O'Reilly logo

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

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

3.4. Introduction to digital filtering

We suppose again that θ = 1.

Given a WSS process Ximages and a sequence of real numbers h = {hjimages|jimages}, we are interested in the operation which at Ximages makes a new process Yimages correspond, defined by:

images

(h 0T0 is also denoted as h1 where 1 is the identical mapping of L2 in L2).

In what follows we will still assume that images; this condition is generally denoted himages1 and is called (for reasons which will be explained later) the condition of stability.

DEFINITION.– We say that the process Yimages is the transform (or filtration) of the process X by the filter and we write =

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required