Time-domain distortion as criterion for design of IIR Hilbert transformers

The ideal Hilbert transformer can be defined as the system with unity magnitude and odd-symmetric impulse response. Based on this definition, the measure for time-domain distortion of transformed signal is defined. The measure is suitable for the design as well as for the comparison of the IIR all-pass Hilbert transformers. These applications are illustrated by examples, which consider the relationship between the transformers designed in the frequency domain and the transformers obtained by minimization of the proposed measure. It is shown that, under certain conditions, the least-squares approximation is suboptimal in the sense of time-domain distortion.