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Quantization Grid, Split from Topic ID #55966
KMD
post Mar 21 2012, 15:35
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David - What does the frequncey spectrum analysis of that 50 HZ dithered look like


Owen

This post has been edited by KMD: Mar 21 2012, 15:38
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2Bdecided
post Mar 21 2012, 15:40
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QUOTE (pdq @ Mar 21 2012, 13:50) *
What would be the point?
None. I don't think KMD fully grasps the implications of the questions that they are asking.

QUOTE
We have established that low level signals can be severely distorted by quantization, and that a nominal application of dither removes much, but not all, of that distortion.
It removes all the audible distortion.

True, there's still a visible relationship between the original signal, and the dither+quantisation - i.e. if you subtract the 8-bit version from the 16-bit version, you can see the difference isn't purely uncorrelated noise...
Attached Image


...but it certainly sounds like uncorrelated noise...
Attached File  difference_8_bit_dithered_quantisation_noise.flac ( 1014.23K ) Number of downloads: 50


I also attach the original 16-bit sweep and the 8-bit quantised version for reference...
Attached File  16bit_version.flac ( 256.91K ) Number of downloads: 47

Attached File  8bit_version.flac ( 195.28K ) Number of downloads: 32


Cheers,
David.
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2Bdecided
post Mar 21 2012, 15:45
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QUOTE (KMD @ Mar 21 2012, 14:35) *
David - What does the frequncey spectrum analysis of that 50 HZ dithered look like
At 44.1kHz or 352.8kHz? Using what parameters?

Whichever, it looks like you'd expect - white noise 0-22kHz, a peak at 50Hz about 40dB above it, and (in the 352.8kHz version) more white noise 22kHz-176kHz about 65dB below it.

No other features.

Cheers,
David.
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2Bdecided
post Mar 21 2012, 15:48
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QUOTE (KMD @ Mar 21 2012, 14:08) *
pdq -look at the 2nd image in 2bdecided post68 above . On first looking the dither seems to have not removed the distortions at all.
That post shows you that quantisation "quantises" - and that the resulting discrete levels remain fairly intact even when oversampling at higher resolution.

It says nothing about whether dither removes distortion or not. It's not intended to.

Correct dither removes audible distortion perfectly.

Cheers,
David.
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KMD
post Mar 21 2012, 16:07
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Use the FFT to check that the harmonics are not there and the dither is doing what is expected
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2Bdecided
post Mar 21 2012, 16:12
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QUOTE (KMD @ Mar 21 2012, 15:07) *
Use the FFT to check that the harmonics are not there and the dither is doing what is expected
http://en.wikipedia.org/wiki/Teaching_gran...er_to_suck_eggs
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KMD
post Mar 21 2012, 16:16
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do the fft to confirm that the harmonics are not there. Anyone looking at the statisticle analysis would suspect that they are.


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2Bdecided
post Mar 21 2012, 16:34
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QUOTE (KMD @ Mar 21 2012, 15:16) *
do the fft to confirm that the harmonics are not there. Anyone looking at the statisticle analysis would suspect that they are.
Yes boss!

with dither...
Attached Image


and without dither...
Attached Image



Who is this person following this thread that suspects dither doesn't work because they've misinterpreted a graph showing that quantisation quantises?

If you want a simple example of dither working, without worrying about subsequent oversampling, look at this old picture...
Attached Image


Cheers,
David.

This post has been edited by 2Bdecided: Mar 21 2012, 16:37
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Rotareneg
post Mar 21 2012, 16:40
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Delta-sigma modulation must be a hoax. biggrin.gif
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KMD
post Mar 21 2012, 17:11
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" yes Boss" LOL


I'm glad we can have a light hearted chat , some of the comments on this forum are really chippy and uptight. not helpfull to getting anywhere at all.

any way so where were we


So the harmonics are not there but the statistical analys shows the quantization levels.

The last step to finally bake the cake is to do step 1, 2, 3, 4 and the statistical analysis with a music waveform.
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KMD
post Mar 21 2012, 17:36
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The image in post 77 is way to square. A reconstructed dithered waveform should look like a fuzzy sine wave .



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2Bdecided
post Mar 21 2012, 17:46
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QUOTE (KMD @ Mar 21 2012, 16:36) *
The image in post 77 is way to square. A reconstructed dithered waveform should look like a fuzzy sine wave .
The image in post 77 isn't "reconstructed", or oversampled - it's the actual 44.1kHz data. The second one in post 49 was 8x oversampled to 352.8kHz to simulate reconstruction.

