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Discrete Stochastic Processes and Optimal Filtering by Roger Ceschi, Jean-Claude Bertein

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3.5. Important example: autoregressive process

DEFINITION.– We call the autoregressive process of degree dimages any WSS centered Ximages process which verifies images:

images where Bimages is a white noise of power images.

The family of autoregressive processes of degree d is denoted by AR (d).

Thus ∀K, XK is obtained from the d previous values XK−d, …, XK−1 (modulo r.v. BK), which can be carried out using the following schema:

images

Figure 3.8. Autoregressive filter

The equality of the definition can be written: H(T) Ximages = Bimages where we have stated that .

This means that we can obtain X by the filtering of B through the filter H(T) whose ...

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