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Complex sinusoid analysis by Bayesian deconvolution of the discrete Fourier transform. (English) Zbl 0886.62028

Hanson, Kenneth M. (ed.) et al., Maximum entropy and Bayesian methods. Proceedings of the 15th international workshop, Santa Fe, NM, USA, July 31–August 4, 1995. Dordrecht: Kluwer Academic Publishers. Fundam. Theor. Phys. 79, 323-328 (1996).
Summary: This paper addresses the mixed detection-estimation of complex sinusoids embedded in noise. Processing the Discrete Fourier Transform (DFT) of the noisy data is regarded as an inverse problem in the frequency domain. Its ill-posed nature may be coped in a Bayesian framework using prior information. To this end, the impulsive structure of the expected complex spectrum is described by a compound Bernoulli-Gaussian (BG) complex process. It is also shown how the Bernoulli process can be driven by Fermi-Dirac statistics.
For the entire collection see [Zbl 0855.00029].

MSC:

62F15 Bayesian inference
62B10 Statistical aspects of information-theoretic topics
62M15 Inference from stochastic processes and spectral analysis
62P99 Applications of statistics
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