Envelope-constrained IIR filter design via H∞ optimization methods

Previously, the envelope-constrained (EC) filtering problem was formulated as designing an infinite impulse response (IIR) filter such that the filter´s l₂ norm is minimized, subject to the constraint that its response to a specified input pulse lies within a prescribed envelope. In this paper we recast this filter design problem as a frequency-domain H_∞ optimization problem with time-domain constraints. Motivations for solving this problem are given. Then, the recently developed H_∞ optimization techniques are used for the design of the required IIR filter. For illustration, we apply the approach to two numerical examples which deal with the design of equalization filters for digital transmission channels