An algorithm for the design of digital filters with finite-wordlength coefficients

This paper presents a novel algorithm for the discrete optimization of the coefficients of digital filters implemented as direct, parallel, or cascade structures. This optimization takes into account arbitrary magnitude specifications. The proposed algorithm is based on several aspects of discrete optimization (e.g. one-variable, two-variable and random search) and on the relation between DC gain and coefficients in a digital filter. Several examples are provided and the results obtained for them are compared with those given by four other methods recently published [2, 3, 5, 10] . The effectiveness of the proposed algorithm is subsequently discussed : For small scale examples [2, 3, 10] , results are very similar to those of some more "mathematical" methods (such as Branch-and-Bound) [2, 3] and, at least for the examples provided elsewhere, better than the results of another heuristic method [10]. For a larger scale example (8th order elliptic filter) [5] the proposed algorithm is shown to be fairly fast, while Branch-and-Bound methods are likely to be more time consuming.