit signal during recording? Not actually - the presence of dither only gives us perceived dynamic range of 16 bits, unless colored dither or noise-shaping is used - which it should never be in a recording environment unless the material is going straight to disk. Those types of dither (or noiseshaping) that are designed specifically to add to the perceived dynamic range cause problems if used in the recording process.

Well, this is what Bob Katz writes in his mastering book anyway.  I've never read the claim that a 16 bit system can give a perceived dynamic range of 115 dB anywhere else, but I bet he has a source or a reason for saying that, maybe it is the noise shaping thing.  Thought I would check it against your findings.

Quote:


Kent wrote previously:

Other books I've read state that 20 and 24 bit systems do not dither the input signal. I wonder if your more recent investigation have found this to be true Nika?


I'm not sure what you mean? Are you talking about the converters? Most 16 bit A/D converters are actually 24 bit converters that dither down to 16 bits internally.


I am seeking your opinion here as to whether or not you think there is any possible value in adding dither to 24 bit audio, even when not changing the bit depth.  This is an option with some DAWs and digital consoles.  Sometimes the implementation is confusing.  E.G. the Sony DMX-R100 console has an option on its 2 track output to dither 24 bits out of the console with either triangular or rectangular dither, but you can only get 24 bits out anyway (not greater bit depth).  I don't know what the internal processing is...  

Are any 24 bit converters using dither?  I know many don't.  I am familliar with the limitations of dynamic range being 120 -something dB.  Just curious if any designers have found it worthwhile to add a little dither anyway.

-Kent

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Re: Digital Resoloution and bit depth
« Reply #23 on: February 12, 2005, 10:45:55 pm »

Kent, many processes create more than 24 bits and those could benefit from being dithered to 24 bits because it will slow the buildup of distortion from successive processes.

I look at this as being a matter of "it couldn't possibly hurt" because the dither will be less audible than the distortion from not dithering. I'll grant that in many cases neither one is likely to be audible but I think it's silly to not use 24 bit dither when it's available.

It's also important to understand that dither does not hide distortion, it eliminates it.

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Re: Digital Resoloution and bit depth
« Reply #24 on: February 12, 2005, 11:10:57 pm »

Bob Olhsson wrote on Sat, 12 February 2005 22:45

Kent, many processes create more than 24 bits and those could benefit from being dithered to 24 bits because it will slow the buildup of distortion from successive processes.

I look at this as being a matter of "it couldn't possibly hurt" because the dither will be less audible than the distortion from not dithering. I'll grant that in many cases neither one is likely to be audible but I think it's silly to not use 24 bit dither when it's available.

It's also important to understand that dither does not hide distortion, it eliminates it.

Thanks Bob,

I understand the importance of dithering when changing bit depths and get that we are not hiding distortion, but what is the purpose of eliminating distortion that we can't hear?  Is that still distortion?  The sony implementation is really confusing because they don't offer any choice to dither or not when taking 24 bits from other digital outs, only the program bus.  Does this mean that they are dithering those outputs?  I honestly don't know for certain.  Why would they give a choice for one output but not another?

I wonder what kinds of dither guys working with DVD-A are using.   Jay might know, you too Bob, I know you are a sonic king.

-Best wishes,

KEnt
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Re: Digital Resoloution and bit depth
« Reply #25 on: February 12, 2005, 11:58:46 pm »

kent walker wrote on Sat, 12 February 2005 21:52

Well, this is what Bob Katz writes in his mastering book anyway. I've never read the claim that a 16 bit system can give a perceived dynamic range of 115 dB anywhere else, but I bet he has a source or a reason for saying that, maybe it is the noise shaping thing. Thought I would check it against your findings.


OK, that's the noise-shaping issue, and it should never be done in the A/D conversion process unless you are going straight to disk.  If it is going to be processed at all the noise-shaped material will bleed around and potentially cause more damage than good.  A 16 bit system can indeed yield as much as even 150dB dynamic range (in certain frequency bands) but this should only be done on the final pass to 16 bits.

Quote:

I am seeking your opinion here as to whether or not you think there is any possible value in adding dither to 24 bit audio, even when not changing the bit depth.


If the bit depth is being reduced then you dither - period.  So if you're going internally from a 32 bit numerical nomenclature to 24 bits on output you dither - period.  If you are going from 24 bits to 16 bits you dither - period.  If you are going from 48 bit to 24 bit you dither - period.

