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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