intvert.mp_dft2

mp_dft2(signal)

Compute the 2D discrete Fourier transform of a signal.

This function computes the 2D discrete Fourier transform (DFT) along the last two axes of signal at the precision specified by the current gmpy2 context.

Parameters:

signal (array_like) – Input signal, can be complex.

Returns:

The 2D DFT of signal along the last two axes.

Return type:

mpc ndarray

See also

mp_idft2

inverse of mp_dft2

mp_dft

analogous 1D function

Notes

This function is implemented with mp_dft. For algorithm notes, see mp_dft.

The DFT convention used in this implementation is

\[\tilde{X}_{kl} = \sum_{m = 0}^{N_1 - 1}\sum_{n = 0}^{N_2 - 1}X_{mn} e^{-2\pi{\rm i}(mk/N_1 + nl/N_2)},\]

where \({\bf X}\) is an \(N_1 \times N_2\) matrix. The inverse DFT is given by

\[X_{mn} = \sum_{k = 0}^{N_1 - 1}\sum_{l = 0}^{N_2 - 1}\tilde{X}_{kl} e^{2\pi{\rm i}(mk/N_1 + nl/N_2)}.\]