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

P. Wahlberg, P.J. Schreier, IEEE Trans.\ Inform.\ Theory 54 (2008) 1670–1682.

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Journal Article
Author
Wahlberg, Patrik; Schreier, Peter J.
Abstract
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.
Publishing Year
Journal Title
IEEE Trans.\ Inform.\ Theory
Volume
54
Issue
4
Page
1670–1682
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Wahlberg P, Schreier PJ. Spectral Relations for Multidimensional Complex Improper Stationary and (Almost) Cyclostationary Processes. IEEE Trans\ Inform\ Theory. 2008;54(4):1670–1682. doi:10.1109/TIT.2008.917626
Wahlberg, P., & Schreier, P. J. (2008). Spectral Relations for Multidimensional Complex Improper Stationary and (Almost) Cyclostationary Processes. IEEE Trans.\ Inform.\ Theory, 54(4), 1670–1682. https://doi.org/10.1109/TIT.2008.917626
@article{Wahlberg_Schreier_2008, title={Spectral Relations for Multidimensional Complex Improper Stationary and (Almost) Cyclostationary Processes}, volume={54}, DOI={10.1109/TIT.2008.917626}, number={4}, journal={IEEE Trans.\ Inform.\ Theory}, author={Wahlberg, Patrik and Schreier, Peter J.}, year={2008}, pages={1670–1682} }
Wahlberg, Patrik, and Peter J. Schreier. “Spectral Relations for Multidimensional Complex Improper Stationary and (Almost) Cyclostationary Processes.” IEEE Trans.\ Inform.\ Theory 54, no. 4 (2008): 1670–1682. https://doi.org/10.1109/TIT.2008.917626.
P. Wahlberg and P. J. Schreier, “Spectral Relations for Multidimensional Complex Improper Stationary and (Almost) Cyclostationary Processes,” IEEE Trans.\ Inform.\ Theory, vol. 54, no. 4, pp. 1670–1682, 2008, doi: 10.1109/TIT.2008.917626.
Wahlberg, Patrik, and Peter J. Schreier. “Spectral Relations for Multidimensional Complex Improper Stationary and (Almost) Cyclostationary Processes.” IEEE Trans.\ Inform.\ Theory, vol. 54, no. 4, 2008, pp. 1670–1682, doi:10.1109/TIT.2008.917626.

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