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A practical method is described for designing recursive digital filters with arbitrary, prescribed magnitude characteristics. The method uses the Fletcher-Powell optimization algorithm to minimize a square-error criterion in the frequency domain. A strategy is described whereby stability and minimum-phase constraints are observed, while still using the unconstrained optimization algorithm. The cascade canonic form is used, so that the resultant filters can be realized accurately and simply. Design examples are given of low-pass, wide-band differentiator, linear discriminator, and vowel formant filters.
K. Steiglitz (Mon,) studied this question.