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Title: An uncertainty principle for real signals in the fractional Fourier transform domain
Authors: GADRE, VM
Keywords: Fourier Transforms
Gaussian Processes
Signal Representation
Time-Frequency Analysis
Issue Date: 2001
Publisher: IEEE
Citation: IEEE Transactions on Signal Processing 49(11), 2545-48
Abstract: The fractional Fourier transform (FrFT) can be thought of as a generalization of the Fourier transform to rotate a signal representation by an arbitrary angle α in the time-frequency plane. A lower bound on the uncertainty product of signal representations in two FrFT domains for real signals is obtained, and it is shown that a Gaussian signal achieves the lower bound. The effect of shifting and scaling the signal on the uncertainty relation is discussed. An example is given in which the uncertainty relation for a real signal is obtained, and it is shown that this relation matches with that given by the uncertainty relation derived.
ISSN: 1053-587X
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