Reference networks for simultaneous realization of complex IIR digital filters

The complex coefficients complementary IIR transfer function pairs (G/sub c/(z/spl circ/) and H/sub c/(z/spl circ/)) can be implemented by means of a single hypercomplex coefficients all-pass filter. In this paper, the construction method of transfer function with hypercomplex coefficients is proposed by extending the complex coefficients wave digital filters (CWDF) to the hypercomplex coefficients wave digital filters (HWDF). Introducing two types of theoretical imaginary resistance (jr and iR), we can construct analog lossless networks for the HWDF. The desired transfer function is obtained by converting the analog network to the HWDF. This construction method has low passband sensitivity.