DocumentCode :
1049733
Title :
Matrix-based higher order spectral analysis for three-wave coupling processes
Author :
Sherman, David Lee ; Zoltowski, Michael D.
Author_Institution :
Sch. of Electr. Eng., Purdue Univ., West Lafayette, IN, USA
Volume :
42
Issue :
2
fYear :
1994
fDate :
2/1/1994 12:00:00 AM
Firstpage :
332
Lastpage :
348
Abstract :
Composite linear and quadratic systems produce three-wave coupling when stimulated by random phase input sinusoids. Due to the nonlinearity of the system, the output frequencies are arithmetically related to the input. Using third-order cumulant statistics and their associated bispectrum, techniques are devised based on phase-insensitive matrix structures for detection and frequency estimation of coupling frequencies. The separation of the third-order cumulant series into symmetric and skew-symmetric portions allows one to exploit their characteristic eigendecompositions for frequency estimation. After symmetrization, biphases can be easily extracted as coefficients of the cumulant sequence. Using a generalized eigenvector representation, one can relate symmetric and skew-symmetric bases by a subspace rotation algorithm. Biphases can be estimated directly from generalized eigenvalues of the matrix pencil formed by symmetric and skew-symmetric matrices. The dimensionality of the matrices can be reduced through the use of cumulant projections that yield a slice of the bispectrum. The Radon transform procedure is related to bispectral processing through an isotropic radial-slice Volterra filter. The compact third-order Kronecker product matrix formulation and algorithms for coupling frequency estimation can also be converted for use in biphase estimation. Simulations showing the performance of the above procedures are also presented for both synthetic and biomedical time series
Keywords :
matrix algebra; parameter estimation; spectral analysis; Radon transform procedure; biphases; bispectral processing; compact third-order Kronecker product matrix formulation; coupling frequencies; detection; eigendecomposition; frequency estimation; generalized eigenvector representation; isotropic radial-slice Volterra filter; linear systems; matrix-based higher order spectral analysis; output frequencies; phase-insensitive matrix structures; quadratic systems; random phase input sinusoids; skew-symmetric portion; subspace rotation algorithm; symmetric portion; symmetrization; third-order cumulant statistics; three-wave coupling processes; Brain modeling; Frequency estimation; Higher order statistics; Matrix converters; Nonlinear systems; Phase detection; Phase frequency detector; Signal processing algorithms; Spectral analysis; Symmetric matrices;
fLanguage :
English
Journal_Title :
Signal Processing, IEEE Transactions on
Publisher :
ieee
ISSN :
1053-587X
Type :
jour
DOI :
10.1109/78.275606
Filename :
275606
Link To Document :
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