30 November 1992 Higher-order Wigner distributions
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Higher-order Wigner distributions are not unique: definitions differ in the lag separations between the terms used in the time-domain product, as well as in how many of the terms are conjugated. We study a class of third-order WDs (TWD), parameterized by a single parameter (alpha) , and show that there is a duality between the choices of (alpha) equals -1/3 (Gerr's definition) and (alpha) equals -1. Interesting signal attributes, such as the instantaneous frequency, the derivative of the log-magnitude, and the group delay can be recovered from the TWD. Important issues such as aliasing problems and sampling requirements, and whether or not the analytic form of a real signal should be used, are addressed. It is shown theoretically that the TWD with (alpha) equals -1 is particularly useful for the detection of transients in the presence of colored Gaussian noise.
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Ananthram Swami "Higher-order Wigner distributions", Proc. SPIE 1770, Advanced Signal Processing Algorithms, Architectures, and Implementations III, (30 November 1992); doi: 10.1117/12.130951; https://doi.org/10.1117/12.130951

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