Bits, Hertz, Shaped Dithering … Part 2
What is behind these concepts?
In theory, this is the only criterion for choosing the scanning resolution. We no longer contribute absolutely without distortions or inaccuracies. The practice, oddly enough, almost completely repeats the theory. This is what guided those people who chose 16-bit resolution for audio CDs. Noise of minus 93 decibels is a pretty good condition, which corresponds almost exactly to the conditions of our perception: the difference between the pain threshold (140 decibels) and the usual background noise in the city (30-50 decibels) is of about a hundred decibels, and if we consider that the painful volume level, no music is heard, which further reduces the range, it turns out that the actual noise from the room or even from the equipment is much louder than the noise from quantification. If we can hear a level below minus 90 decibels in a digital recording, we will hear and perceive quantization noises; otherwise we will simply never determine whether it is live or digital audio. There is simply no other difference in terms of dynamic range. But, in principle, a person can hear significantly in the 120 decibel range, and it would be nice to keep this full range, which apparently 16 bits cannot support.
But this is only at first glance: using a special technique called shape dithering, it is possible to change the frequency spectrum of the sampling noise, bringing them almost completely into the region of more than 7-15 kHz. In a way, we changed the resolution of the frequency (we refused to reproduce quiet high frequencies) to get additional dynamic range in the remaining frequency segment. In combination with the peculiarities of our hearing, our sensitivity to the ejected high-frequency region is tens of dB lower than in the main region (2-4 kHz), this makes possible a relatively quiet transmission of useful signals by 10-20 additional dB quieter than -93 dB; therefore, the dynamic range of human 16-bit audio is approximately 110 decibels. And in general, at the same time, a person simply cannot hear sounds 110 decibels lower than the loud sound that he just heard. The ear, like the eye, adjusts to the volume of the surrounding reality, therefore the simultaneous range of our hearing is relatively small, around 80 decibels. Let’s talk more about dithring after discussing the frequency aspects.
For CD, the sampling frequency is 44100 Hz. There is an opinion (based on a misunderstanding of the Kotelnikov-Nyquist theorem) that all frequencies are reproduced up to 22.05 kHz, but this is not entirely true. We can only say that there are no frequencies above 22.05 kHz in the digitized signal. The actual image of digitized sound reproduction always depends on the specific technique and is not always as ideal as we would like, and as befits the theory. It all depends on the specific DAC (digital to analog converter responsible for receiving an audio signal from a digital stream).
Let’s first find out what we would like to achieve. A middle-aged (quite young) person can feel sounds from 10 Hz to 20 kHz, hear significantly – from 30 Hz to 16 kHz. The loudest and lowest sounds are heard, but are not acoustic sensations. Sounds above 16 kHz are felt as an annoying and unpleasant factor: pressure on the head, pain, especially loud sounds, cause such acute discomfort that one wants to leave the room. The unpleasant sensations are so strong that the action of the security devices is based on this: a few minutes of very loud high-frequency sound will drive anyone crazy and it becomes absolutely impossible to steal anything in such an environment. Sounds below 30 – 40 Hz with sufficient amplitude are perceived as vibrations emanating from objects (speakers). It would be more correct to say, just vibration.
