The sample with 'none' is *without* added noise. It has only quantization artefacts.
In my tests i saw, that the ratio of sampling-frequency to signal frequency is important too.
I find it very difficult to distinguish the different noise types in the sine wave example.
I did some more example with real music files.
Please listen to the files (the second one is Pavels file quantized with my version):
http://www.s1usb.com/ftp/cello1.zip
http://www.s1usb.com/ftp/drumhats1.zip
I have added different noise types and coded the file with 12 bit (13 bit for
the 11-rand noise example). The original file is included too.
Especially with the drumhats example i think i hear differences with the rectangular and the triangular noise type.
I will try the ABX test later.
One question: what program do you use for blind testing? I would like to do looping of a region.
In my tests i saw, that the ratio of sampling-frequency to signal frequency is important too.
I find it very difficult to distinguish the different noise types in the sine wave example.
I did some more example with real music files.
Please listen to the files (the second one is Pavels file quantized with my version):
http://www.s1usb.com/ftp/cello1.zip
http://www.s1usb.com/ftp/drumhats1.zip
I have added different noise types and coded the file with 12 bit (13 bit for
the 11-rand noise example). The original file is included too.
Especially with the drumhats example i think i hear differences with the rectangular and the triangular noise type.
I will try the ABX test later.
One question: what program do you use for blind testing? I would like to do looping of a region.
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Added another example where each File is quantized to 13 bit:
www.s1usb.com/ftp/Bass2.zip
My listening impression is that the undithered file is the quietest.
Maybe the 13 bit quantizer is acting like a noise gate during quiet sections?
In the drumhats example the undithered file is easily recognized by the
"faint tones" in the silent section in the last quarter and the noise
in the quiet section at the beginning sounds not quite right...
The triangle sounds a bit more noisier maybe.
www.s1usb.com/ftp/Bass2.zip
My listening impression is that the undithered file is the quietest.
Maybe the 13 bit quantizer is acting like a noise gate during quiet sections?
In the drumhats example the undithered file is easily recognized by the
"faint tones" in the silent section in the last quarter and the noise
in the quiet section at the beginning sounds not quite right...
The triangle sounds a bit more noisier maybe.
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Without dither, you can actually expect a line spectrum for any rational relation between signal and sample frequency. For example, 1 kHz and 44.1 kHz gives lines at multiples of 100 Hz (greatest common divisor of 1 kHz and 44.1 kHz).
1 LSB peak-to-peak uniform dither is enough to get rid of this and replace it with a white spectrum, but the level of the noise still depends on the fractional part of the signal (noise modulation). 2 LSB peak-to-peak triangular PDF dither is enough to make the power spectral density of the total error white and independent of the signal.
Stated otherwise, 2 LSB peak-to-peak triangular PDF dither is sufficient to fool a spectrum analyser, but definitely not sufficient to fool the ears of Mooly and PMA!
In my opinion, the results of this test are absolutely fascinating because they totally contradict what Wannamaker wrote in his PhD thesis (see jcx's post #5 in this thread) and in various peer-reviewed articles about the audibility of dithered quantization. I didn't expect that at all, but the test results are clear.
"For audio signal processing purposes, there seems to be little point in rendering any moments of the total error other than the first and second independent of the input. Variations in higher moments are believed to be inaudible and this has been corroborated by a large number of psycho-acoustic tests conducted by the authors and others [13, 21]."
The very first test in this thread already showed that it is not just the average and the RMS value that determine the audibility, with other words, that higher moments matter.
"When 2RPDF [ triangle PDF ] dither was employed, no instance was found in which the error was audibly distinguishable from a steady white noise entirely unrelated with the input."
The later tests show directly that this is nonsense, even with equal RMS and peak values and as similar a probability distribution as possible.
Mooly and PMA, if you are willing to listen to more noisy recordings, we could check what order of dither is required to really make dithered quantization indistinguishable from additive noise.
"For audio signal processing purposes, there seems to be little point in rendering any moments of the total error other than the first and second independent of the input. Variations in higher moments are believed to be inaudible and this has been corroborated by a large number of psycho-acoustic tests conducted by the authors and others [13, 21]."
The very first test in this thread already showed that it is not just the average and the RMS value that determine the audibility, with other words, that higher moments matter.
"When 2RPDF [ triangle PDF ] dither was employed, no instance was found in which the error was audibly distinguishable from a steady white noise entirely unrelated with the input."
