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All-Pass Hilbert Filters

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This paper presents a method to generate all-pass filters whose phase is defined by the magnitude response of traditional IIR filter prototypes. The purpose of this is to make the overall shape of the filter controllable in an intuitive way so that the end user can specify arbitrary, but well-behaved, phase responses. At the core of the algorithm is the Hilbert transformer, which has been throughly studied with different implementations. However, with a simple modification we obtain the "Phase Displacer" which can produce an arbitrary constant phase shift at all frequencies. Expanding this idea per frequency we obtain the "Phase Equalizer": an all-pass filter whose shape is the magnitude response of either a shelving or peaking IIR filter.

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