Nonrecursive multiple filters on an integer residue ring

The finite ring is used for efficient computation of filters. This paper discusses nonrecursive multiple filtering systems on an integer residue ring. The number theoretic transform, which is the Fourier transform on the finite ring, has been used for the design of FIR digital filter on an integer residue ring. A set of filters can be combined to a single filter on a finite ring, using the isomorphism derived from the Chinese remainder theorem. This equivalence is used to compute the outputs of the set of filters efficiently. An efficient algorithm is also presented to find a primitive 2t-th root of unity which is needed for the construction of the numbers theoretic transform. For filtering multiplicity ranging from two to five, possible choices of moduli are presented. Finally, an example and evaluations of the nonrecursive multiple filter are shown.