Nearly monotonic passband low‐pass filter design by using sum‐of‐squared Legendre polynomials

Abstract

SUMMARYA new type of filter approximation, which utilizes orthonormal Legendre polynomials, referred to as sum‐of‐squared Legendre polynomials, is presented in this paper. Power transmission coefficient and the group delay of the proposed filter are compared with those of the Butterworth, Legendre–Papoulis, and Halpern filters. In order to illustrate the design of the proposed filter function, sum‐of‐squared Legendre polynomials coefficients and normalized element values of the low‐pass LC (inductor‐capacitor) ladder network prototype are given, up to the 10th degree. For continuous‐time domain filtering, doubly terminated LC ladder network topologies have very low sensitivities to changes of component values. In order to determine the effect of variation of all reactive components on the filter attenuation characteristic, the new sensitivity function has been proposed. Copyright © 2015 John Wiley & Sons, Ltd.