The later tests show directly that this is nonsense, even with equal RMS and peak values and as similar a probability distribution as possible.
Mooly and PMA, if you are willing to listen to more noisy recordings, we could check what order of dither is required to really make dithered quantization indistinguishable from additive noise.
I disagree; if you want to know whether higher moments are audible, this is the most sensitive test you can think of.
Of course! In most practical cases you won't notice any difference, but when the volume is turned up so high and the music is so soft that you do hear a difference, the dithered version will always sound better.
Another question I had, and you and Mooly should know the answer to that by now: the total error with triangular dither sounds different from additive noise, as you have shown, but does it sound worse? If not, then triangular dither may still be the best compromise for audio: getting rid of the worst quantization artefacts at a limited SNR penalty.
Marcel, you are doing a great job, but frankly, I have big troubles to listen to those noisy samples. That's why I have humbly asked you to process that almost noiseless file with added noise at 12-th bit, not the 8th or 10th.
Re "better or worse", I do not dare to answer, I was just trying to find a difference. Generally speaking, I have preferred a TPD dither to noise shaping dithers in another tests.
Re "better or worse", I do not dare to answer, I was just trying to find a difference. Generally speaking, I have preferred a TPD dither to noise shaping dithers in another tests.
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Hi PMA and Mooly,
Today I suddenly realized that there might be a fatal flaw in the tests done so far. If you can hear a difference between two realizations of the same stochastic process, then all tests done so far are meaningless. For example, if you have two recordings of additive noise with the same probability distribution, do they necessarily sound exactly the same or can they sound slightly different because noise by definition has random variations?
The only way I can think of to exclude this effect from affecting the experiment is this:
-I make one file with additive noise that is marked as having additive noise
-I make one file with dither and requantization that is marked as being requantized
-I make ten files marked X1...X10 or so with either additive noise or dither and requantization, depending on the flip of a coin, and keep a secret list of what is what. (The files have to have the same format to get equal file sizes and bit rates.)
-You listen to it, try to categorize the files as additive noise / dithered and requantized and send the result to me by PM
I could do this for the drum music with 12 bits for PMA and with "I do like to be beside the seaside" and 8 bits for Mooly, if you are prepared to do this experiment.
Regards,
Marcel
Today I suddenly realized that there might be a fatal flaw in the tests done so far. If you can hear a difference between two realizations of the same stochastic process, then all tests done so far are meaningless. For example, if you have two recordings of additive noise with the same probability distribution, do they necessarily sound exactly the same or can they sound slightly different because noise by definition has random variations?
The only way I can think of to exclude this effect from affecting the experiment is this:
-I make one file with additive noise that is marked as having additive noise
-I make one file with dither and requantization that is marked as being requantized
-I make ten files marked X1...X10 or so with either additive noise or dither and requantization, depending on the flip of a coin, and keep a secret list of what is what. (The files have to have the same format to get equal file sizes and bit rates.)
-You listen to it, try to categorize the files as additive noise / dithered and requantized and send the result to me by PM
I could do this for the drum music with 12 bits for PMA and with "I do like to be beside the seaside" and 8 bits for Mooly, if you are prepared to do this experiment.
Regards,
Marcel
Ten ! Ten files 
I hope there is a good prize on offer
I suspect the idea of ten such files fills Pavel with as much horror as it does me
To my way of thinking it would only be feasible if there was a long time period to play around with them, perhaps just trying one or two a day at most. It would be to much of a chore otherwise, even if it is gratifying to get a positive result at the end... if that makes sense.
I hope there is a good prize on offer I suspect the idea of ten such files fills Pavel with as much horror as it does me
To my way of thinking it would only be feasible if there was a long time period to play around with them, perhaps just trying one or two a day at most. It would be to much of a chore otherwise, even if it is gratifying to get a positive result at the end... if that makes sense.
You could take as long as you like, of course, but the amount of work would be similar to the ABX tests you've already done. The difference is that you don't need the ABX plugin now. You simply have files marked X1 to X10 and have to listen whether they sound more similar to file A (additive noise) or to file B (dithered quantization).
I finally made the 8 bits files and files with matching additive noise. If you are still prepared to do the test, you can download them here:
WeTransfer
and PM me to tell me which of the X files have noise that sounds like additive noise and which have requantization.
WeTransfer
and PM me to tell me which of the X files have noise that sounds like additive noise and which have requantization.
I have just tried an ABX with the two master files and seem to be able to get a reliable result.
