Splitting Magnitude Response into Real and Imaginary Parts

Institute for Material Mechanics, University of Latvia, Riga LV 1006, Latvia

^* Corresponding author: strauss@pmi.lv

Abstract

The determination of real and imaginary parts from magnitude responses is studied for causal linear time-invariant systems having monotonic impulse responses. It is demonstrated that the problem can be interpreted as a special filtering task in the Mellin transform domain having a diffuse magnitude response bounded by the magnitude responses of the filters corresponding to zero and maximum imaginary parts prescribed by the Kronig-Kramers relations. Discrete-time filters processing geometrically sampled magnitude responses are designed for determining the real and imaginary parts. Testing results are presented verifying the performance of the filters.