Spectral Relations for Multidimensional Complex Improper Stationary and (Almost) Cyclostationary Processes

We study continuous-time multidimensional wide- sense stationary (WSS) and (almost) cyclostationary processes in the frequency domain. Under the assumption that the correlation function is uniformly continuous, we prove the existence of a unique sequence of spectral measures, which coincide with the...

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Bibliographic Details
Published in:IEEE transactions on information theory 2008-04, Vol.54 (4), p.1670-1682
Main Authors: Wahlberg, P., Schreier, P.J.
Format: Article
Language:English
Subjects:
(Almost) cyclostationary processes
analytic signals
Applied sciences
Array signal processing
Baseband
Communications networks
complementary correlation
Constrictions
Correlation analysis
Exact sciences and technology
Frequency domain analysis
Frequency domains
harmonizable processes
improper processes
Information systems
Information technology
Information theory
Information, signal and communications theory
Mathematical analysis
Miscellaneous
multidimensional processes
Multidimensional signal processing
Multidimensional systems
Representations
Scalars
Signal analysis
Signal processing
Signaling
Spectra
Statistics
Stochastic processes
Sufficient conditions
Technology (byts ev till Engineering)
Teknik
Telecommunications and information theory
wide-sense stationary (WSS) processes
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Summary:We study continuous-time multidimensional wide- sense stationary (WSS) and (almost) cyclostationary processes in the frequency domain. Under the assumption that the correlation function is uniformly continuous, we prove the existence of a unique sequence of spectral measures, which coincide with the restrictions to certain subdiagonals of the spectral measure in the strongly harmonizable case. Moreover, the off-diagonal measures are absolutely continuous with respect to the diagonal measure. As a consequence, for strongly harmonizable scalar improper almost cyclostationary processes, we obtain representation formulas for the components of the complementary spectral measure and the off-diagonal components of the spectral measure, in terms of the diagonal component of the spectral measure. We apply these results to analytic signals, which produces sufficient conditions for propriety for almost cyclostationary analytic signals.
ISSN:0018-9448
1557-9654
1557-9654
DOI:10.1109/TIT.2008.917626