For anyone following this I flunked the identification of the 10 random files getting just 4 out of 10 correct. I didn't ABX those but tried to rely on audible memory. Interesting
For anyone following this I flunked the identification of the 10 random files getting just 4 out of 10 correct. I didn't ABX those but tried to rely on audible memory. Interesting
Code:
foo_abx 2.0.4 report
foobar2000 v1.3.16
2017-11-29 08:12:55
File A: silverysea8bits.wav
SHA1: a0046ce776698edb27e49beaf4ca8951e175adb8
File B: silveryseaaddednoise.wav
SHA1: 901a09aa1c3a66f333ec1930536213c1c98975fe
Output:
DS : Primary Sound Driver
Crossfading: NO
08:12:55 : Test started.
08:13:21 : 01/01
08:13:30 : 02/02
08:13:42 : 03/03
08:13:57 : 03/04
08:14:06 : 04/05
08:14:23 : 05/06
08:14:37 : 06/07
08:14:52 : 07/08
08:14:52 : Test finished.
----------
Total: 7/8
Probability that you were guessing: 3.5%
-- signature --
8ef7b547476e3e21e79e1004b151b508f1cbc793
Code:
foo_abx 2.0.4 report
foobar2000 v1.3.16
2017-11-29 08:20:23
File A: silverysea8bits.wav
SHA1: a0046ce776698edb27e49beaf4ca8951e175adb8
File B: silveryseaaddednoise.wav
SHA1: 901a09aa1c3a66f333ec1930536213c1c98975fe
Output:
DS : Primary Sound Driver
Crossfading: NO
08:20:23 : Test started.
08:20:43 : 01/01
08:21:10 : 02/02
08:21:25 : 03/03
08:21:36 : 04/04
08:21:46 : 05/05
08:21:58 : 06/06
08:22:23 : 06/07
08:22:32 : 07/08
08:22:32 : Test finished.
----------
Total: 7/8
Probability that you were guessing: 3.5%
-- signature --
7565797d24b61bfcca856eb7a6431ceb753a0e0cTo elaborate on this a bit:
Noise is by definition a random signal, so you always have random differences between two recordings of noise with the same probability distribution. As a working hypothesis, suppose that the differences between two recordings of noise with the same probability distribution are more audible than the "average" difference between additive noise and the noise of a dithered quantizer.
You will then hear a difference in ABX tests where the same additive noise file and the same dithered and quantized file are used over and over again for all "X" trials. The same holds for ABX tests where two different additive noise files are used over and over again.
It then becomes far more difficult when an ABX test is done where each X file is generated separately. Each X file then sounds different, and you will try to categorize them as "similar to A" or "similar to B", but this categorization will depend more on the random variations between the files than on whether they have additive noise or dither and quantization noise.
This hypothesis could explain a lot:
1. Why you get significant results in the Foobar ABX tests, but not in the test with X1 to X10 files.
2. Why the results of the Foobar ABX tests were so different from what Wannamaker wrote.
Noise is by definition a random signal, so you always have random differences between two recordings of noise with the same probability distribution. As a working hypothesis, suppose that the differences between two recordings of noise with the same probability distribution are more audible than the "average" difference between additive noise and the noise of a dithered quantizer.
You will then hear a difference in ABX tests where the same additive noise file and the same dithered and quantized file are used over and over again for all "X" trials. The same holds for ABX tests where two different additive noise files are used over and over again.
It then becomes far more difficult when an ABX test is done where each X file is generated separately. Each X file then sounds different, and you will try to categorize them as "similar to A" or "similar to B", but this categorization will depend more on the random variations between the files than on whether they have additive noise or dither and quantization noise.
This hypothesis could explain a lot:
1. Why you get significant results in the Foobar ABX tests, but not in the test with X1 to X10 files.
2. Why the results of the Foobar ABX tests were so different from what Wannamaker wrote.
That's another hypothesis that could explain the results so far. Is there any convenient way you can compare a third file against two known files without needing to rely on your auditory memory?
If we can somehow show that my hypothesis that it's all due to different realizations of the same stochastic process sounding audibly different is wrong, then we've also proven Wannamaker's claim that dithered quantization sounds exactly like noise incorrect. If not, then we are stuck with results that are open to more interpretations.
If we can somehow show that my hypothesis that it's all due to different realizations of the same stochastic process sounding audibly different is wrong, then we've also proven Wannamaker's claim that dithered quantization sounds exactly like noise incorrect. If not, then we are stuck with results that are open to more interpretations.
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