Quote:

Are any 24 bit converters using dither?


Absolutely - it is inherent by means of the thermal noise from resistors, etc.  They don't have to "add" dither - it is there by default.

Having said this, one thing they do to decouple predictable error is they actually use multiple converters simultaneously and then randomly vary, sample by sample, as to which is in use and what weight it is given.  This removes any predictable error from any given converter by randomly toggling between the various options.  It is dither, in a sense - the addition of random noise (because we randomly toggle between various components) in order to eliminate the distortion caused by a single device's error.  It really is dither, though a bit removed from our normal means of discussing it.  This, by the way, was the solution to the 1 bit problem we run across with DSD - the industry abandoned DSD for traditional PCM converters in 2000 or so because it was better to randomly vary the various components in the converter's design.  This can't be done in the way I describe with DSD in the way that Sony has codified the format, so this method of removing the predictable error in the system is reserved for exclusively "traditional PCM" systems.  

Nika
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Re: Digital Resoloution and bit depth
« Reply #26 on: February 13, 2005, 12:04:02 am »

kent walker wrote on Sat, 12 February 2005 23:10

I understand the importance of dithering when changing bit depths and get that we are not hiding distortion, but what is the purpose of eliminating distortion that we can't hear?


Further processing or other variables in the listening system may expose it.

Quote:

Is that still distortion?


Absolutely!  Just because it falls below the noise floor does not mean it isn't distortion!

Quote:

I wonder what kinds of dither guys working with DVD-A are using.


All I can tell you is that if they are producing 24 bit results then the choice of dither is much less significant.  They're probably using 2 LSB TPDF dither.  Either way, a very wide variety of options can be used here without audibly affecting the signal.  One could argue that in this final pass they could probably even get away with no dither because in typical listening environments the distortion will never get loud enough to hear.  It really makes a difference in intermediate processing where the buildup of repeated truncation can cause problems, and in dithering to 16 bits where we need all of the dynamic range we can get.  Yes, it SHOULD be done everywhere bit reduction is done, but if the pass from 48 to 24 is the final pass - no further processing to be done - then I can imagine they audibility would be moot.

Nika
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Re: Digital Resoloution and bit depth
« Reply #27 on: February 13, 2005, 12:08:24 am »

Could we be clearer about the difference between noise and distortion here ?  
I understand quantization error as "truncation distortion"; which can be mitigated by adding "dither noise". So I have failed to absorb the part of Nika's lesson regarding quantization errors = [random or uncorrelated] noise; which does not make sense to me when it is examined outside of the context it was presented in, where it makes perfect sense to me.  There was a caveat about whether quantization error is really correlated to the signal or not. And the rest of the explanation seemed to hinge on the proof that it's "noise". I guess I am hung up on that.

Nika wrote

Of course, as I said in my post, we were just going to "accept" for the time being that the quantization error is noise. This is not inherently so. It is indeed distortion unless noise at an adequate amplitude is present prior to the conversion process. This delves into the area of "stochastics," an area that we aren't quite ready to go into with respect to the poster who framed the question, but certainly open for dialogue beyond his initial question.


Well now that I've read further down this page; I guess I am not the only one who has a slight problem "accepting".... If stochastics can be explained to a lay person, please try.

Also I have found that dithering 32 bit float signals to 24 bits and then mixing them together gives a very audible effect from the dither. Imagine transferring 100 32 bit tracks to a 24 bit system.. Do you want to hear 100 dithers ?  My answer after trying the strategy is: no. (...or I used the wrong dither)

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Re: Digital Resoloution and bit depth
« Reply #28 on: February 13, 2005, 12:49:16 am »

cerberus wrote on Sun, 13 February 2005 00:08

Could we be clearer about the difference between noise and distortion here ?


If you add a signal to another signal and it is related, or correlated to the original signal it is distortion.  This means that as the original signal changes in some way the added signal changes with it in some way.  If the behavior of the new signal is completely unrelated to the original signal then it is noise.  It is said to be "uncorrelated" error.
 
Quote:

I understand quantization error as "truncation distortion"; which can be mitigated by adding "dither noise".


If there is no random behavior in the original waveform and we quantize it then the amplitude of the quantization error indeed is directly related to the amplitude of the signal.  This is distortion.  The error signal is correlated to the original signal.

