24bit vs 16bit, the myth exploded!

[ILikeMusic]

Obviously, this is highly imperfect or to put it another way, we have a great deal of error (resulting in a perfect waveform and a great deal of noise).

The 'perfect waveform' is the part I'm missing, at least in the amplitude domain. My understanding is that in terms of frequency, sample rate needs to be only twice that of the highest frequency you intend to encode since that will provide sufficient sample points to fit a sine function that will allow exact reproduction of the input, hence a perfect waveform in the frequency domain. However, with regard to bit depth you are attempting to quantize amplitude and there will always be some error. I understand how this error becomes broadband noise but I don't understand how we reconstruct a perfect reproduction of amplitude in the reproduced signal. Is the idea that dither provides sufficient randomization to eliminate all error down to a mathematical certainty?

 

[pinnahertz]

It's semantics bro! It is based on perception, because µ-law/A-law coding increases intellibility of speech. What is inaccurate about that?

Did your read the link?

Is it my fault µ-law/A-law is not called what it is for historical reasons? Later much more advanced coders don't change things.

"μ-law encoding effectively reduced the dynamic range of the signal, thereby increasing the coding efficiency while biasing the signal in a way that results in a signal-to-distortion ratio that is greater than that obtained by linear encoding for a given number of bits. This is an early form of perceptual audio encoding."

https://en.wikipedia.org/wiki/Μ-law_algorithm

I completely disagree with that based on the link that defines what perceptual coding is. "an early form" is not the same as the actual thing defined completely differently.

 

[old tech]

The 'perfect waveform' is the part I'm missing, at least in the amplitude domain. My understanding is that in terms of frequency, sample rate needs to be only twice that of the highest frequency you intend to encode since that will provide sufficient sample points to fit a sine function that will allow exact reproduction of the input, hence a perfect waveform in the frequency domain. However, with regard to bit depth you are attempting to quantize amplitude and there will always be some error. I understand how this error becomes broadband noise but I don't understand how we reconstruct a perfect reproduction of amplitude in the reproduced signal. Is the idea that dither provides sufficient randomization to eliminate all error down to a mathematical certainty?

I believe, and I'm no expert here so others may chime in, that dither just adds white noise to the signal which decorrelates the amplitude errors. So the errors are still there but it now randomised at the cost of a higher noise floor which sounds like tape hiss (but, at least with 16bits, you are unlikely to hear the hiss unless it is a quiet passage played at insane loud levels). The main point is that there is no perfection even in the natural audio world, let alone audio recording/playback technology. With analog recordings/playback the quantiitasion like imperfections manisfests itself as hiss, which is the sound of the random errors, with digital there is no random errors, they are precise errors so all dither does is randomises the errors in a similar way which analog media does through its inherent imperfections.

 

[old tech]

Let me preface my reply by saying I am very surprised right now, this is the greatest number of intelligent responses I have ever gotten from posting in a forum before, EVER. Even posting in forums about circuits, I haven't had responses like these before. Thank you!

Now I do understand why 24 bit can, and always will encode a larger dynamic range than 16 bit, but I'm not so clear on why the added resolution does not mean higher quality. I get that with dither 16 bit can record an essentially perfect waveform with some noise, but wouldn't 24 bit with dither still be better than 16 bit with dither?

While Greg explained it well, I find many people understand this concept a bit better after reading this article from Ian Sheppard.

http://productionadvice.co.uk/no-stair-steps-in-digital-audio/

 

[TheSonicTruth]

While Greg explained it well, I find many people understand this concept a bit better after reading this article from Ian Sheppard.

http://productionadvice.co.uk/no-stair-steps-in-digital-audio/

I prefer this guy's presentation of the matter over that of the Wolf in Shep's clothing(!):



Skip ahead to 5:58 for the nitty-gritty on "stair steps" in digital sound.

 

[pinnahertz]

1. I believe, and I'm no expert here so others may chime in, that dither just adds white noise to the signal which decorrelates the amplitude errors. So the errors are still there but it now randomised at the cost of a higher noise floor which sounds like tape hiss (but, at least with 16bits, you are unlikely to hear the hiss unless it is a quiet passage played at insane loud levels). 2. The main point is that there is no perfection even in the natural audio world, let alone audio recording/playback technology. 3. With analog recordings/playback the quantiitasion like imperfections manisfests itself as hiss, which is the sound of the random errors, with digital there is no random errors, they are precise errors so all dither does is randomises the errors in a similar way which analog media does through its inherent imperfections.

