cated by `axes`, or the last two axes if `axes` is not given. Raises ------ ValueError If `s` and `axes` have different length, or `axes` not given and ``len(s) != 2``. IndexError If an element of `axes` is larger than the number of axes of `x`. See Also -------- ifft2 : The inverse 2-D FFT. fft : The 1-D FFT. fftn : The N-D FFT. fftshift : Shifts zero-frequency terms to the center of the array. For 2-D input, swaps first and third quadrants, and second and fourth quadrants. Notes ----- `fft2` is just `fftn` with a different default for `axes`. The output, analogously to `fft`, contains the term for zero frequency in the low-order corner of the transformed axes, the positive frequency terms in the first half of these axes, the term for the Nyquist frequency in the middle of the axes and the negative frequency terms in the second half of the axes, in order of decreasingly negative frequency. See `fftn` for details and a plotting example, and `fft` for definitions and conventions used. Examples -------- >>> import scipy.fft >>> import numpy as np >>> x = np.mgrid[:5, :5][0] >>> scipy.fft.fft2(x) array([[ 50. +0.j , 0. +0.j , 0. +0.j , # may vary 0. +0.j , 0. +0.j ], [-12.5+17.20477401j, 0. +0.j , 0. +0.j , 0. +0.j , 0. +0.j ], [-12.5 +4.0614962j , 0. +0.j , 0. +0.j , 0. +0.j , 0. +0.j ], [-12.5 -4.0614962j , 0. +0.j , 0. +0.j , 0. +0.j , 0. +0.j ], [-12.5-17.20477401j, 0. +0.j , 0. +0.j , 0. +0.j , 0. +0.j ]]) r