CANONICAL REPRESENTATIONS OF SECOND ORDER PROCESSES WITH APPLICATIONS,
Abstract
Some second order random processes are modeled in this study as the output of a causal and causally invertible linear system driven by white noise. Such a model becomes significant in considering the whitening filter techniques of Bode and Shannon for solution of the Wiener filtering problem. In the whitening filter approach, the given observation process is replaced, without loss of information, by a white-noise process; and the linear least-squares estimation problem is then easily solved in terms of the equivalent process obtained by the whitening. The causal and causally invertible model, called the canonical representation (CR), is shown to specify the whitening filter for the process. For processes that are the sum of a white noise process and a smooth process, sufficient conditions for existence of the CR are shown in terms of the existence of solution of a Wiener-Hopf integral equation. The solution for additive white noise yields the CR for a large class of differentiable processes which have an additive white noise appearing in a derivative process. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1969
- Accession Number
- AD0698765
Entities
People
- Roger A. Geesey
Organizations
- United States Air Force Academy