Probability, Random Variables, and Random Processes: Theory and Signal Processing Applications

B.14 SINC FUNCTION

Definition: Sinc Function The sinc function is

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Note that π is not shown explicitly in the notation sinc(x). The sinc function is plotted in Figure B.8, demonstrating that the zero crossings occur for except zero. There is a form of this function used primarily in mathematics that does not include π, given by

Figure B.8 Sinc and Sa functions.

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which is also plotted in Figure B.8. It is also called the unnormalized sinc function, and its zero crossings occur at integer multiples of π except zero.

The sinc function is related to the gamma function (described in Section B.15) as follows:

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The sinc function and the rectangle function are a Fourier transform pair:

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which shows that it has unit area:

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The sinc function can also ...