The Envelope of Spectral Power for Stochastic Processes

Craig R. Shankwitz, Tryphon T. Georgiou

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


It is well known that the maximum likelihood (ML) spectral estimate represents an envelope on spectral power which is consistent with estimated covariance lags. However, in computing the envelope, the ML method allows for spectra corresponding to complex-valued stochastic processes. We study the respective envelope for processes constrained to be real-valued at the outset The resulting envelope is less conservative than the one provided by the ML method. A closed form expression exists for the new envelope.

Original languageEnglish (US)
Pages (from-to)584-588
Number of pages5
JournalIEEE Transactions on Information Theory
Issue number2
StatePublished - Mar 1994

Bibliographical note

Funding Information:
Manuscript received April 11, 1991; revised January 18, 1992. This work was supported in part by the National Science Foundation and the Air Force Office for Scientific Research. The authors are with the Department of Electrical Engineering, University of Minnesota, Minneapolis, MN 55455 USA. IEEE Log Number 9400233.


  • Maximum likelihood method
  • spectral estimation


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