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1 November 1993 N-th order cumulant-spectral principal domain, stationary set, and transient set
J. W. Dalle Molle
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Proceedings Volume 2027, Advanced Signal Processing Algorithms, Architectures, and Implementations IV; (1993) https://doi.org/10.1117/12.160444
Event: SPIE's 1993 International Symposium on Optics, Imaging, and Instrumentation, 1993, San Diego, CA, United States
Abstract
From first principles, a method is presented to generate the minimal region in the n- dimensional frequency space necessary for a complete nonredundant representation of the support of an N-th order joint cumulant spectral function. This region is commonly referred to as the N-th order principal domain (PD) or the support set of the N-th order cumulant spectral function (which is the Fourier transform of the N-th order joint cumulant function). The procedure is derived from a composition of the symmetry operations inherent to an N-fold product of the Fourier transforms of a random time series. For exposition, we present an example using the second-order cumulant spectral function. Explicit representations of the PDs for cumulant spectra of orders up to and including order five are included.
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J. W. Dalle Molle "N-th order cumulant-spectral principal domain, stationary set, and transient set", Proc. SPIE 2027, Advanced Signal Processing Algorithms, Architectures, and Implementations IV, (1 November 1993); https://doi.org/10.1117/12.160444
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KEYWORDS
Fourier transforms
Space operations
Palladium
Associative arrays
Correlation function
Distortion
Statistical analysis
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