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Originally Posted by

**infinitesymphony** Quote:

The Nyquist theorem is perfect in theory, imperfect in practice. No real-world filters can brickwall from 22.05 kHz to 0 Hz without severely affecting the rest of the frequency range.

The theorem is not imperfect in practice, it's real world physics that (in some ways) complicate the implementation of the theorem. The theorem works exactly as predicted.

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To compromise, the cut-off frequency is moved further back into the audible range to allow for a smoother roll-off. The most effective solution to this problem requires using a higher sampling rate and moving the cut-off frequency further into the higher frequencies, which gives it the dual benefits of being inaudible (because the roll-off is outside of the range of hearing) and affecting the audible range less because a more gradual roll-off can be used.

The roll-off is not a problem. Modern converters run at MHz speeds and use advanced digital filters, so the frequency response can be completely flat 20Hz-20kHz in a 44.1kS/s system.

And modern filters are, of course, phase linear and the ringing is minimal.

Higher sample rates would have made more sense in the past, when good filters were expensive and difficult to optimize. A good converter will sound the same at 44.1kHz as it does at higher sample rates, but a converter with shoddy or improperly implemented filters will in some cases sound better at 48 or 96kHz.

If you want to optimize the sample rate to allow better performance from the worst converters, then it would probably be somewhere between 48 and 60kHz. Dan Lavry suggested 60kHz 10 years ago, but today 48kHz (or maybe even 44.1kHz) is probably enough:

http://www.lavryengineering.com/documents/Sampling_Theory.pdf

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I understand the definition of dynamic range and that bit-depth essentially is a measurement of possible dynamic range. My point is that if a higher bit-rate gives greater dynamic range *overall*, then it also affects dynamic range at a *local level*. This, IMO, is the whole point of using higher bit-rates.

I'm not sure what you mean by *"local level"*. Do you mean at specific frequencies? The dynamic range refers to (unless a specific frequency range is specified) the total amount of noise in the system, but how the noise is distributed is antoher thing.

You can, for example, have 144dB of dynamic range at critical frequencies in a 16 bit system. Another example is DSD/SACD. The total dynamic range is only 1 bit (~6dB), but thanks to the high bandwidth (1.4Mhz) you can move large amounts of quantization noise to ultrasonic frequencies and get what's roughly equivalent to 20 bits of dynamic range up to 20kHz. That's also how most modern converters work (but with a few more bits and at higher speeds).

The goals when choosing bit depth (and noise shaping) are:

a) That the dynamic range is sufficient for the signal.

b) That the noise floor is low enough to not be audible in the intended listening environment at the intended SPL.

If both a) and b) are covered by the bit depth there are no additional benefits (at least not for playback) in using higher bit depths.

Sidenote: Bit rate is **not** the same thing as bit depth.