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

First we show that generally, the attenuation of equalizers should be optimized rather than their magnitude responses. Then we present 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, we modify the Remez algorithm in order to be able to approximate also nontrivial attenuation functions, Finally, we extend our design to minimum-phase FIR filters, which can also equalize the phase response of minimum-phase systems. We show that here, phase optimization is a consequence of attenuation optimization.