Multiple fir digital filters on a complex integer residue ring
Hideo Murakami · Electronics and Communications in Japan (Part I Communications) · 1987
Abstract This paper proposes recursive and non‐recursive multiple filters, as a method to realize efficiently a bank of FIR filters on a finite ring. Both types are essentially the application of the isomorphism of the integer residue ring based on the Chinese remainder theorem. For the recursive multiple filter, a bank of filters is realized based on the transfer function defined by z‐transform on the recently introduced complex integer residue ring. Under the isomorphism of the residue ring, the equivalent single filter to the filter bank is realized. For the nonrecursive multiple filter, the number‐theoretic transform on the complex integer residue ring is used to realize the filter based on the equivalence similar to the recursive case. This paper emphasizes the recussive multiple filter. The integer of the form 2n‐1 is proposed as the modulus for the residue operation to be used in the design. The determination of the factors of such an integer and the construction of the residue operation unit are discussed. Finally, the multiple filter is evaluated, and a design example is shown.