Z-Transform based method for coefficient computation and generating function derivation for sincN FIR filters

Sinc^N FIR filters, constituted of a cascade of N sinc filters, each of length M, are encountered in digital signal processing applications. It is shown that the use of Z-Transform techniques is an efficient method to derive straightforward recurrence relations for fast computation of the impulse response. A simple general expression, valid for all the filter coefficients, can also be obtained. In addition, generating functions for the sinc^N FIR filters transfer functions are given.