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Tutorial on higher-order statistics (spectra) in signal processing and system theory: theoretical results and some applications

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1 Author(s)
Mendel, J.M. ; Dept. of Electr. Eng.-Syst., Univ. of Southern California, Los Angeles, CA, USA

A compendium of recent theoretical results associated with using higher-order statistics in signal processing and system theory is provided, and the utility of applying higher-order statistics to practical problems is demonstrated. Most of the results are given for one-dimensional processes, but some extensions to vector processes and multichannel systems are discussed. The topics covered include cumulant-polyspectra formulas; impulse response formulas; autoregressive (AR) coefficients; relationships between second-order and higher-order statistics for linear systems; double C(q,k) formulas for extracting autoregressive moving average (ARMA) coefficients; bicepstral formulas; multichannel formulas; harmonic processes; estimates of cumulants; and applications to identification of various systems, including the identification of systems from just output measurements, identification of AR systems, identification of moving-average systems, and identification of ARMA systems

Published in:

Proceedings of the IEEE  (Volume:79 ,  Issue: 3 )