ABSTRACT
Abstract. In this work, we present a number theoretic approach to obtaining new polynomial transforms that may be used to compute two-dimensional cyclic convolution of sequences defined in finite integer and complex integer rings. A fundamental result of this work is that under the non-restrictive condition, (N 1, M) = (N 2, M) = 1, the polynomial transforms defined in finite integer rings are as intensive computationally as the polynomial transforms defined in rational and complex rational number systems only in the worst case. They simplify considerably for many special cases of significance in digital signal processing.
