Coefficients and generating functions of sincN FIR filters

Sinc
^N
FIR filters are used in a number of digital signal processing applications. They are constituted of a cascade of N sinc filters, each of length M. Straightforward recurrence relations for fast computation of the impulse response coefficients can be derived using Z-Transform techniques. A simple general expression, valid for all the filter coefficients, can be obtained as well. Moreover, generating functions for the transfer functions of sinc
^N
FIR filters are presented.