Cross spectral analysis of nonstationary processes
- 1 July 1990
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Information Theory
- Vol. 36 (4) , 830-835
- https://doi.org/10.1109/18.53742
Abstract
Consideration is given to the generalization of stationary cross spectral analysis methods to a class of nonstationary processes, specifically, the class of semistationary finite energy processes possessing sample functions that are of finite energy almost surely. A new quantity called the time-frequency coherence (TFC) is defined, and it is demonstrated that its properties are analogous to those possessed by the stationary coherence function. The problem of estimating the TFC by using elements of L. Cohen's (1966) class of joint time-frequency representations is investigated. It is shown that the only admissible estimators are those based on the class of time-frequency smoothed periodograms. Thus, the familiar procedure of segmentation and (smoothed) short-time Fourier analysis cannot be improved upon (within the framework considered) by the use of the higher-resolution nonparametric time-frequency methods. Procedures for selection of the appropriate estimators and a possible application are suggestedKeywords
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