Table of Sample Rate vs Quality and note on Nyquist theorem.

Hi Folks,

On the subject of sample rates, here's a table that CoolEdit has in
its "tips" file:

Sample
Rate Quality
-------- -------
11025 Hz Speech
22050 Hz FM Radio
32075 Hz Tape
44100 Hz CD
48000 Hz DAT
96000 Hz DVD

Now for my own note:

Given that 20000 Hz seems to be the upper limit of human hearing
(apparently even 16000 Hz is the upper limit for a lot of people) and
since Nyquist's sampling theorem tells us that the highest frequency
which can be accurately represented is one-half of the sampling rate, it
would seem that sample rates of 40000 Hz or greater should be sufficient
to accurately represent all of the frequencies that we can hear.

I hope this helps and I apologize for any repetition of information that
has already been posted on the list.

Cheers,
Christopher

>From: "Christopher J. Chapman" <christopher.chapman@conexant.com>
>
>On the subject of sample rates, here's a table that CoolEdit has in
>its "tips" file:
>
> Sample
> Rate Quality
> -------- -------
> 11025 Hz Speech
> 22050 Hz FM Radio
> 32075 Hz Tape
> 44100 Hz CD
> 48000 Hz DAT
> 96000 Hz DVD
>
>Now for my own note:
>
>Given that 20000 Hz seems to be the upper limit of human hearing
>(apparently even 16000 Hz is the upper limit for a lot of people) and
>since Nyquist's sampling theorem tells us that the highest frequency
>which can be accurately represented is one-half of the sampling rate, it
>would seem that sample rates of 40000 Hz or greater should be sufficient
>to accurately represent all of the frequencies that we can hear.

From: "Mats �ljare" <oljare@hotmail.com>

>Actually there�s problems with everything above 1/4 or 1/3 of the sample
>rate,especially with closely spaced frequencies as in inharmonic
>timbres.

There are some oversimplifications here. First, it is true that the Nyquist
Theorem states that you only need a sampling rate two times the highest
frequency to preserve all frequency information up to that frequency.
However, in a real digital recording/playback system, there has to be some
filtering on the output. A so-called anti-imaging filter is necessary in
order to prevent artifacts higher than the Nyquist being reproduced (even
though they were not recorded). Early CD players had analog filters with
extremely sharp roll-offs, resulting in much less than a full frequency
response up to the Nyquist and phase distorion. This made them sound
relatively "harsh" and "grainy."

However, with the advent of oversampling and MASH anti-imaging, few if any
of these artifacts are perceptible anymore. (Much more of a problem are the
awful analog opamps used in many consumer CD players.) There is a recent
trend among some sound engineers to work at 96K sampling rates, sampling
down only when mastering to CD. Though there could possibly be some benefit
to this if there is a lot of DSP going on in the mix, I have yet to see any
hard data that this practice has any audible benefit.

Of course, the standard CD sampling rate is 44.1K, an odd number bullied
through the IEEE committee by Sony to support their early video-based PCM
recorders. The IEEE preferred 48K, which was retained on digital
multitracks. The DAT standard specifies several possible sampling rates,
including 48K and 44.1K. However, because of crazy US laws, it is
impossible to buy a "consumer" DAT deck that records at 44.1K, though all
of them play back at both rates. "Professional" decks record at both.

The other standards CoolEdit mentions are of course analog, and those are
simply the rough equivalent sampling rates to the top of the frequency
response of those media. However, the actual frequency responses vary
widely and are much more of a continuous curve. That said, I think
CoolEdit's numbers are rather generous.

It is possible that the relationship of the recorded frequencies to the
sampling rate can have audible effects (intermodulation distortion,
resulting in combination tones), though Dan Wolf's anecdotes are the only
evidence I've heard of that these artifacts are audible down in musical
frequency ranges (say, the range of the piano). Most texts present them as
only audible when close to the Nyquist itself. Of course, Dan records some
highly specialized music, and I've never had a problem with this.

I've also recorded and synthesized quite a few noisy sources, including
cymbals, and I've never had any trouble with frequency content above 1/3 to
1/4 the sampling rate (at least with modern anti-imaging filters). If you
have any references of studies of this effect, let me know.

Of course, sampling rate is only part of the equation. The other main part
is the bit depth (number of bits per sample), which determines
signal-to-error ratio and thus dynamic range. Other issues include dither
and granulation noise, and all are discussed well in Ken Pohlmann's books
on digital audio.

Bill

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