Selected problems of frequency analysis for time varying, discrete-time systems using singular value decomposition and discrete Fourier transform

The paper develops tools and methods for linear time-varying, discrete-time systems analysis. It consists of two parts. The first one gives a theoretical background. There are definitions and numerical algorithms for approximating frequency characteristics. The main method is based on singular value decomposition, discrete Fourier transform and power density spectrum approach. The second part of the paper contains numerical examples. Six different models have been analyzed. Three for frequency characteristics approximation and the other three for evaluating the degree of system non-stationarity. Some of the models are time-variant and some are time-invariant. For better evaluation, results yielded by the proposed method are compared with classical Bode characteristics.