Hilbert transformers have found many signal processing applications, from single-sideband communication systems to audio effects. IIR implementations are attractive for computational efficiency. In this paper, we present a complete design procedure for an efficient IIR Hilbert transformer filter. We start from a half-band filter design, and show how the poles move as the half-band filter is transformed into summed all-pass filters and then into a Hilbert transformer filter. The design technique is based entirely on pole locations, and creates a numerically robust filter in cascaded first-order allpass form.
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