Uncertainty Principle of the 2-D Affine Generalized Fractional Fourier Transform

The uncertainty principles of the 1-D fractional Fourier transform and the 1-D linear canonical transform have been derived. We extend the previous works and discuss the uncertainty principle for the two-dimensional affine generalized Fourier transform (2-D AGFFT). We find that derived uncertainty principle of the 2-D AGFFT can also be used for determining the uncertainty principles of many 2-D operations, such as the 2-D fractional Fourier transform, the 2-D linear canonical transform, and the 2-D Fresnel transform. These uncertainty principles are useful for time-frequency analysis and signal analysis. Moreover, we find that the rotation and the chirp multiplication of the 2-D Gaussian function can satisfy the lower bound of the uncertainty principle of the 2-D AGFFT.