On 13/08/2015, Peter S <peter.schoffhau...@gmail.com> wrote:
>
> Bonus experiment: try to see if you can hear the difference between
> sine_fadeout16_noise.wav and sine_fadeout8_noise.wav in a blind ABX
> test. If not, then having extra bits of noise make zero sense.

I did a blind ABX test between them. Despite both signals have a -36
dB noise floor, I could discern the difference, the quantized signal
sounding slightly more noisy.

I examined the noise (quantization error) in detail. Here is how it sounds like:
http://morpheus.spectralhead.com/wav/quantization_noise.wav

This is 1-bit of white noise, which is the quantization error. Its
spectrum looks entirely flat:
http://morpheus.spectralhead.com/img/quantization_noise_spectrum.png

The "bump" at 0 Hz is caused by a DC offset, since it was truncated
and not rounded, so the error is not symmetrical between -0.5 .. 0.5
bit, but is rather between -1 .. 0 bit.

The waveform - when normalized to 0 dB, looks entirely like white noise:
http://morpheus.spectralhead.com/img/quantization_noise_waveform.png

Its spectrogram also looks like white noise - there are absolutely no
harmonics or signal-related artifacts, it looks like fully
uncorrelated, pure white noise:

http://morpheus.spectralhead.com/img/quantization_noise_spectrogram.png

The amplitude of the error is 1 LSB, which - in the case of 8-bit
quantization - means -42 dB amplitude. Since 42 dB is a small SNR, I
could discern the difference in blind ABX tests, though the difference
is quite minor (do an ABX test yourself to hear yourself).

If the quantization were to 24 bits instead of 8 bits, the amplitude
of the quantization error in a similar situation would be -140 dB (= 1
LSB at 24 bits precision). That is absolutely beyond both every
soundcards' dynamic range, and the human hearing's dynamic range.

Since discerning the difference in a signal quantized to 8-bits was
already not trivial and needed careful listening, I am absolutely 100%
convinced that the difference in a 24-bit signal would be absolutely
imperceptible in a blind ABX listening test under ideal listening
conditions with the most high-end gear available.

Therefore, based on two different tests, I still hold my original
opinion that having extra 8 bits of noise in a properly dithered
converter beyond the 24th bit is absolutely useless, and makes
absolutely zero practical difference.

There is not even a single soundcard on the planet that could even
properly reproduce signals with -140 dB amplitude (most high-end ones
have an SNR of only around 115-127 dB), therefore this couldn't even
be properly tested. And even if there were an equipment capable of
such precision, it is already beyond the dynamic range of the human
hearing, which is around 120 decibels (excluding signal levels beyond
the pain threshold), beyond which, the signal is perceived as
noise-free. If it's already "noise-free", there is no way of getting
any better than that...

-P
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