The Sinc Function

The sinc function, or cardinal sine function, is the famous ``sine x over x'' curve, and is illustrated in Fig.D.2. For bandlimited interpolation of discrete-time signals, the ideal interpolation kernel is proportional to the sinc function

where denotes the sampling rate in samples-per-second (Hz), and denotes time in seconds. Note that the sinc function has zeros at all the integers except 0, where it is 1. For precise scaling, the desired interpolation kernel is sinc, which has a algebraic area (time integral) that is independent of the sampling rate .

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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.