An approximation technique for the design of recursive digital and continuous filters with and without fixed zeros in the stop band

Abstract

The bilinear z-transformation has been used by various authors (Golden and Kaiser 1964, Broomer 1966) to design recursive digital filters. The necessity to select an equivalent. continuous filter makes this method very laborious. Remes exchange algorithm has also been used in the design of recursive filters (Remes 1957, Deczky 1974) but not will the same success as for the design of non-recursive filters (McClennan and Parks 1973. Holt et al. 1975 ) due to its dependence on the initial conditions on optimization methods. In this paper we-present a design technique, based on Remes second exchange algorithm. This provides a versatile approximation method for the design of a wide range of minimax-type digital recursive filters. Furthermore, the method is extended to the design of continuous filters using suitable mapping methods. In the examples given, filters arc designed with various frequency characteristics for the pass band and the stop band and also with predefined zeros in the stop band.