Modulated Hermite series expansions and the time-bandwidth product

A.C. Brinker, den, B.E. Sarroukh

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Abstract

The harmonically modulated Hermite series constitute an orthonormal basis in the Hilbert space of square-integrable functions. This basis comprises three free parameters, namely a translation, a modulation, and a scale factor. In practical situations, we are interested in series expansions that are as compact as possible. We can use the free parameters as the means to obtain a compact series expansion for a given function. We choose as the compactness criterion the first-order moment of the energy distribution in the transform domain. It is shown that, in that case, the optimum compaction parameters can be given in a simple analytic form depending on signal measurements only. Furthermore, these parameters have a clear physical interpretation, and the minimum of the compactness criterion is directly related to the time-bandwidth product.
Original languageEnglish
Pages (from-to)243-250
Number of pages8
JournalSignal Processing
Volume80
Issue number2
DOIs
Publication statusPublished - 2000

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Bandwidth
Hilbert spaces
Compaction
Modulation

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Brinker, den, A.C. ; Sarroukh, B.E. / Modulated Hermite series expansions and the time-bandwidth product. In: Signal Processing. 2000 ; Vol. 80, No. 2. pp. 243-250.
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Modulated Hermite series expansions and the time-bandwidth product. / Brinker, den, A.C.; Sarroukh, B.E.

In: Signal Processing, Vol. 80, No. 2, 2000, p. 243-250.

Research output: Contribution to journalArticleAcademicpeer-review

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AU - Sarroukh, B.E.

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