5.1 - What is sampling? What is a sampling rate?
Description
This article is from the Audio Professional FAQ, by with numerous contributions by Gabe M. Wiener others.
5.1 - What is sampling? What is a sampling rate?
Sampling can be (roughly) defined as the capture of a continuously
varying quantity at a precisely defined instant in time. Most usually,
signals are sampled at a set of sample-points spaced regularly in
time. Note that sampling in itself implies nothing about the
representation of sample magnitude by a number. That process is called
quantisation.
The Nyquist theorem states that in order to faithfully capture all of
the information in a signal of one-sided bandwidth B, it must be
sampled at a rate greater than 2B. A direct corollary of this is that
if we wish to sample at a rate of 2B then we must pre-filter the
signal to a one-sided bandwidth of B, otherwise it will not be
possible to accurately reconstruct the original signal from the
samples. The frequency 2B that is the minimum sample rate to retain
all of the signal information is called the Nyquist frequency.
The spectrum of the sampled signal is the same as the spectrum of the
continuous signal except that copies (known as aliases) of the
original now appear centred on all integer multiples of the sample
rate. As an example, if a signal of 20 kHz bandwidth is sampled at 50
kHz then alias spectra appear from 30 - 70 kHz, 80 - 120 kHz, and so
on. It is because the alias spectra must not overlap that a sample
rate of greater than 2B is required. In digital audio we are
concerned with the base-band - that is to say the signal components
which extend from 0 to B. Therefore, to sample at the standard digital
audio rate of 44.1 kHz requires the input signal to be band-limited to
the range 0 Hz to 22.05 kHz. [Chris]
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