Theory of filter banks over finite fields

The theory of digital filter banks for subband coding is well developed. The purpose of this paper is to develop an analogous framework for the multiresolution analysis of sequences of elements belonging to a finite field. The discussion starts with analysis of decimation and interpolation over finite fields. N-band digital filters are defined over finite fields. Then filter banks are studied. A design theory of orthogonal and biorthogonal filter banks is advanced and examples are given.