If, however, there is noise added to the original waveform prior to quantizing (and at significant enough amplitude - let's say a couple of quantization steps in amplitude) then the quantization error after sampling will no longer be related to the signal itself and will instead be related to the random noise that we added first.  Therefore, this quantization error is no longer correlated - it is no longer distortion.  Instead it is completely random - determined by the (also) random noise that was added in the first place.  This turns the quantization distortion into quantization noise.  

Of course, if the signal itself has enough noise present from natural sources then it doesn't have to be added first.  So if we just take a signal and record it in a noisy room with a noisy mic and a noisy pre, through some cables to a noise front-end of a converter then the natural noise is enough to decouple the quantization error from the signal itself.  

Therefore my lesson all holds, but I simply did not want to venture into having to explain that the quantization error is only random if sufficient noise is present in the signal.   This is why I asked him to just "accept" that the quantization error was random - if the recording is done properly it is.  For the sake of the original poster, however, we just wanted to go one step at a time.

Quote:

If stochastics can be explained to a lay person, please try.


That's it.  Stochastics is, in layman's terms, the study of random behavior.  That's what we touched on above.  We have to ensure random behavior is present (and at sufficient amplitude) before we can ensure that quantization error is random.

Nika
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Re: Digital Resoloution and bit depth
« Reply #29 on: February 13, 2005, 01:16:47 am »

kent walker wrote on Sat, 12 February 2005 20:10


I wonder what kinds of dither guys working with DVD-A are using


There are many who feel that flat dither (TDPF) is the most neutral, and given the low level of it in 24 bit systems, additional noise shaping seems unnecessary. When noise shaping is called for or preferred by a mastering engineer, there are several that are used. POW-r is very popular. There are actually three choices in the POW-r scheme. In other instances a curve from a particular converter or SRC box will be used. Lavry and Weiss both have SRC boxes that are common in mastering studios and the curves in those are sure to be used (Weiss offers POW-r as well). Near-Nyquist implimentations seem to be out of vogue at the moment, though some still use them. These include Apogee UV22 and POW-r type 1. Plenty of other dithers are used as well, but these are some popular ones.
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Re: Digital Resoloution and bit depth
« Reply #30 on: February 13, 2005, 01:47:46 am »

kent walker wrote on Sat, 12 February 2005 21:52



Well, this is what Bob Katz writes in his mastering book anyway.  I've never read the claim that a 16 bit system can give a perceived dynamic range of 115 dB anywhere else, but I bet he has a source or a reason for saying that, maybe it is the noise shaping thing.  Thought I would check it against your findings.




Hi, guys. Didn't I write something like "it is possible to hear a test tone of as low as -115 dBFS in a properly-dithered 16 bit system".    That's the ABSOLUTE limit of conceivable audibility in a dithered 16 bit system. You can prove it yourself with a pair of headphones, an excellent, low-noise and linear D/A converter.

Whether this translates to 115 dB of true dynamic range is another question. It's probably more like 105 or so before the dither noise overcomes the signal. We're talking "very low" here...  ironically, though, I do believe that 24 bit masks the low level signal less than 16 bit, though it is an EXTREMELY subtle difference, and mostly makes a difference in cumulative processing. In other words, "start at 16 bit, process (at 24 to 48 bits), and end at 16 bit" sounds more veiled than "start at 24 bit, process (at 24 to 48 bits) and end up at 16 bit".

I've mastered some pretty transparent-sounding masters that originated in 16 bit by using noise shaped dither, but the number of "A pluses" I give to some of my "originally 16 bit sources" is far less than the number that my 24 bit sources have received. So, on the average, sounds better.

The irony is that 1/2" tape sounds great, and has a noise floor 20-30 dB noisier than 16 bit digital. I think I have some grasp on an explanation for this apparent contradiction, but would like to leave that for another time.

Regardless, to my ears, it's really a matter of noise accumulation, as we have seen that a properly dithered processing chain will not add quantization distortion.

Quote:



Are any 24 bit converters using dither?  I know many don't.  I am familliar with the limitations of dynamic range being 120 -something dB.  Just curious if any designers have found it worthwhile to add a little dither anyway.

-Kent




On the A to D converter side, I'm pretty certain that the laws of physics will take over and adequately self dither nearly every source we can conceive of to 21 or 22 bits, I'll bet my life. But if you were going for 20, 19, 18 or below, I'd recommend using proper dither in the converter, since, as Jay Frigoletto mentioned, it is highly unlikely that the "natural" noise sources will be random enough or have enough high frequency energy to totally and properly dither all the source to less than, say, 21 bits for the sake of argument.

