Special Signal Models and Extensions

Abstract

Until now, we have only considered the problem of predicting a process from its own subspace of past observations. The algorithms obtained for this simple case can, however, be extended to more involved problems. Assume that one needs to predict a process from the subspace of a related (correlated) process. This case is commonly referred to as the “joint-process” case of linear prediction. A second case of interest is system identification, where we assume not the simple AR process model, but possibly an MA (all-zero) process model, or even a more general ARMA (pole-zero) process model. This leads directly to the most general one-dimensional problem, namely, the identification of a multichannel (vector-autoregressive) process. In fact, it turns out that we can handle the MA (FIR) system identification problem with the joint-process approach, whereas the ARMA system identification problem can be embedded in a two-channel vector autoregressive process model.