Algorithm for the reduction of the order of recursive digital filters

Recursive digital filters of high order are necessary to provide a sharp cut-off response; the implementation of these necessarily involves high cost. This paper presents an algorithm for the design of lower order filters whose amplitude response approximates those of higher order filters. The algorithm makes use of the phase correction technique PCT 1 applied to the numerator and denominator of the filter separately and the filter is then stabilized, using the technique of 2. The algorithm is iterative in nature, the error being defined as the integral of the squared difference between the frequency response of the high and low order filter. Convergence of the algorithm is discussed and examples show that the error decreases within the first few iterations and then remains practically constant.