Wave digital filters with minimum multiplier for discrete Hilbert transformer realization

This paper describes the design of wave digital filters for discrete Hilbert transformer realization. A method for designing real and complex half-band wave digital filters (WDFs) with a minimum number of multipliers is afforded where the multiplier coefficients for the adaptors are calculated directly from the digital domain transfer functions. This technique uses the equations derived for a class of infinite impulse response (IIR) filter and hence avoids the conventional technique of synthesizing a WDF from an analogue reference filter. The selection of the adaptor configuration is determined from the multiplier coefficient values. A minimum multiplier realization of real half-band WDFs can be obtained to meet the low-pass digital filter magnitude specifications. By applying a transformation equation, a complex half-band WDF suitable for the realization of the discrete Hilbert transformer with a minimum number of multiplier is obtained.