Frequency-domain design method for linear-phase and minimum-phase FIR equalizers

First the author shows that generally, the attenuation of equalizers should be optimized rather than their magnitude responses. Then he presents an algorithm for the design of linear-phase finite-impulse response (FIR) filters with Chebyshev approximation of desired attenuation functions. The design is quite similar to the Parks-McClellan algorithm, with two decisive deviations. The first concerns the choice of a weighting function, and secondly, the Remez algorithm is modified in order to be able to approximate also nontrivial attenuation functions. Finally, the design is extended to minimum-phase FIR filters, which can also equalize the phase response of minimum-phase systems. It is shown here that phase optimization is a consequence of attenuation optimization.