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The Manifold Joys of Conformal Mapping: Applications to Digital Filtering in the Studio

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Conformal mapping is a well-known technique for modifying the cut-off or resonant frequencies of filters. Conformal mapping is applied to the problem of digital filters for professional audio production. Methods are examined for computing the coefficients of presence filters, such as parametric equalizers with or without shelving, and of band-pass or band-reject filters. Formulas are given for the coefficients of these filters in terms of the specifications (center frequency, boost/cut, and so on), which are exact and relatively straightforward to compute. A new kind of shelving filter is introduced that is equiripple in the passbands and can have an arbitrarily narrow transition band (with increasing filter order).

JAES Volume 31 Issue 11 pp. 826-841; November 1983
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AES - Audio Engineering Society