The locally quasi-stationary processing by the sigular value decomposition

A parametric analysis of non-stationary signals is one of the most difficult problems in digital signal processing. In this paper a locally quasi-stationary processing is proposed to give an autoregressive model with time-varying parameters precisely. The processing is a kind of block least-squares estimation. In a locally stationary processing, the fixed p-dimensional parameters in a finite interval are estimated. On the other hand, the locally quasi-stationary model has the extra p-dimensional parameters. The new added components are the first-order deviations of the time-varying parameters. The 2p-dimensional parameters are estimated straightforwardly by solving the normal equation of the model. The singular value decomposition technique allows us to get the solution without noticing information about the rank deficiency of the model matrix in the applications to biomedical signals. The computer simulation and the experimental results of electromyogram are given to demonstrate the efficiency of the method.