The following figure shows the distribution of the auto-term and the cross-term of a multi-component signal in both the ambiguity and the Wigner distribution function.

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For multi-component signals in general, the distribution of its auto-term and cross-term within its Wigner distribution function is generally not predictable, and hence the cross-term cannot be removed easily. The following is an example that demonstrates how the cross-term is filtered out. The definition of Wigner distribution is as follows:. The Rihaczek and Choi—Williams distributions are examples of affine invariant Cohen's class distributions. The kernel of Choi—Williams distribution is defined as follows:.

The kernel of Rihaczek distribution is defined as follows:. See Transformation between distributions in time-frequency analysis. More such QTFDs and a full list can be found in, e. A time-varying spectrum for non-stationary processes is defined from the expected Wigner—Ville distribution.

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Locally stationary processes appear in many physical systems where random fluctuations are produced by a mechanism that changes slowly in time. Such processes can be approximated locally by a stationary process. For locally stationary processes, the eigenvectors of K are well approximated by the Wigner—Ville spectrum. From above we can write. Here, the Wigner—Ville stochastic integral is interpreted as a mean-square integral: [2]. From Wikipedia, the free encyclopedia. This article includes a list of references , but its sources remain unclear because it has insufficient inline citations.

## Time-Frequency Signal Analysis and Processing

Please help to improve this article by introducing more precise citations. November Learn how and when to remove this template message. Main article: Wigner distribution function. Main article: Ambiguity function. Main article: Modified Wigner distribution function.

### Time-Frequency Signal Analysis and Processing

Main article: Cone-shape distribution function. Categories : Signal processing Fourier analysis Digital signal processing Time—frequency analysis. Hidden categories: Articles lacking in-text citations from November All articles lacking in-text citations. Namespaces Article Talk.

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## OSA | Time-frequency methods for coherent spectroscopy

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