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Maximum Entropy Spectrum Analysis Technique - A Review of Its Theoretical Properties.

David Alfred Gray

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Abstract

The maximum entropy method estimates the power spectrum of a random process by extrapolating the autocorrelation function outside the observation interval. The extrapolation is such that a minimal number of constraints is imposed on it. The equivalence of various derivation of the maximum entropy spectrum is proved in this paper and various examples are given to illustrate the properties of the maximum entropy spectrum. Finally the relation of the maximum entropy method to other techniques for estimating the spectrum is given. (Author)

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What this paper is about

The maximum entropy method estimates the power spectrum of a random process by extrapolating the autocorrelation function outside the observation interval. The extrapolation is such that a minimal number of constraints is imposed on it. The equivalence of various derivation of the maximum entropy spectrum is proved in this paper and various examples are given to illustrate the properties of the maximum entropy spectrum. Finally the relation of the maximum entropy method to other techniques for estimating the spectrum is given. (Author)

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Available abstract

The maximum entropy method estimates the power spectrum of a random process by extrapolating the autocorrelation function outside the observation interval. The extrapolation is such that a minimal number of constraints is imposed on it. The equivalence of various derivation of the maximum entropy spectrum is proved in this paper and various examples are given to illustrate the properties of the maximum entropy spectrum. Finally the relation of the maximum entropy method to other techniques for estimating the spectrum is given. (Author)

Key concepts: Maximum entropy spectral estimation, Principle of maximum entropy, Extrapolation, Mathematics, Autocorrelation, Maximum entropy probability distribution, Entropy (arrow of time), Statistical physics

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