Digital Hilbert Transformers Composed of Identical Allpass Subfilters

In this paper we introduce digital Hilbert transformers composed of identical allpass subÞlters that are interconnected via extra multipliers. In the simplest case the overall transfer function corresponds to M Hilbert transformers in cascade where each transformer is derived by frequency shift of a half-band IIR Þlter. The overall transformer can also be designed to have a smaller passband ripple than for a pure cascade design. The values for the extra multipliers are computed using simple recurrence formulas. One advantage of the proposed structures is that the sensitivity to coefÞcient errors of the recursive parts, i.e. of the allpass subÞlters, are lower than for the corresponding conventional structures. One consequence of this is that the maximal sample frequency is higher for the new structures. Since the coefÞcients of the allpass subÞlters in the new structures are shorter, the overall arithmetic complexity can under certain conditions also be reduced. Examples are included that demonstrate this.