Fractional Indexes Impulse Responses Approximation for Discrete-Time Weyl Symbol Computation

Abstract

Time-frequency transformations including definitions of the Weyl symbol and generalised Weyl symbol are well known tools for linear time-varying systems analysis. Unfortunately known discrete-time analogy to Weyl symbol uses only half of the information contained in the discrete-time system transfer operator (system impulse responses with even indexes differences are only taken account for the computation). Moreover the method cannot be used for computation of the discrete-time analogy to generalized Weyl symbol. In the paper a novel computation approach is proposed. First of all the concept of fractional indexes for discrete-time systems is introduced. Secondly the algorithm for approximation impulse responses of the discrete-time system with fractional impulse responses is proposed. Our method can be used for computation of the generalised Weyl symbol as well as for computing Weyl symbol based on full information available in the discrete-time system transfer operator. Differences between the existing and the proposed computation method for Weyl symbol are illustrated on the numerical example in the time domain.