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
sincwhere 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 .
Reconstruction from Samples--The Math
Reconstruction from Samples--Pictorial Version