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Lessons in Estimation Theory for Signal Processing, Communications, and Control, Second Edition by Jerry M. Mendel - Department of Electrical Engineering, University of Southern California, Los Angeles, California

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Lesson B Introduction to Higher-order Statistics

Summary

When signals are non-Gaussian, higher than second-order statistics can be very useful. These higher-order statistics are called cumulants and are related to higher-order moments. We prefer to use cumulants rather than higher-order moments because cumulants have some very desirable properties, which moments do not have, that let us treat cumulants as operators.

Higher-order statistics are defined in this lesson. In general, they are multidimensional functions; e.g., third-order statistics are functions of two variables and fourth-order statistics are functions of three variables. Cumulants, which are analogous to cor-relation functions, work directly with signals in the time domain. Polyspectra, ...

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