Examining 8-bit quantisation with and without dither using typical pop music won't show much. If you're lucky, you'll be able to see+hear the added noise, but it'll be hard to spot any distortion on a graph.

Suitable classical recordings, or anything with quiet passages, will reveal the same as you've seen with the sine wave.

You'd hear the same too.
e.g. original: http://mp3decoders.mp3-tech.org/audio/brief_original.mp3
6-bit no dither: http://mp3decoders.mp3-tech.org/audio/brief_rounded.mp3
6-bit with dither: http://mp3decoders.mp3-tech.org/audio/brief_dithered.mp3
6-bit with noise shaped dither: http://mp3decoders.mp3-tech.org/audio/brief_nsdithered.mp3

Not much use for waveform analysis as these are mp3s, but they illustrate the different sound very well.

Cheers,
David.
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KMD
post Mar 21 2012, 18:02
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When you say 8x oversampled to simulate reconstruction can you confirm that that includes simulation the 22Khz low pass filter.

I would not expect anything to be immediately audible in the pop music either. But to see that statistical analysis done on music would prove that digital audio is fundamentally constrained in amplitude variation, with a statistical variance, around the quantization levels, which could effect the listening experience, and is a genuinely original revelation in digital audio engineering. I am a member of the Audio Engineering Society by the way.


-
Owen.

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lvqcl
post Mar 21 2012, 18:49
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QUOTE (KMD @ Mar 21 2012, 21:02) *
which could effect the listening experience

omg.
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greynol
post Mar 21 2012, 20:40
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QUOTE (KMD @ Mar 21 2012, 10:02) *
is a genuinely original revelation in digital audio engineering

To anyone who has had sophomore-level college (or equivalent) exposure in digital signals and has some knowledge in audiology, this would not be a revelation by any stretch of the imagination.

Before we get all caught up in the constraint of digital audio in amplitude variation, you might want to consider whether the human ear and its listening environment isn't also constrained in amplitude variation.

That you are a member of AES does little to demonstrate any competence in this discussion, by the way. IEEE would have gotten you farther, but we'd then have reason to wonder why you seem to be so confused.


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Arnold B. Kruege...
post Mar 21 2012, 21:25
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QUOTE (KMD @ Mar 21 2012, 13:02) *
But to see that statistical analysis done on music would prove that digital audio is fundamentally constrained in amplitude variation, with a statistical variance, around the quantization levels, which could effect the listening experience, and is a genuinely original revelation in digital audio engineering.


You are aware that the grid for 16 bits is composed of lines that are 0.00026 dB apart at FS, more or less, right? 60 dB below FS they are about 0.1 dB apart. None of those level differences will ever be heard! Below -60 dB even hearing the peak signal above the ambient noise, let alone the microscopic difference, will be a challenge.
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drewfx
post Mar 22 2012, 01:18
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QUOTE (KMD @ Mar 21 2012, 12:02) *
But to see that statistical analysis done on music would prove that digital audio is fundamentally constrained in amplitude variation, with a statistical variance, around the quantization levels, which could effect the listening experience, and is a genuinely original revelation in digital audio engineering.


The fact that the reconstructed output waveform of a dithered digital signal might tend to follow the quantization levels is irrelevant.

The quantization error is what makes the reconstructed signal fall closer to the quantization levels. When you have no dither, the quantization error is correlated to the signal, which if audible, is undesirable.

When you add dither (while you are still in the digital domain), you end up with a quantized version of your signal plus dither. Since the dither is random and of an appropriate level compared to the quantization step size, you end up with your original signal plus uncorrelated noise.

It's still quantization error that makes the reconstructed dithered signal tend to follow the quantization level, but now the quantization error is based on the signal plus dither instead of just the signal. And if it's audible, it can indeed affect the listening experience - it sounds like noise. But there's nothing new, original or revelatory about it.
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KMD
post Mar 22 2012, 10:00
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QUOTE (2Bdecided @ Mar 20 2012, 18:52) *
I'm not sure why anyone thinks a filter at 22kHz is going to change a square-ish low frequency waveform that much. The example I posted was a low amplitude sine wave at 50Hz; at 8-bits it ends up with square-wave-like transitions at ~250Hz due to quantisation. In this example, you can comfortably fit the first 40 harmonics within the transition band. That's more than you need to make a square wave look something like a square wave.

Cheers,
David.


Because that is how it is taught in textbooks. Typically a stream of spiky samples is shown going into a reconstruction filter and out the other side comes a smooth wave. As the cooledit images shows the reconstruction filter and dither do neither. As your plot shows the output is a stream of jumps between quantization levels, which illustrates my original point in the listening test topic about a quantization grid except rather than a grid it is more of a vertically spaced grating.

