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Gabor’s Signal Expansion and Its Relation to Sampling of the Sliding-Window Spectrum

  • Martin J. Bastiaans
Part of the Springer Texts in Electrical Engineering book series (STELE)

Abstract

It is sometimes convenient to describe a time signal ϕ(t), say, not in the time domain, but in the frequency domain by means of its frequency spectrum, i.e., the Fourier transform \(\bar{\varphi}(\omega)\) of the function ϕ(t) which is defined by
$$\bar{\varphi }(\omega ) = \int {\varphi (t){{e}^{{ - j\omega t}}}dt;}$$
a bar on top of a symbol will mean throughout that we are dealing with a function in the frequency domain. (Unless otherwise stated, all integrations and summations in this contribution extend from -∞ to +∞.) The frequency spectrum shows us the global distribution of the energy of the signal as a function of frequency. However, one is often more interested in the momentary or local distribution of the energy as a function of frequency.

Keywords

Window Function Elementary Signal Inversion Formula Middle Plane Window Sequence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York, Inc. 1993

Authors and Affiliations

  • Martin J. Bastiaans

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