Implementation of real coefficient two-dimensional denominator-separable digital filters based on decomposition techniques

Abstract

In the paper, the implementation of two-dimensional digital filters is dealt with for the processing of real sequences. The approach is based on decomposition techniques to obtain separable one-dimensional polynomials from a two-dimensional polynomial, and then one-dimensional techniques are used to express the one-dimensional transfer functions as a sum of two reduced-order transfer functions with complex coefficients. Thus, new realisation structures are obtained for the equivalent reduced-order complex-coefficient transfer functions for the processing of real sequences. The authors concentrate more on two-dimensional denominator-separable digital filters and also confine themselves to the parallel-form structures as the emphasis is now on low data throughput delay and high parallelism due to recent advances in VLSI technology. All these structures consist only of one-dimensional first-order minimum-norm sections. Thus, these structures possess low round-off noise and freedom from overflow limit cycles. A comparison of different structures is made based on data throughput delay, efficiency in multiprocessor environment and round-off noise properties.