A closed theory for the measurement of linear distortions

The present investigation is concerned with the distortions of linear time-invariant systems, taking into account attenuation distortion and phase distortion. The classical theory for the study of linear distortions is analyzed. It is found that, in general, neither group delay nor phase delay measurements provide necessary and sufficient criteria for a transmission which is free of phase distortion. It is not possible to derive measures for the quality of the transmission on the basis of such measurements. A formulation for the characterization of phase distortion considered for all-pass filters is used as a starting point for the development of a closed theory regarding the measurement of distortion. An approach is shown for the design of a 'fidelity evaluation function' according to Shannon and Weaver (1969). The relation of this function with the defined distortion measures is shown. An approach is illustrated for obtaining the distortion measures directly from this function in the time and frequency domain.