Gabor's signal expansion and degrees of freedom of a signal

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Abstract

Gabor's expansion of a signal into a discrete set of properly shifted and modulated versions of an elementary signal is introduced, and a way to determine the expansion coefficients is derived. The way in which the expansion coefficients are transformed when the signal propagates through a linear system, is described; in particular, the basic coherent-optical system consisting of a 4f-arrangement with rectangular apertures in the input and the Fourier plane, is considered. As a result, the well-known property that a signal which is roughly limited both in space and in spatial frequency has a number of complex degrees of freedom which is equal to the space-bandwidth product, is re-established.
Original languageEnglish
Pages (from-to)1223-1229
Number of pages7
JournalOptica Acta
Volume29
Issue number9
DOIs
Publication statusPublished - 1982

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