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2Bdecided
post Mar 22 2012, 11:03
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QUOTE (KMD @ Mar 22 2012, 09:00) *
Because that is how it is taught in textbooks. Typically a stream of spiky samples is shown going into a reconstruction filter and out the other side comes a smooth wave. As the cooledit images shows the reconstruction filter and dither do neither. As your plot shows the output is a stream of jumps between quantization levels, which illustrates my original point in the listening test topic about a quantization grid accept rather than a grid it is more of a vertically spaced grating.
KMD, I think that you may be guilty of a little knowledge being a dangerous thing. And maybe misunderstanding the graphs.

I posted these graphs in response to a claim that the quantisation levels were never visible after reconstruction. The graphs show that, where the original signal is low frequency, and contains only a few levels, it's easy to see that the quantisation levels are visible after reconstruction.

However, this doesn't show a "fault" in reconstruction or digital audio. It shows that I know how to choose a signal that is largely unaffected by reconstruction wink.gif i.e. effectively a very low frequency square-ish wave, which really is a square-ish wave, and so after reconstructions still looks like a square-ish wave.

All the graphs you have seen in textbooks are true.

I can do them do wink.gif

20kHz sine wave, sampled at 44.1kHz...
Attached Image


...44.1kHz version 8x oversampled...
Attached Image


...44.1kHz version 100x oversampled...
Attached Image


Cheers,
David.
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2Bdecided
post Mar 22 2012, 11:13
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QUOTE (KMD @ Mar 21 2012, 17:02) *
When you say 8x oversampled to simulate reconstruction can you confirm that that includes simulation the 22Khz low pass filter.
Yes, of course.

QUOTE
But to see that statistical analysis done on music would prove that digital audio is fundamentally constrained in amplitude variation, with a statistical variance, around the quantization levels
Of course it is. At the sample points, without noise, with an ideal reconstruction filter, it's absolute constrained. That's what quantisation does. Between the sample points, the reconstructed signal could go anywhere - though for a given input signal there's only one "correct" place for it go (defined by the sinc function) and that may or more likely may not be on an original quantisation step.

QUOTE
which could effect the listening experience
The ear has no conceivable mechanism to detect (i.e. hear) this, even in signals where the effect is visible.

QUOTE
I am a member of the Audio Engineering Society by the way.
My membership has lapsed, but I attend lectures when I can.

I wish I could get to tonight's...
http://www.aes-uk.org/event/loss-of-our-mu...ster-cambridge/
...though they would be preaching to the choir if I was there wink.gif . I suspect they are anyway.

Cheers,
David.
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greynol
post Mar 22 2012, 13:55
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QUOTE (2Bdecided @ Mar 22 2012, 03:13) *
Between the sample points, the reconstructed signal could go anywhere - though for a given input signal there's only one "correct" place for it go (defined by the sinc function) and that may or more likely may not be on an original quantisation step.

Since you're talking about time being filled between points that are sampled you would expect the waveform to fall between quantization levels. The amplitude in between may still be in error just as it may be at the sampled points and likely will be if those sampled points are in error, but this is hardly ground breaking.

My text books on the subject speak clearly about quantization error, so I reject KMD's claim to the contrary. Maybe the problem has to do with glancing at pictures instead of reading the text and equations?

This post has been edited by greynol: Mar 22 2012, 14:14


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pdq
post Mar 22 2012, 14:24
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QUOTE (greynol @ Mar 22 2012, 08:55) *
Since you're talking about time being filled between points that are sampled you would expect the waveform to fall between quantization levels.

The sampled points on either side of a maximum are both below the maximum of the reconstructed waveform. Similarly for a minimum.
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greynol
post Mar 22 2012, 14:41
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What about ringing?


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2Bdecided
post Mar 22 2012, 14:57
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QUOTE (greynol @ Mar 22 2012, 12:55) *
My text books on the subject speak clearly about quantization error, so I reject KMD's claim to the contrary. Maybe the problem has to do with glancing at pictures instead of reading the text and equations?
I think the fact that people believe they can look at something for five minutes and make a genuine ground breaking discovery in a field that's been well understood for decades tells you a lot about 21st century culture.

Or something. I'm probably trying to be philosophical, and I know nothing about that field myself.

Cheers,
David.
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WernerO
post Mar 22 2012, 14:59
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QUOTE (greynol @ Mar 22 2012, 14:41) *
What about ringing?


You mean the ringing that is seen in the reconstruction filter's impulse response?

There would be none, provided the original signal was indeed correctly bandlimited
prior to sampling.

If you meant something else then pray unread the above.

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