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A Generalization of the Biquadratic Parametric Equalizer

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An efficient implementation of parametric equalizers is a cascade of biquadratic filter sections. Traditionally, a section operates in one of 3 operating modes offering Low Shelf, Bell Shaped or High Shelf families of responses. In either mode, each section offers 3 user parameters: Boost/cut gain G, corner frequency fc and bandwidth/slope Q. This paper describes the derivation and implementation of a new 4th user parameter, Symmetry, producing a smooth transition between the 3 above mentioned operating modes while retaining the meaning of the 3 conventional user parameters. All degrees of freedom in the bi-quadratic filter blocks are utilized. Therefore an inverse mapping exists, converting arbitrary (e.g. computer generated) biquadratic coefficient sets back into meaningful EQ parameters allowing further human interpretation and adjustment.

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