Generalised Fractional Indexes Approximation with Application to Discrete-Time Generalised Weyl Symbol Computation
AbstractUnique description of discrete-time, linear time-invariant systems on infinite time horizon requires only definition of finite number of coefficients, usually relatively small. In contradistinction the description of discrete-time linear time-varying systems requires in general definition of an infinite number of coefficients. Nevertheless neither analyzing nor processing data with infinite dimensional size is impossible. The main aim of the paper is to develop new generalised fractional indexes – computational method which allows to determine generalised Weyl symbol for arbitrary real a not only for a=±0.5 (integer indexes) and a=0. Parameter a allow to shape the set of parameterised impulse responses. The selection of the parameter a in the generalised Weyl symbol enable selection of the best accuracy region for the time-frequency transform. Numerical examples illustrates how the approximation of the system response with generalised fractional indexes increase accuracy for the computation of the discrete-time, time-frequency transformation calculated on finite time horizon. Ill. 4, bibl. 18 (in English; abstracts in English and Lithuanian).
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