Multiple FIR filters on a finite ring

Abstract

Efficient design techniques for implementing a bank of recursive FIR (finite-impulse response) filters are introduced. The bank of filters is transformed to an equivalent single recursive FIR filter on a finite ring, using the integer residue ring isomorphism directly derived from the Chinese remainder theorem. This equivalent filter provides an efficient implementation scheme on a general-purpose computer. Design schemes are described for bank sizes ranging from two to five. Proper choices of moduli numbers and the residue arithmetics are presented, along with the efficient Chinese remainder transform algorithms for the chosen moduli. >