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Audibility thresholds of amp and DAC measurements

pma

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Psychoacoustic treatment is not limited by using masking. Dithering is a signal processing that always results in degradation of a signal waveform (adding noise) but the same time it improves auditory perception of that signal. Such “magic” processing can be based only on some knowledge of perception - a product of psychoacoustic research. So, dithering is a perfect example of psychoacoustic treatment of audio signal. I think it is obvious.

No. No degradation and no magic.
 

Serge Smirnoff

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Here is what I hope is a definitive explanation of dithering being both 1) required, and 2) a mathematical issue, not a perceptual issue.
Thanks for separating the discussion. I will participate for sure.
 

Serge Smirnoff

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No degradation
It is. Adding noise is degradation. Dithering is adding noise (nothing more). So, the dithering is degradation. But in audio it is used in combination with quantizing and there are two cases - initial signal is below LSB and above. In these cases the dithering has different consequences. But this is better to discuss in the separate thread.
 

xr100

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I used the term "digital silence" in a way as it is used in Audio Precision waveform generator - dithered silence, not equal to zero.

They aren't silence + noise (dither), the release stage of the piano and reverb tails are coded and audible.
 

xr100

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Yes, I can do sometimes as English is not my native tongue. That is why I use sometimes two words (slashed) instead of one.

Sample = sound sample. Excerpt is probably a better word for this.

It wasn't a problem, I just wanted to make sure that no-one reading my post would be confused. :)
 

Serge Smirnoff

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They aren't silence + noise (dither), the release stage of the piano and reverb tails are coded and audible.
Yes, indeed. In my current listening environment I did not discern the tail. I saw in audio editor that there is something there but did not check. Now, after amplification of that portion, I can hear the sound (even without amplification)). My fault.
 

SIY

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It is. Adding noise is degradation. Dithering is adding noise (nothing more).

It is clear that you do not understand dithering. Dithering linearizes the system and (unlike "adding noise, nothing more") INCREASES information, i.e., decreases entropy. This is not only demonstrable, it's been demonstrated to you.

Admittedly, the concept is not intuitive, but when entropy is decreased, it is clearly NOT "adding noise, nothing more." First principles.
 

j_j

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I think that comparison of error signals with one another results in more useful results than comparison of error signal to original.

You may think so, you're wrong. It's that simple.

The only time error signal, alone, is meaningful is if it's down at least 90-100dB.
 

exaudio

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16-bit dithered can carry e.g. a 1kHz sine wave at far, far below -100dB where truncated would yield absolute silence.

Wow. I had to test this, and sure enough, it's like mathematical magic. I used SoX to generate two wav files. Both files were 1kHz sine waves with an amplitude of -101dBFS sampled at 48kHz with 16 bits/sample. The first wav file was encoded with SoX's dithering disabled. The second one was encoded with SoX's default dither applied.

I used a hex editor to examine the non-dithered file, and as expected (because -101dBFS is below the -96dB limit of 16 bit encoding), the file was all zeros--digital silence.

Next, I took the dithered file, imported it into Wolfram Mathematica, and plotted the spectrum. And, presto, like a rabbit out of a hat, out popped the signal (see spectrum on the lower right). Pretty cool.


dither-study-1khz--101db-48-16.png
 

xr100

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Wow. I had to test this, and sure enough, it's like mathematical magic.

:) It seems too good to be true. I suppose the first time one learns of this, it's hard to believe.

But, as you did, try it for yourself... and you can try signals by far below -101dBr before hitting the (FFT'd) noise floor. ;-)
 

BDWoody

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:) It seems too good to be true. I suppose the first time one learns of this, it's hard to believe.

But, as you did, try it for yourself... you can get much lower than -101dBr before hitting the (FFT'd) noise floor. ;-)

I love math...

Great discussion...another thread where I have no ability to contribute in any meaningful way, but learned a ton.
Just a thanks to those willing to teach.
 

KSTR

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FWIW, here I made a measurement that shows dithering can correctly render sub-1LSB signals, and that's been an LSB of a 24-bit DAC! Heavy time-domain averaging was needed to peel out a signal level at 18% of that 24 bit converter's LSB from the inherent (analog) noise.
 
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