Dither also involves noise-shaping, the result of which does not raise the audible noise floor. Dither adds a small amount of randomization so that signal levels below the LSB can be recorded, but it doesn't need to be in the most audible spectrum to work, so noise-shaping moves noise power into the portion of the spectrum that is least audible. There are several types of noise found in analog tape, including the basic tape hiss which is not shaped of course, but also other types of signal-dependent noise. Dither does not sound like tape noise.

2. The concept of "perfection" definitely depends on point of view. Even on-line definitions have a range from the absolute to the practical. I favor the practical, which means there are many examples of perfection, even in audio. But it seems a silly point to debate.

3. There is no quantization in analog recording. The imperfections caused by the media and method are all consequences of the physical nature of magnetics and physics. They happen to distort, modulate, and add noise to the desired signal. Tape his is not the sound of random errors, it's caused by the size of the magnetic particles involved. If you recorded no signal, not even an erase signal, you'd still have tape hiss. It's not an error, it's the noise floor. Small, but important difference. Theoretical digital has no random errors, but practical digital always does in the form of Least Significant Bit jitter, that's the built-in dithering of the LSB. The errors therefore are not precise, but rather always slightly dithered. Dithering further randomizes using a signal that doesn't raise the apparent noise floor.

 

[old tech]

Dither also involves noise-shaping, the result of which does not raise the audible noise floor. Dither adds a small amount of randomization so that signal levels below the LSB can be recorded, but it doesn't need to be in the most audible spectrum to work, so noise-shaping moves noise power into the portion of the spectrum that is least audible. There are several types of noise found in analog tape, including the basic tape hiss which is not shaped of course, but also other types of signal-dependent noise. Dither does not sound like tape noise.

2. The concept of "perfection" definitely depends on point of view. Even on-line definitions have a range from the absolute to the practical. I favor the practical, which means there are many examples of perfection, even in audio. But it seems a silly point to debate.

3. There is no quantization in analog recording. The imperfections caused by the media and method are all consequences of the physical nature of magnetics and physics. They happen to distort, modulate, and add noise to the desired signal. Tape his is not the sound of random errors, it's caused by the size of the magnetic particles involved. If you recorded no signal, not even an erase signal, you'd still have tape hiss. It's not an error, it's the noise floor. Small, but important difference. Theoretical digital has no random errors, but practical digital always does in the form of Least Significant Bit jitter, that's the built-in dithering of the LSB. The errors therefore are not precise, but rather always slightly dithered. Dithering further randomizes using a signal that doesn't raise the apparent noise floor.

Thanks for the information, I'm always learning something. While dither itself does not sound like tape hiss, I always thought that the effect it has on the noise floor (ie the noise addition) does. That is certainly how it sound like to me when, for example, 8 bits is dithered and it is how many others describe it. The hiss you hear from vinyl records, when isolated from other noises of vinyl playback sounds like tape hiss too. I can hear this on my records that were sourced from a digital recording, so it can't be a recording of tape hiss from the master.

Another question, and this is more 'absolute than practical', I thought quantitisation exists in all audio, even in the natural world but is randomised by natural errors or man-made errors. The paper from from St Andrews Uni demonstrates, for example, quantitisation effects on vinyl records though it is randomised by tracking errors from stylus in the groove, and the movement of the actual vinyl molecules pressed against the stylus. Air molecules have the same effect in the natural world.

 

[71 dB]

Did your read the link?

Yes.

I completely disagree with that based on the link that defines what perceptual coding is. "an early form" is not the same as the actual thing defined completely differently.

You're splitting hairs here. Early baroque (say as Johann Rosenmüller or Heinrich Scheidemann) is a form of baroque. Nobody is saying Rosenmüller is the same as Handel, but both are baroque music.

 

[pinnahertz]

Thanks for the information, I'm always learning something. While dither itself does not sound like tape hiss, I always thought that the effect it has on the noise floor (ie the noise addition) does. That is certainly how it sound like to me when, for example, 8 bits is dithered and it is how many others describe it. The hiss you hear from vinyl records, when isolated from other noises of vinyl playback sounds like tape hiss too. I can hear this on my records that were sourced from a digital recording, so it can't be a recording of tape hiss from the master.

Another question, and this is more 'absolute than practical', I thought quantitisation exists in all audio, even in the natural world but is randomised by natural errors or man-made errors. The paper from from St Andrews Uni demonstrates, for example, quantitisation effects on vinyl records though it is randomised by tracking errors from stylus in the groove, and the movement of the actual vinyl molecules pressed against the stylus. Air molecules have the same effect in the natural world.

