On the multidimensional prediction and filtering problem and the factorization of spectral matrices

✍ Scribed by E. Wong; J.B. Thomas

• Publisher: Elsevier Science
• Year: 1961
• Tongue: English
• Weight: 461 KB
• Volume: 272
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(61)90735-9

✦ Synopsis

Since the liuear prediction and filtering of nmltiple correlated stationary randonl signals involves the solution of a matrix integral equation, several methods of solution of this equation have been developed. In this paper the direct solution by complex variable techniques is extended from the one-dimensional case. The problem reduces to the factorization of a spectral density matrix and this factorization is the principal topic of the paper.

Under very general conditions, a factorization procedure has been developed by Wiener and Masani (1) 3 for discrete time series. Their technique is applied here with some modifications to the factorization of the spectral density matrices of continuous processes. A simplified procedure is developed also for the case where the elements of the spectral density matrix are rational functions of frequency. Examples illustrate the general technique and the simplified procedure.