The envelope-constrained(EC) filtering problem is to design a time-invariant filter in order to minimize the effect of input noise or disturbance while satisfying the time-domain constraint that the noiseless response of this filter to a specified excitation fits into a prescribed level. In this paper, using discrete-time Laguerre function and ∞-norm minimization, the envelope-constrained IIR filter design problem has been reformulated as a $H_∞$ model matching problem. and solved by using a convex optimization techniques. In cases in which the input signal is subject to random disturbance with unknown but bounded power spectrum, the ∞-norm minimization approach would offer a more robust filter.
To illustrate the better performance of the proposed design algorithm, a numerical example is presented which is concerned with the design of an equalization filter for a digital transmission channel.
