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Summary of Results

In this paper we derive closed-form expressions for the poles and zeros of spectral roll-off filters having any desired slope to a controllable degree of accuracy. The accuracy desired and the bandwidth over which the approximation holds dictate the order of the filter required, but the basic structure of the filter never varies. The poles and zeros are all real, and they alternate, with exponentially increasing spacing (uniformly spaced on a log scale). A simple initial derivation can be based on Bode Plot analysis, as described in the next section.


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``Spectral Tilt Filters'', by Julius O. Smith IIIand Harrison F. Smith, adapted from arXiv.org publication arXiv:1606.06154 [cs.CE].
Copyright © 2021-06-18 by Julius O. Smith IIIand Harrison F. Smith
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA