Nonparametric estimation of autocorrelation and spectra using cumulants and polyspectra

Georgios B. Giannakis; Anastasios N. Delopoulos

doi:10.1117/12.23504

1 November 1990 Nonparametric estimation of autocorrelation and spectra using cumulants and polyspectra

Georgios B. Giannakis, Anastasios N. Delopoulos

Proceedings Volume 1348, Advanced Signal Processing Algorithms, Architectures, and Implementations; (1990) https://doi.org/10.1117/12.23504
Event: 34th Annual International Technical Symposium on Optical and Optoelectronic Applied Science and Engineering, 1990, San Diego, CA, United States

Abstract

Autocorrelation and specira 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 frequencydomain 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. I.

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Georgios B. Giannakis and Anastasios N. Delopoulos "Nonparametric estimation of autocorrelation and spectra using cumulants and polyspectra", Proc. SPIE 1348, Advanced Signal Processing Algorithms, Architectures, and Implementations, (1 November 1990); https://doi.org/10.1117/12.23504

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