Transform decomposition in two-dimensional digital filter realization (Q1062955)

The Very Large Scale Integrated (VLSI) circuit requires powerful parallel filter structures with small interconnections between modules. In the paper some transform decompositions that meet this requirement are investigated in the connection with the two-dimensional filter realization. The transforms under investigation are rectangular, fast Fourier and Walsh-Hadamard ones. The idea for all these three situations is to factorize a two-variable polynomial H over a field F by division modulo a polynomial product of irreducible factors over F. The reconstruction is achieved by the use of the Chinese remainder theorem. The decomposition is discussed for finite impulse response filters as well as for infinite response filters. Finally, a comparison between the proposed method and other methods used in the literature is presented. We think the paper represents a basic contribution to the theory of digital filtering and at the same time is a convincing example for the power of modern algebra in the area of circuit theory.