Elements of information theory
Elements of information theory
Signal Processing
Fractional quaternion Fourier transform, convolution and correlation
Signal Processing
The uncertainty principle: global, local, or both?
IEEE Transactions on Signal Processing
Two-dimensional affine generalized fractional Fourier transform
IEEE Transactions on Signal Processing
Uncertainty Principle for Real Signals in the Linear Canonical Transform Domains
IEEE Transactions on Signal Processing - Part I
An uncertainty principle for real signals in the fractional Fouriertransform domain
IEEE Transactions on Signal Processing
Relations between fractional operations and time-frequencydistributions, and their applications
IEEE Transactions on Signal Processing
Information theoretic inequalities
IEEE Transactions on Information Theory
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The uncertainty principle plays an important role in mathematics, physics, signal processing, and so on. Firstly, based on definition of the linear canonical transform (LCT) and the traditional Pitt's inequality, one novel Pitt's inequality in the LCT domains is obtained, which is connected with the LCT parameters a and b. Then one novel logarithmic uncertainty principle is derived from this novel Pitt's inequality in the LCT domains, which is associated with parameters of the two LCTs. Secondly, from the relation between the original function and LCT, one entropic uncertainty principle and one Heisenberg's uncertainty principle in the LCT domains are derived, which are associated with the LCT parameters a and b. The reason why the three lower bounds are only associated with LCT parameters a and b and independent of c and d is presented. The results show it is possible that the bounds tend to zeros.