An uncertainty principle for quaternion Fourier transform
Computers & Mathematics with Applications
Uncertainty principles for linear canonical transform
IEEE Transactions on Signal Processing
New inequalities and uncertainty relations on linear canonical transform revisit
EURASIP Journal on Advances in Signal Processing
On uncertainty principle for the linear canonical transform of complex signals
IEEE Transactions on Signal Processing
The fractional Fourier transform and quadratic field magnetic resonance imaging
Computers & Mathematics with Applications
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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