Non-parametric estimation of autocorrelation and spectra using cumulants and polyspectra

Georgios B. Giannakis, Anastasios Delopoulos

Research output: Contribution to journalConference article

15 Scopus citations

Abstract

Autocorrelation and spectra of linear random processes can be expressed in terms of cumulants and polyspectra, respectively. The insensitivity of the latter to additive Gaussian noise of unknown covariance, is exploited in this paper to develop spectral estimators of deterministic and linear non-Gaussian signals using polyspectra. In the time-domain, windowed projections of third-order cumulants are shown to yield consistent estimators of the autocorrelation sequence. Both batch and recursive algorithms are derived. In the frequency-domain, a Fourier-slice solution and a least-squares approach are described for performing spectral analysis through windowed bi-periodograms. Asymptotic variance expressions of the time- and frequency-domain estimators are also presented. Two-dimensional extensions are indicated, and potential applications are discussed. Simulations are provided to illustrate the performance of the proposed algorithms and compare them with conventional approaches.

Original languageEnglish (US)
Pages (from-to)503-517
Number of pages15
JournalProceedings of SPIE - The International Society for Optical Engineering
Volume1348
DOIs
StatePublished - Nov 1 1990
EventAdvanced Signal Processing Algorithms, Architectures, and Implementations 1990 - San Diego, United States
Duration: Jul 8 1990Jul 13 1990

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