## Sampling Theory

Nowadays, audio processing is typically carried out in discrete time.
As a result, *sampling theory* is fundamental to digital audio
signal processing. The sampling theorem is credited to Harold Nyquist
(1928), extending an earlier result by Cauchy (1831) based on series
expansions. Claude Shannon is credited with reviving interest in the
sampling theorem after World War II when computers became
public.^{A.8} As a
result, the sampling theorem is often called ``Nyquist's sampling
theorem,'' ``Shannon's sampling theorem,'' or the like. The
*sampling rate* has been called the ``Nyquist rate'' in honor of
Nyquist's contributions [333]. Often in common
usage, however, the term ``Nyquist rate'' is used to refer instead to
*half* the sampling rate. To preserve the historically correct
meaning, we might encourage use of the term *Nyquist limit* to
mean half the sampling rate, and simply say ``sampling rate'' instead
of ``Nyquist rate'', so as to minimize confusion.

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