On chebychev approximations for FIR digital filter design

Abstract

An iterative minimax approximation technique, based on the Lawson``s algorithm coupled with the weighted least square approximation is proposed for the design of linear phase FIR discrete filters. The Lawson``s algorithm is an iterative approximation technique which minimizes a Chebychev error norm. For each iteration, the weight is adjusted according to the approximation errors of the previeous iteration and the weighted least square approximation using the adjusted weight is made. The technique is quiet general and can be applied to the design of various types of FIR discrete filters including one and two dimensional FIR digital filters, non-uniformly sampled discrete filters and two-dimensional hexagonally sampled FIR digital filters. New design technique is especially useful for the design of two-dimensional FIR digital filters and two dimensional hexagonally sampled FIR digital filters, for which there are only a few design techniques proposed thus far. The existing techniques are computationally very complex and it is difficult to visualize the design processes. The efficiency of the new design technique based on the Lawson``s iteration is directly related to an efficient implimentation of the weighted least square approximation using FFT and vector Toeplitz inversion. To demonstrate the capabilities of the new technique, several cicular symmetric two-dimensional FIR digital filters are designed. The results are comparable to the filters designed using the accent exchange algorithm. The new design technique allows design of filters of size as large as 25 * 25 without exponential increase in computation time. Besides the ability of large size filter design, another advantage of the new technique is that it can be directly applicable to the design of non-rectangularly sampled FIR filters such as hexagonally sampeld FIR digital filters. Several examples of hexagonally sampled FIR digital filters are also shown. As an alternative to Lawson``s iteration, Bandl...