Iterative algorithms for envelope constrained recursive filter design via Laguerre functions

The envelope constrained (EC) filtering problem is concerned with the desig n of a time-invariant filter to process a given input pulse such that the o utput waveform is guaranteed to lie within a prescribed output mask. Using the orthonormal Laguerre functions the EC filtering problem can be posed as a quadratic programming (QP) problem with affine inequality constraints. A n iterative algorithm for solving this QP problem is proposed. We also show that for the EC filtering problem, filters based on Laguerre functions off er a more robust and low-order alternative to finite impulse response (FIR) filters. A numerical example, concerned with the design of an equalization filter for a digital transmission channel, is presented to illustrate the effectiveness of the iterative algorithm and the Laguerre filter.