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.^E.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 [340]. 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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written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.