Largest eigenvalues of truncated averaging operators

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Abstract

In this paper we consider the maximization of frequency-domain criteria for non-negative, band-limited functions with frequency-weight functions assigning higher weights to lower frequencies. It is shown that, within some 6%, these criteria are maximized simultaneously by the square of the sinc function. This result, which is relevant to optical filter design, is obtained by studying the largest eigenvalues of truncated averaging operators (for both the discrete- and continuous-variable case) in detail.
Original languageEnglish
Pages (from-to)413-432
Number of pages11
JournalPhilips Journal of Research
Volume45
Issue number6
Publication statusPublished - 1991

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