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Properties of the frequency SVD-DFT for discrete LTV systems based on first order examples
(2006) Orlowski, Przemyslaw; Technical University of Szczecin
The paper develops frequency analysis tools for linear time-varying (LTV), discrete-time systems. The main method is based on the properties of the Singular Value De-composition (SVD), Discrete Fourier Transform (DFT) and Power Spectral Density (PSD). The analysis is carried out for a system with first order dynamics. The general objective of this paper is to examine how system frequency diagrams are depend on the variability of particular parameters. Especially, it is examined how the variability of three matrices of the state space model (scalars, in the 1st order case) influence the approximated Bode diagrams. A few cases of the variability of each matrix, in particular with different frequencies and phase shifting, are considered. Moreover, the analysis is carried out for different cases of the system parameters. The results of analysis for each case are shown in four diagrams: amplitude, phase, impulse and step responses. On the basis of these examples the most important features in each example are characterized.