It has long been assumed that in order to provide sets of filters with arbitrary frequency responses but matching phase responses, symmetrical, finite impulse response filters must be used. A method is given for the construction of sets of infinite impulse response (recursive) filters that can achieve this aim with lower complexity, power, and delay. The zeros of each filter in a set are rearranged to provide linear phase while the phase shift due to the poles of each filter is counteracted by all-pass compensation filters added to other members of the set.
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