But once you get past that and into processing, yup, it's desirable to dither every 48 bit (or 32 bit, or whatever) calculation upon reduction to 24. Is it REALLY REALLY important? Well, cumulatively it is. But the audibility of the quantization distortion from a single conversion from 48 to 24 is VERY VERY slight, and I would fail a blind test on that one.]
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Re: Digital Resoloution and bit depth
« Reply #31 on: February 13, 2005, 02:49:49 am »

Thanks to everybody for the great replies!

I love to hear everybody's slightly different answers for finicky questions that many would dismiss as silly.

-best wishes,

Kent
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Re: Digital Resoloution and bit depth
« Reply #32 on: February 13, 2005, 10:06:18 am »

Nika Aldrich wrote on Sun, 13 February 2005 00:49

Of course, if the signal itself has enough noise present from natural sources then it doesn't have to be added first.


OK I think that is clear...and I think it means:  

Dither noise that already is added could theoretically be effective later in the signal chain; But after the whole signal passes another process, the noise becomes correlated with the process the same way the signal does, and is not noise anymore , so we need to add noise again ?


bobkatz wrote on Sun, 13 February 2005 01:47

... But the audibility of the quantization distortion from a single conversion from 48 to 24 is VERY VERY slight, and I would fail a blind test on that one.]


If you would fail a blind test then that is the answer i am looking for. I never fail the test when dither is involved.   So perhaps it is legitimate to always choose the distortion in these types of cases, because there is much less of it, including potential cumulative effects.



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Re: Digital Resoloution and bit depth
« Reply #33 on: February 13, 2005, 10:39:48 am »

cerberus wrote on Sun, 13 February 2005 10:06

Nika Aldrich wrote on Sun, 13 February 2005 00:49

Of course, if the signal itself has enough noise present from natural sources then it doesn't have to be added first.


If you would fail a blind test then that is the answer i am looking for. I never fail the test when dither is involved.   So perhaps it is legitimate to always choose the distortion in these types of cases, because there is much less of it, including potential cumulative effects.

cerberus


Well, NO, that's not the case in my experience. You should ALWAYS choose to add the dither at the 24th bit if you want your sound to be subtly warmer. It took me 15 minutes with the most pristine material to be 100% sure (non-blind) that the 24 bit dithered choice sounded a bit warmer than the truncated choice. It only takes me 5 minutes or less to be sure about TWO generations of 24 bit truncation in a row versus two generations of 24 bit dithered. And so on.

I would vote on ALWAYS ADDING the dither at the 24th bit before truncating to 24. The noise of the dither is 144 dB down (actually -141, but who's counting), but if you DO NOT USE the DITHER, the distortion components due to NOT using the dither are somewhat higher than -144 dBFS and contain ugly harmonics that start to annoy the ears. It's just that at levels approaching the 24th bit, the accumulation of this distortion starts at a VERY subtle level that is usually masked by other noises in the chain.

But do not forget that each successive truncation increases the inharmonic distortion we call quantization distortion. The sound gets colder and colder with each successive truncation in the chain, even at 24 bits. It's just that the first time is so subtle that you would probably fail a blind test on it. How many truncations in a row? Before I hear it? Before the public notices it?

BK
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Re: Digital Resoloution and bit depth
« Reply #34 on: February 13, 2005, 01:14:21 pm »

cerberus wrote on Sun, 13 February 2005 07:06


If you would fail a blind test then that is the answer i am looking for. I never fail the test when dither is involved.   So perhaps it is legitimate to always choose the distortion in these types of cases, because there is much less of it, including potential cumulative effects.



The distortion products are higher in level and correlated, so the dither is a more benign choice that will have less cumulative effect. Are you saying you can hear dither added in 24 bit reliably in blind testing? You can't be claiming this, and if you are, it should be easier to hear the distortion, so we're back to "dither is better than distortion."

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Re: Digital Resoloution and bit depth
« Reply #35 on: February 13, 2005, 02:53:24 pm »

You add 6dB of distortion with each successive undithered process while you only add 3dB of noise from each dithering.

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Re: Digital Resoloution and bit depth
« Reply #36 on: February 13, 2005, 09:27:37 pm »

bobkatz wrote on Sun, 13 February 2005 10:39

.... You should ALWAYS choose to add the dither at the 24th bit if you want your sound to be subtly warmer.



