Lesson C Estimation and Applications of Higher-order Statistics

Summary

Higher-order statistics can either be estimated from data or computed from models. In this lesson we learn how to do both. Cumulants are estimated from data by sample-averaging techniques. Polyspectra are estimated from data either by taking multidimensional discrete-time Fourier transforms of estimated cumulants or by combining the multidimensional discrete Fourier transform of the data using windowing techniques. Because cumulant and polyspectra estimates are random, their statistical properties are important. These properties are described.

Just as it is important to be able to compute the second-order statistics of the output of a single-input, single-output dynamical ...

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