VARIATION OF INITIAL PARAMETERS OF WEIGHTED CHEBYSHEV APPROXIMATION IN MULTIPLIERLESS FIR FILTER DESIGN
Alexander T. Mingazin · 2005
A variation of initial parameters of weighed Chebyshev approximation for multiplerless FIR linear phase digital filter design is used. Design examples are presented. 1. Introduction. For synthesis of digital filters with finite wordlength coefficients, in particular mul- tiplierless, the various algorithms based on a variation of coefficients (VC) either initial parameters (VIP) or their combination are applied. Good potential opportunities of VIP in a window method (VIP/Window) are shown on examples of multiplierless FIR linear phase digital filter design (1). In the window method the elementary expressions for computation of coefficients (that depends on a type win- dow) are frequently used but it can give the overestimated filter length N. An optimum method of FIR filter design is weighted Chebyshev approximation (WCA), and the most effective means for its perform- ance is the Remez exchange algorithm (2). In literature the appropriate filters often name as optimum FIR linear phase digital filters. The use of VIP for these filters can lead to more simple multiplierless struc- tures in comparison to the VIP/Window method. Coefficients of optimum filters are not explicit functions of approximation parameters and are defined numerically. In this connection VIP/WCA algorithms will be essentially more slowly than similar VIP/Window algorithms but they can be faster in comparison to VC procedures. The aim of given paper is to show opportunities of the VIP/WCA method for multiplier- less FIR filter design. After statement of the problem and description of certain possible VIP algorithms, the results for set of design examples are presented and their comparison to the known received by VC solutions is lead. 2. Statement problem. The design problem of multilierless FIR digital filters with application of the VIP/WCA we shall formulate as ) ( S