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For signal-to-noise ratio (SNR), SNR=6B dB is called the dynamic range of the quantizer.

The dynamic range of the 16-bit quantizer is 6B = 6·16 = 96 dB. Note that the dynamic range of the human ear is about 100 dB. Therefore, the quantization noise from 16-bit quantizers is about at the threshold of hearing. This is the reason why “CD quality” digital audio requires at least 16-bit quantization.

How can we obtain(calculate) the fact that the dynamic range of the human ear is about 100 dB?

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  • $\begingroup$ An increase of 6 dB means a doubling in amplitude, therefore 16-bit quantizer provides a 96 dB dynamic range. $\endgroup$ – ZR Han Dec 31 '20 at 9:37
  • $\begingroup$ @ ZR Han your answer is irrelevant to what I asked. $\endgroup$ – DSPinfinity Dec 31 '20 at 10:45
  • $\begingroup$ Sorry, I didn't get your point before. Please check my answer. $\endgroup$ – ZR Han Dec 31 '20 at 14:10
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Where does this quote come from? It does NOT look like a reliable source of information to me.

The dynamic range of the 16-bit quantizer is 6B = 6·16 = 96 dB.

Wrong. The quantization noise for a 16 bit bipolar rounding quantizer is about -101dB dFS. That makes the signal to noise ratio for a sine wave 98dB and for the "average" music file about 8dB-90dB.

Note that the dynamic range of the human ear is about 100 dB.

Grossly oversimplified and misleading. The dynamic range of human auditory systems depends highly on frequency (and unfortunately also and age and how much rock& roll you have played, sigh). Max dynamic range is about 120 dB at the midrange.

This is the reason why “CD quality” digital audio requires at least 16-bit quantization.

16-bit quantization was chosen as a complicated trade off between audibility of quantization noise and cost & technical complexity at the time the standard was created. 16-bit per se is in many cases not sufficient unless proper "dithering" and "noise shaping" is applied as well.

The explanation really misses the main point. SNR and audibility of quantization noise depends A LOT on frequency and the specific signal. 16-bit PCM quantization is a "brute force" approach with most bits being wasted and a few important ones missing. Perceptual codecs such as AAC, MP3, Ogg, etc. do this much better and generate way more "sound quality per bit".

Finally, the question:

How can we obtain(calculate) the fact that the dynamic range of the human ear is about 100 dB?

Through listening test performed over a wide range of diverse subjects and test signals. The hearing threshold is determined as the sound pressure where the subject says "I can't hear this anymore" and the pain threshold corresponds to "ow, that hurts. Stop it!". The pain threshold is particularly difficult to test since it's fairly subjective and the testing can cause physical damage to the test subject. The results of the hearing test are then compiled using statistical analysis. You end up with a set of curves like this: https://en.wikipedia.org/wiki/Equal-loudness_contour .

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  • $\begingroup$ Good answer. I’d be curious to know in what cases 16-bit is not sufficient without noise shaping/dithering. In the audio work I’ve done, I can’t think of an instance where I could hear the difference, and mostly just use those features during mastering by way of sensibility. $\endgroup$ – Dan Szabo Dec 31 '20 at 15:15
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The dynamic range of the human ear is related to the ratio of the maximum sound intensity it can tolarate, and the minimum sound intensity it can hear.

An example of the maximum sound intensity is given by a close passing Jet motor aircraft, while an example of minimum sound intensity is a spining HDD drive (which is about 21 dB above hearing threshold).

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  • $\begingroup$ @ Fat32 still the following is not clear to me: what is the connection of the SNR of a quantizer to dynamic range of the human ear? $\endgroup$ – DSPinfinity Dec 31 '20 at 16:19
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    $\begingroup$ @DSPinfinity Hilmar's answer touches upon that matters... $\endgroup$ – Fat32 Dec 31 '20 at 22:52
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Firstly you should know that the sound pressure level is defined as $$ SPL = 20log_{10}\frac{p}{p_{ref}} $$ where $p$ is sound pressure and $p_{ref}$ represents the reference pressure. The reference pressure is the minimum sound pressure that human ear can perceive, which is 20 uPa in air and 1 uPa in water. Therefore 0 dB is the minimal audible level.

As for the maximum level, long-term exposure to a noise environment above 100 dB can cause irreversible damage to human ears, although a louder sound also can be heard.

This should explain the fact that the dynamic range of human ear is about 100 dB.

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  • $\begingroup$ still the following is not clear to me: what is the connection of the SNR of a quantizer to dynamic range of the human ear? $\endgroup$ – DSPinfinity Dec 31 '20 at 15:33

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