Parametrizations in digital system design

Abstract

In the early days, a digital filter characterized by its transfer function was usually implemented directly in one of several possible ‘canonical forms’— more often called ‘direct forms’ in the signal processing community — because these forms minimize the number of coefficients and arithmetic operations that are required. A minimal number of coefficients corresponds to minimal complexity, an attribute that may be important if the operation count or memory space plays a significant role. It was found, however, that the performance of a digital filter implemented in these forms can be seriously degraded by Finite Word Length (FWL) effects. In fact, these structures have undesirable numerical properties as will be made clear throughout this book. This problem can be partially alleviated by the use of other parametrizations of the filter such as the parallel and cascade forms of a series of first or second order sub-filters.