Modulated Hermite series expansions and the time-bandwidth product

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

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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
Issue number2
Publication statusPublished - 2000


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