Autoregressive state-space approach for numerical signal analysis

Abstract 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 state-space approach for numerical treatment of discrete-time signals, where the signal is parametrized via the autoregressive AR( p ) process using the SVD based subspace method. An autoregressive state-space model is then constructed, where the state transition matrix is obtained from the AR( p ) coefficients. The numerical algorithms perform as operation matrices based on the state transition matrix. The proposed method combines differentation, integration and interpolation into one general operation. With this method integration and derivation can be employed fractionally, and furthermore it allows the computation of fractional complex derivatives and integrals.