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[Andy Simpson]

crm0922 wrote on Fri, 07 October 2005 03:20

andy_simpson wrote on Thu, 06 October 2005 19:43 Perhaps I can put this into the perspective that I missed previously..... Consider a binaural recording (or the auditory system itself). The sounds we hear are not 1-dimensional sine waves, with 1-dimensional origins, and the ear is not physically 1-dimensional  - so the interactions between the 3D ear and the 3D soundwave with a 3D origin will undoubtedly be 3D. Somewhere in this binaural recording we must encode 3 dimensions worth of spatial timing information into stereo. Each pair of stereo quantization steps must represent, together, spatial timing resolution in 3 dimensions, no matter how the ear encodes this information. ......thinking aloud again......sorry..... Andy Andy, weren't you informed already that the audio is not quantized in time, per se?  The audio is not pushed or pulled into a "grid" matching up with the samples.   As Jon said, most of the stereo information is "decoded" from cues within the audio signal.  Reverb, delay, level differences, and the like.  If the left and right are in sync, the brain will decode the signals as best it can.  But the 3D image is a concoction of the mind. Phase accuracy is extremely important, but it can be shown that most digital systems are incredibly accurate in this regard. Chris

But it is quantized in time, by bit-depth quantization.
Sorry, I should have made that clear.

I completely agree that sample rate is not the major factor.
Bit depth is.

(I'd like to see some graphs where bit-depth differences are substituded for sampling rate differences, and where we can see where the error 'goes' - time or amplitude, after reconstruction?)

Yes. Cues. Reverb, delay, level differences, timing differences. HRTF.
These cues are also quantized in time by the bit-depth quantization.
This quantization error may seem small, but when you think about the order of timing differences it represents......

Or consider this unintuitive analogy -

When looking at a digital photograph, large circles appear relatively round, but small circles highlight the quantization error & resolution.

If it were possible to take a stereo recording and render a picture of the sound source in 3D, from the recording, what would it look like? Presumably higher bit-depth would give a sharper image, where distant sources were more accurately shown?

If we are to represent circles in space (circular sources), the quantization error is significant as it governs the 'roundness' of the circle, and with distance this becomes more significant as the timing and level differences are smaller with distance (as in photographs).

Andy

[Jon Hodgson]

andy_simpson wrote on Fri, 07 October 2005 13:15

crm0922 wrote on Fri, 07 October 2005 03:20 Phase accuracy is extremely important, but it can be shown that most digital systems are incredibly accurate in this regard. Chris But it is quantized in time, by bit-depth quantization. Sorry, I should have made that clear. I completely agree that sample rate is not the major factor. Bit depth is. (I'd like to see some graphs where bit-depth differences are substituded for sampling rate differences, and where we can see where the error 'goes' - time or amplitude, after reconstruction?)

Andy,

You seem to have trouble grasping this...

There is no timing error.

It's provable mathematically, but since seeing is believing yesterday I thought I'd give it a try experimentally with adobe audition. It is quite reassuring when you see the theory working in from of you.

Here's what I did

1) make a new file at 192khz
2) create a band limited signal (I made a 2kHz sawtooth, with the top harmonic being the 5th at 10k), give this a peak 12dB below full scale
3) shift one channel 3 samples
4) downsample to 24kHz, 8 bits with dither (because I used a -12db peak, this is actually about 6 bits of resolution)
5) Upsample the result back to 192kHz and 32 bits
6) subtract one from the other, and what do you get?...

White noise.

The errors in quantization DO NOT manifest themselves as timing errors in your signal, they manifest themselves as extra components. These are signal dependent, so they can be considered distortion, however if you have some low level signal randomization (i.e. noise, whether you inject it intentionally as dither for coarse sampling as I did here, or it is there because of johnson noise in your circuits and background noise in the room as it already is at 20 bits), then the error also becomes randomized.

Random error = white noise.

[Andy Simpson]

Jon Hodgson wrote on Fri, 07 October 2005 13:52

andy_simpson wrote on Fri, 07 October 2005 13:15 crm0922 wrote on Fri, 07 October 2005 03:20 Phase accuracy is extremely important, but it can be shown that most digital systems are incredibly accurate in this regard. Chris But it is quantized in time, by bit-depth quantization. Sorry, I should have made that clear. I completely agree that sample rate is not the major factor. Bit depth is. (I'd like to see some graphs where bit-depth differences are substituded for sampling rate differences, and where we can see where the error 'goes' - time or amplitude, after reconstruction?) Andy, You seem to have trouble grasping this... There is no timing error. It's provable mathematically, but since seeing is believing yesterday I thought I'd give it a try experimentally with adobe audition. It is quite reassuring when you see the theory working in from of you. Here's what I did 1) make a new file at 192khz 2) create a band limited signal (I made a 2kHz sawtooth, with the top harmonic being the 5th at 10k), give this a peak 12dB below full scale 3) shift one channel 3 samples 4) downsample to 24kHz, 8 bits with dither (because I used a -12db peak, this is actually about 6 bits of resolution) 5) Upsample the result back to 192kHz and 32 bits 6) subtract one from the other, and what do you get?... White noise. The errors in quantization DO NOT manifest themselves as timing errors in your signal, they manifest themselves as extra components. These are signal dependent, so they can be considered distortion, however if you have some low level signal randomization (i.e. noise, whether you inject it intentionally as dither for coarse sampling as I did here, or it is there because of johnson noise in your circuits and background noise in the room as it already is at 20 bits), then the error also becomes randomized. Random error = white noise.

That is somewhat enlightening, and food for thought, thanks.
Yes, I am having trouble grasping this and how it relates to the reconstruction filter.

I think I begin to see the significance of dither.....

Also, I am struggling to assign amplitude error & dither with its correct weight.

Andy

[Jon Hodgson]

andy_simpson wrote on Fri, 07 October 2005

17:57That is somewhat enlightening, and food for thought, thanks. Yes, I am having trouble grasping this and how it relates to the reconstruction filter. I think I begin to see the significance of dither..... Also, I am struggling to assign amplitude error & dither with its correct weight. Andy

Hi Andy,

A lot of this isn't intuitive, so it can be hard to grasp.

Adobe audition is useful in this respect, because as the graphs people have posted show, it shows you what a reconstruction filter will do with the signal, and it has down and up sampling, so you can play around and see the effects of doing these things.

Dan has explanations of dither on his website, but in simple terms it smooths out errors and spreads them out, better a small error everywhere (noise) than a big error in a few places (distortion).

[Graham Jordan]

Jon Hodgson wrote on Thu, 06 October 2005 17:31

This statement is worrying coming from Apogee... because it is wrong, as people have been showing in graphs in earlier posts, sampling rate does not affect phase accuracy.

Precisely!