AUTOREGRESSIVE STATE-SPACE APPROACH FOR NUMERICAL SIGNAL ANALYSIS

The basic operations in numerical discrete-time signal processing are the differentation, integration and interpolation. The performance of the conventional algorithms usually decreases when the signal contains additive noise. In this work we introduce a novel autoregressive stat e-space approach for numerical treatment of discrete-time signals, whe re the signal is parametrized via the autoregressive AR(p) process usi ng the SVD based subspace method. An autoregressive state-space model is then constructed, where the state transition matrix is obtained fro m the AR(p) coefficients. The numerical algorithms perform as operatio n matrices based on the state transition matrix. The proposed method c ombines differentation, integration and interpolation into one general operation. With this method integration and derivation can be employe d fractionally, and furthermore it allows the computation of fractiona l complex derivatives and integrals. (C) 1997 Elsevier Science B.V. Al l rights reserved.