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

3.2. WSS processes and spectral measure

In this section it will be interesting to note the influence on the spectral density of the temporal spacing between the r.v. For this reason we are now about to consider momentarily a WSS process images where θ is a constant and where has the significance of duration.

3.2.1. Spectral density

DEFINITION.– We say that the process Ximagesθ possesses a spectral density if its covariance images can be written in the form: images and SXX (u) is then called the spectral density of the process Ximagesθ.

PROPOSITION.–

Under the hypothesis images:

1) the process Ximagesθ admits a spectral density SXX;

2) SXX is continuous, periodic of images period, real and even.

Figure 3.2. Covariance function and spectral ...

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