Time Signals Whose Standard Deviations Diverge

Authors: Majerník, V.; Majerníková, E.

Source: Acta Physica Hungarica A, Volume 23, Numbers 1-2, 22 April 2005 , pp. 97-105(9)

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Abstract:

The Gábor time–frequency uncertainty relation of a wave process (a time signal) is given by the product of its effective duration and bandwidth represented by standard deviations of its normed duration and spectral functions. We show that there exists a class of time signals whose one of the said standard deviations diverges independently of the signal durations. In that case the Gábor uncertainty relation can not be applied and one has to use another type of uncertainty relation, e.g. the entropic time–frequency uncertainty relation.

Keywords: standard deviation; uncertainty relation; acoustics; time signal

Document Type: Research article

Publication date: 2005-04-22

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