A method for FIR filter design from joint amplitude and group delay characteristics

In this contribution we propose a method for the design of Finite Impulse Response (FIR) filters from joint specifications in amplitude and group delay responses. The fundamental concepts rely on the use of root moments, a set of parameters directly related to the transfer function of the desirable FIR filter. We derive appropriate relationships that link both the amplitude response and the group delay response of an FIR filter with the root moments of the required transfer function. From the relationship between the estimated root moments and the filter coefficients we finally determine the required transfer function. The results demonstrate that the proposed approach is eminently useful as a design tool.