The simultaneous approximation of magnitude and phase by fir digital filters .1. A new approach

The non-linear problem of simultaneous approximation of the magnitude and phase by an FIR digital filter is studied, Usually this problem is solved indirectly by solution of the complex Chebyshev approximation problem of the frequency response of the filter, which can be described as a linear or non-linear convex semi-infinite programming problem. In the present first part of the paper the relationship between the magnitude/phase problem and the Chebyshev problem is investigated and an alternative approximate representation in the form of a convex semi-infinite programming problem is derived. The latter problem can be solved by the same methods for such problems which were used previously by the authors for the solution of (constrained) complex Chebyshev approximation problems. In part II of the paper some earlier approaches to FIR filter design are reconsidered and discussed with regard to the magnitude/phase problem, It is further demonstrated there by several examples of filter designs that the new approach of this paper leads to very good results. (C) 1997 by John Wiley & Sons, Ltd.