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Data-Dependent Spectral Windows: Generalizing the Classical Framework to Include Maximum Entropy Estimates

Clifford M. Hurvich
Technometrics
Vol. 28, No. 3 (Aug., 1986), pp. 259-268
DOI: 10.2307/1269082
Stable URL: http://www.jstor.org/stable/1269082
Page Count: 10
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Data-Dependent Spectral Windows: Generalizing the Classical Framework to Include Maximum Entropy Estimates
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Abstract

Two well-known methods of spectrum estimation are the classical windowed-periodogram method described by Blackman and Tukey and the maximum entropy method (MEM) proposed by Burg. Comparisons of the two methods are difficult, in part because their motivations are based on differing sets of assumptions. My development, aimed at unification, rests on two new but simple formulas that extend a classical concept, thereby exhibiting an element common to both methods: the spectral window. The first formula expresses the MEM estimate as a convolution of the spectrum with a data-dependent and spectrum-dependent equivalent spectral window. The second formula gives the MEM estimate as a convolution of the periodogram with a data-dependent periodogram window. These formulas provide a new outlook on MEM that may be quite useful for a variety of purposes, including (a) the development of heuristic interpretations of line splitting and peak shifting and (b) the motivation of natural definitions of bandwidth for MEM estimates.

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