But....  I already made it warmer. My mixes come out too dull then. To rectify this, I am bumping things up to 88.2khz now.   I don't like the very idea of the compromise you are implying. I want to be in control.


Quote:

It took me 15 minutes with the most pristine material to be 100% sure (non-blind) that the 24 bit dithered choice sounded a bit warmer than the truncated choice.

I think that whatever dither you use nowadays; I cannot afford it.  But I wish I could get a hold of the kind of [milder] dither that plug-in makers might be using for internal reductions.

Quote:

But do not forget that each successive truncation increases the inharmonic distortion we call quantization distortion. The sound gets colder and colder with each successive truncation in the chain, even at 24 bits. It's just that the first time is so subtle that you would probably fail a blind test on it. How many truncations in a row? Before I hear it? Before the public notices it?



I agree totally, I don't take issue with any of it at all. (...but how many dithers before you have had one too many ? )   I am feeling childish now because it seems I want a level of control that perhaps is impossible   I am frustrated now to hear that with all the great processors you might have access to, you use dither for "warming", which is basically a general application for vintage analog hardware.

Anyway another disturbing thought is that bit depth is about dynamics and the issue we are talking about manifests itself as a frequency issue. This makes it all a bit un-intuitive to reconcile the big picture and find the best strategy for processing.



jfrigo wrote on Sun, 13 February 2005 13:14

... Are you saying you can hear dither added in 24 bit reliably in blind testing?


No, that is too general a statement. And of course I do not claim to hear dither itself, only the effect of dithers I have used in my own studio on music. I prefer to use L2 or L3 for brickwall limiting, but every time I use it, it quantizes it's output to a minimum of 24 bits.  I can hear all the dither and noise shaping options in these plug-ins and also from UV-22 on my system.  L2 and L3 both use 9th order noise shaping, but I don't like it. I also don't like UV-22. POWr and Megabit Max are available to me, but I do not know how to use them with L2 or L3, and I don't really think I like noise shaping at all !

Bob Katz mentioned here me a few months ago that Waves type 2 is not random enough, I think.  But for me Type 1 is not warm at all, it makes extra brightness to my ears, I tried it again because BK's criticism of Waves Type 2 dither was pointed, but I do not want any extra "HF excitement" or "percieved dynamics" in my mixes to come from dither.  Listeners are supposed to hear that effect in some dithers, so they -should- be able to be heard if they work as advertised.  

Quote:

 You can't be claiming this, and if you are, it should be easier to hear the distortion, so we're back to "dither is better than distortion."



A full scale 24 bit signal is equal to a full scale 32 bit signal. So in that hypothetically perfect case, there is no distortion to hear.  I am suggesting that if the signal is within 6 db of full scale at 24 bits, then the distortion product could be lower than the dither noise, in fact infinitely lower.  (I have never done a controlled experiment with 48 signals, so I don't know if my observations for 32 bit float apply to 48 bit fixed or not, but float is very different than fixed here, and perhaps that is where we differ, I do not use a TDM system, and most people here do...)  I suggest that this applies in practice. It explains the results of my own experiments from which I became interested enough in this subject matter to try and learn more.


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Re: Digital Resoloution and bit depth
« Reply #37 on: February 14, 2005, 01:37:47 am »

Mixes that are too dull would probably benefit a lot more from a bit of HF eq. than from using distortion to add sizzle.

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Re: Digital Resoloution and bit depth
« Reply #38 on: February 14, 2005, 01:48:30 pm »

Bob Olhsson wrote on Mon, 14 February 2005 01:37

Mixes that are too dull would probably benefit a lot more from a bit of HF eq. than from using distortion to add sizzle.


That is a good way to put it, certainly we don't want sizzle from -that- kind of distortion.

My aversion to boost EQ must be holding me back; but this could be a good place to make exception... So your advice, which may seem obvious to some, is a help to me.

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Re: Digital Resoloution and bit depth
« Reply #39 on: March 17, 2005, 04:04:04 am »

The answer to me is clear now, Mix at a high enough sample rate and everything will be more natural sounding by the time you get to 16/44.1.  Every decent digital box is oversampling.. Why it took me so long to figure this out; dunno, pretty obvious actually.... Perhaps I wanted to think in terms of -more- plug-ins; the first thing I did with the  G5 was to see how many reverbs....  Thanks to all who offered advice to me here, especially Bob Ohlsonn.


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