I must take exception with the at least some of the analysis in that "paper", especially if the conclusion is to be quantization in vinyl being comparable at all to digital.

The paper mentions the thickness of a layer of a crystalline carbon (diamond) as an example, then goes on:

"Each carbon atom has an effective diameter of around half a nanometre so the thickness of each layer will be approximately 0·5 nm. The position of the stylus is determined by resting on top of the uppermost layers of atoms. Hence we can see that the stylus position will be roughly quantised by the finite thickness of the atomic layers. When playing a sinewave whose peak size is 8 microns the movement of the stylus would take place in 1 nm steps. Instead of smoothly varying, the stylus offset would therefore always adopt one of the set of available levels,

, where m is an integer and

is the thickness of the atomic layers. The effect is to divide the

microns swing of a 0 dB 1 kHz sinewave into 32,000 steps — just as if the signal had passed through an ADC! "

The problem with the conclusion here is that we'd have to have a stylus that contacts only a single atom at a time to define a specific quantization level that would be comparable in nature to digital quantization, which is not the case, far from it. The stylus contacts a large number of carbon atoms at any moment, and the number changes continuously.

He's correct that technically (a very specific point here) any system that takes a large sampling of data and reduces it to a smaller set is quantization, so technically, analog recording qualifies, but specifically, it's nothing like what happens in a digital system which assigns specific and repeatable values to the quantized data. So his concluding statement is technically correct, but specifically wrong. It's not at all like the signal was passed through an ADC, other than to match the very general definition of quantization.

I find it pointless to micro-analyze and system like this because apart from the highly specific definitions, the results are completely different, with analog adding quite a number of additional distortions and signals that have nothing to do with its reduced data set at all. It's clearly "spun" to make a point, yet the point is, in the end, lost because of the results.

 

[pinnahertz]

Yes.

And yet you are still arguing...

You're splitting hairs here. Early baroque (say as Johann Rosenmüller or Heinrich Scheidemann) is a form of baroque. Nobody is saying Rosenmüller is the same as Handel, but both are baroque music.

Agreed with your example, but µ-law/A-law have none of the things that differentiate perceptual coding. More like comparing Handel to Cage. Both are music, but that's pretty much where it ends.

 

[71 dB]

1. And yet you are still arguing...

2. Agreed with your example, but µ-law/A-law have none of the things that differentiate perceptual coding. More like comparing Handel to Cage. Both are music, but that's pretty much where it ends.

1. Unfortunately.
2. µ-law/A-law is for speech, telecommunication. Later perceptual coding methods are for high quality audio/music. Both are perceptual coding even if completely different.

 

[castleofargh]

it's not using a form of psychoacoustic coding. but as a codec for speech, it's hard to argue that perception wasn't a relevant factor. everybody won

oh you bunch of highly educated old kids

 

[pinnahertz]

1. Unfortunately.
2. µ-law/A-law is for speech, telecommunication. Later perceptual coding methods are for high quality audio/music. Both are perceptual coding even if completely different.

I’m having extreme difficulty caring any less about this.

 

[bigshot]

It can't be over until someone cries.

 

[danadam]

The 'perfect waveform' is the part I'm missing, at least in the amplitude domain. My understanding is that in terms of frequency, sample rate needs to be only twice that of the highest frequency you intend to encode since that will provide sufficient sample points to fit a sine function that will allow exact reproduction of the input, hence a perfect waveform in the frequency domain. However, with regard to bit depth you are attempting to quantize amplitude and there will always be some error. I understand how this error becomes broadband noise but I don't understand how we reconstruct a perfect reproduction of amplitude in the reproduced signal. Is the idea that dither provides sufficient randomization to eliminate all error down to a mathematical certainty?

(the way I understand it) At some point in ADC you have samples with perfect amplitude that you need to quantize (at least conceptually):

input[n] -> [ quantization ] -> output[n]

What happens in "quantization" box? We modify sample value so that it can be represented digitally. We can write:

input[n] + q[n] = output[n]

So you can see that the output, our digitalized signal, is: input which is perfect plus some error/noise. To your question "how we reconstruct a perfect reproduction of amplitude", we don't do anything specific. Perfect input is "baked in" in the output. So you just play the output and you get perfect input with noise.

If you were asking how we get perfect input without the noise (maybe you did?), then that is not possible, as far as I know.