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The Wold isomorphism for cyclostationary sequences
2004 (English)In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 84, no 5, 813-824 p.Article in journal (Refereed) Published
Abstract [en]

In 1948 Wold introduced an isometric isomorphism between a Hilbert (linear) space formed from the weighted shifts of a numerical sequence and a suitable Hilbert space of values of a second-order stochastic sequence. Motivated by a recent resurrection of the idea in the context of cyclostationary sequences and processes, we present the details of the Wold isomorphism between cyclostationary stochastic sequences and cyclostationary numerical sequences. We show how Hilbert-space representations of cyclostationary sequences are interpreted in the case of numerical CS sequences.

Place, publisher, year, edition, pages
2004. Vol. 84, no 5, 813-824 p.
Keyword [en]
periodically correlated time series, Marcinkiewicz spaces, ergodic, properties, linear spaces generated by shifts of a sequence, time-series, linear-system, cumulant theory, probability
URN: urn:nbn:se:kth:diva-23358DOI: 10.1016/j.sigpro.2004.01.002ISI: 000221009000001OAI: diva2:342056
QC 20100525Available from: 2010-08-10 Created: 2010-08-10Bibliographically approved

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Koski, Timo
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Signal Processing

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