# FFT Functions¶

## Standard FFTs¶

 cupy.fft.fft Compute the one-dimensional FFT. cupy.fft.ifft Compute the one-dimensional inverse FFT. cupy.fft.fft2 Compute the two-dimensional FFT. cupy.fft.ifft2 Compute the two-dimensional inverse FFT. cupy.fft.fftn Compute the N-dimensional FFT. cupy.fft.ifftn Compute the N-dimensional inverse FFT.

## Real FFTs¶

 cupy.fft.rfft Compute the one-dimensional FFT for real input. cupy.fft.irfft Compute the one-dimensional inverse FFT for real input. cupy.fft.rfft2 Compute the two-dimensional FFT for real input. cupy.fft.irfft2 Compute the two-dimensional inverse FFT for real input. cupy.fft.rfftn Compute the N-dimensional FFT for real input. cupy.fft.irfftn Compute the N-dimensional inverse FFT for real input.

## Hermitian FFTs¶

 cupy.fft.hfft Compute the FFT of a signal that has Hermitian symmetry. cupy.fft.ihfft Compute the FFT of a signal that has Hermitian symmetry.

## Helper routines¶

 cupy.fft.fftfreq Return the FFT sample frequencies. cupy.fft.rfftfreq Return the FFT sample frequencies for real input. cupy.fft.fftshift Shift the zero-frequency component to the center of the spectrum. cupy.fft.ifftshift The inverse of fftshift().

## Normalization¶

The default normalization has the direct transforms unscaled and the inverse transforms are scaled by $$1/n$$. If the ketyword argument norm is "ortho", both transforms will be scaled by $$1/\sqrt{n}$$.

## Code compatibility features¶

FFT functions of NumPy alway return numpy.ndarray which type is numpy.complex128 or numpy.float64. CuPy functions do not follow the behavior, they will return numpy.complex64 or numpy.float32 if the type of the input is numpy.float16, numpy.float32, or numpy.complex64.

Internally, cupy.fft always generates a cuFFT plan (see the cuFFT documentation for detail) corresponding to the desired transform. When possible, an n-dimensional plan will be used, as opposed to applying separate 1D plans for each axis to be transformed. Using n-dimensional planning can provide better performance for multidimensional transforms, but requires more GPU memory than separable 1D planning. The user can disable n-dimensional planning by setting cupy.fft.config.enable_nd_planning = False. This ability to adjust the planning type is a deviation from the NumPy API, which does not use precomputed FFT plans.

Moreover, the automatic plan generation can be suppressed by using an existing plan returned by cupyx.scipy.fftpack.get_fft_plan() as a context manager. This is again a deviation from NumPy.