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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.