Spectral analysis of harmonic random processes in an unknown noise environment
Abstract
This work is concerned with identifying sums of periodic signals which have been corrupted by additive noise of unknown color. Specifically, it investigates a recently proposed multichannel point spectrum identification scheme of (FFS2), which utilizes the convergence properties of the sequence of minimum-variance spectral estimates. A number of technical issues associated with this scheme are developed and discussed, including convergence tests to identify signal frequencies and the associated spectral matrix. Two examples are utilized to demonstrate the theoretical and data-based performance of these tests for detecting signal frequencies, estimating the (matrix-valued) corresponding point spectrum, and determining the number of uncorrelated signal sources. This work also addresses this problem in the more general multichannel random field setting. Specifically, a method will be presented which utilizes the multichannel convergence-based method of (FFS2) designed for the random process setting. Rather than extend it to the random field setting, the method proposed will be applied to derived covariance data corresponding to each direction of the field. This data may be as simple as the covariance data in the prescribed direction, or it can encompass information contained in other directions as well. This information is then combined to arrive at the signal spectral information including wavenumbers and corresponding power matrices. A number of examples are presented to demonstrate the utility of the method.
Degree
Ph.D.
Advisors
Sherman, Purdue University.
Subject Area
Mechanical engineering
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