Iterative algorithms for envelope constrained recursive filter design via Laguerre functions

The envelope constrained (EC) filtering problem is concerned with the design of a time-invariant filter to process a given input pulse such that the output 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. An iterative algorithm for solving this QP problem is proposed. We also show that for the EC filtering problem, filters based on Laguerre functions offer 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