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

sinc

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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