Uncertainty principles for linear canonical transform
IEEE Transactions on Signal Processing
On uncertainty principle for the linear canonical transform of complex signals
IEEE Transactions on Signal Processing
The fractional Fourier transform and time-frequency representations
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
Fresnelets: new multiresolution wavelet bases for digital holography
IEEE Transactions on Image Processing
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The uncertainty principles of the 1-D Fourier transform (FT), the 1-D fractional Fourier transform (FRFT), and the 1-D linear canonical transform (LCT) have already been derived. In this paper, we extend the previous works and derive the uncertainty principles for the two-dimensional nonseparable linear canonical transform (2-D NSLCT), including the complex input case, the real input case, and the case where det(B)=0 where B is a parameter subset of the 2-D NSLCT. Since the 2-D NSLCT is a generalization of many operations, with the derived uncertainty principles, the uncertain principles of many 2-D operations, such as the 2-D Fresnel transform, the 2-D FT, the 2-D FRFT, the 2-D LCT, and the 2-D gyrator transform, can also be found. Moreover, we find that the rotation, scaling, and chirp multiplication of the 2-D Gaussian function can minimize the product of the variances in the space and the transform domains.