Design of digital filters with amplitude and group delay specifications

This paper considers the design of a digital filter with prescribed magnitude and group delay specifications. First, we outline the derivation of the phase and group delay functions of an Nth order digital Laguerre filter and show that the group delay function of the filter can be written as a ratio of quadratic functions in the filter coefficients. Then, we formulate our filter design problem as a constrained L₂ space minimization problem in which the performance requirement on the group delay and magnitude in the pass-band are treated as constraints while minimizing the L₂ norm of the error function between the designed and the desired filters. Methods for solving the proposed nonlinear optimization problem are outlined. Numerical results are presented to illustrate the usefulness of the proposed method. As a special case, corresponding results for general FIR filters are also derived.