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.