Hector Martin

This is all graphically easy to see on a spectrum analyzer, which is a good visual tool to look at audio the way our ears perceive it. That's why the noise spectrum of dithered silence at 44.1kHz/16 is not -96dB, but significantly lower (depending on FFT parameters).

@xiphmont has a footnote in the article I linked that notes how with an infinite window size, the dynamic range is effectively infinite; of course our ears don't have an effectively infinite window size. We can come up with a representative approximation for perceptual purposes.

Ultimately the real point is: the dynamic range of our ears is defined as the difference between the loudest (ear-damage level) sound and the quietest sound *we can perceive*. Since *we can perceive* a sound encoded at <-96dB in 16bit PCM, that is *not* the dynamic range.

Remember the absolute threshold of hearing is defined for a *pure tone*, not broadband noise! It would be way higher for broadband white noise.

I just did a little test, and I can perceive a pure tone at 800Hz at about -30dB relative to white noise. That means the dynamic range of a 16-bit PCM signal should be somewhere around 96+30 = 126dB. Shaped dither would improve this further.

Understood, thanks for the explanation. Just one tiny remark. Ear response is logarithmic (both in amplitude and frequency), so instead of measuring the noise floor using an FFT, it would be more suited to use something like 1/3 octave frequency bands...

When using these kind of measurements, if you have white noise, the obtained noise for each frequency band will be higher, as frequency increases (since the higher the frequency is, the more bandwidth the 1/3 octave band has).

It could be interesting repeating your experiment for higher frequencies (e.g. 8 kHz) to see if the result differs.