New improved method for the design of weighted- Chebyshev, nonrecursive, digital filters

Two techniques are described which can be used in the design of weighted-Chebyshev nonrecursive digital filters. The first technique is a new initialization scheme for 3-band filters which improves convergence in the design of bandstop filters. The second technique is an improved search algorithm which can be used to locate the maxima of the error function. It incorporates cubic interpolation with a selective step-by-step search and it replaces the exhaustive step-by-step search proposed by Rabiner, McClellan, and Parks in the past as well as the selective step-by-step search proposed by Antoniou recently. The two techniques as well as an improved technique for the rejection of superfluous maxima of the error function, proposed recently by Antoniou, are used to construct a filter-design package which can be used for the design of equiripple nonrecursive filters. When applied for the design of a large number of low-pass, high-pass, bandpass, and bandstop filters, the new design method leads to an average saving in the amount of computation of about 87 percent relative to the amount required by the Rabiner, McClellan, and Parks method. It is demonstrated that this improvement is achieved without degrading the robustness of the Remez exchange algorithm to a significant extent.