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Application to Audio Filter Design

Frequency warping is generally employed in audio filter design by

  1. warping the desired frequency response, thus ``horizontally stretching'' the more important low-frequency region of the spectrum.
  2. performing a filter design over the warped frequency axis, and
  3. transforming the resulting filter to eliminate the frequency warp, returning it to the normal frequency axis.
The third step may be carried out using a conformal map (i.e., substituting some rational-function-of-$ z$ for $ z$ in the filter transfer function). Since bilinear-transform frequency-mappings are first order, when the resulting filter transformed back to unwarped form, its order remains the same [258].

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``Spectral Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2011, ISBN 978-0-9745607-3-1.
Copyright © 2021-11-23 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University