Optimum Filters of Even Orders with Monotonic Response

Recently, Papoulis has developed a new class of filters, which has the maximum cutoff rate under the condition of a monotonically-decreasing response. These new filters are based on the optimum monotonically-increasing polynomials of odd degrees. In this paper, the optimum polynomials of even degrees are presented in general forms, from which the optimum filters with monotonic response are derived. Characteristics of these filters are illustrated by several examples which include frequency response, pole locations and the ladder realizations.