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On the uncertainty principle in discrete signals
L.C. Calves,P. Vilbe +1 more
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In this article, the authors proved the uncertainty relation in the general case of a complex Fourier transform and with somewhat extended definitions of durations, and showed that the uncertainty principle holds true by appropriate definitions of the durations even if discrete signals are considered.Abstract:
It has recently been shown that the uncertainty principle holds true by appropriate definitions of the durations even if discrete signals are considered. A basic inequality was derived in the particular case where the Fourier transform is real. As an extension to this work, the authors prove the uncertainty relation in the general case of a complex Fourier transform and with somewhat extended definitions of durations. >read more
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Spectral analysis of signals
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TL;DR: 1. Basic Concepts. 2. Nonparametric Methods. 3. Parametric Methods for Rational Spectra.
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Analysis and design of OFDM/OQAM systems based on filterbank theory
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A Spectral Graph Uncertainty Principle
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TL;DR: A spectral graph analogy to Heisenberg's celebrated uncertainty principle is developed, which provides a fundamental tradeoff between a signal's localization on a graph and in its spectral domain.
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Cosine-modulated filterbanks based on extended Gaussian functions
Pierre Siohan,C. Roche +1 more
TL;DR: This analytical design method can be used to produce, with a controlled accuracy, filterbanks with practically no upper limitations in the number of coefficients and subbands.
References
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Journal ArticleDOI
The uncertainty principle in discrete signals
R. Ishii,K. Furukawa +1 more
TL;DR: The uncertainty principle in discrete signals is presented and the relation between time duration and band duration is known as the uncertainty principle and it is shown thatBand duration and time uncertainty are closely related.
Journal ArticleDOI
Optimal property of class of finite-energy signals with application to estimation of duration, power and amplitude of transients
TL;DR: An optimal energy property derived in this paper provides the foundation for a unifying definition of duration valid for both continuous and discrete signals, and a useful concept of effective amplitude is introduced to define effective amplitude.