dpnp.fft.fft

dpnp.fft.fft(a, n=None, axis=-1, norm=None, out=None)[source]

Compute the one-dimensional discrete Fourier Transform.

For full documentation refer to numpy.fft.fft.

Parameters:

  • a ({dpnp.ndarray, usm_ndarray}) -- Input array, can be complex.

  • n ({None, int}, optional) -- Length of the transformed axis of the output. If n is smaller than the length of the input, the input is cropped. If it is larger, the input is padded with zeros. If n is not given, the length of the input along the axis specified by axis is used. Default: None.

  • axis (int, optional) -- Axis over which to compute the FFT. If not given, the last axis is used. Default: -1.

  • norm ({None, "backward", "ortho", "forward"}, optional) -- Normalization mode (see dpnp.fft). Indicates which direction of the forward/backward pair of transforms is scaled and with what normalization factor. None is an alias of the default option "backward". Default: "backward".

  • out ({None, dpnp.ndarray or usm_ndarray of complex dtype}, optional) -- If provided, the result will be placed in this array. It should be of the appropriate shape and dtype. Default: None.

Returns:

out -- The truncated or zero-padded input, transformed along the axis indicated by axis, or the last one if axis is not specified.

Return type:

dpnp.ndarray of complex dtype

See also

dpnp.fft

For definition of the DFT and conventions used.

dpnp.fft.ifft

The inverse of dpnp.fft.fft.

dpnp.fft.fft2

The two-dimensional FFT.

dpnp.fft.fftn

The n-dimensional FFT.

dpnp.fft.rfftn

The n-dimensional FFT of real input.

dpnp.fft.fftfreq

Frequency bins for given FFT parameters.

Notes

FFT (Fast Fourier Transform) refers to a way the discrete Fourier Transform (DFT) can be calculated efficiently, by using symmetries in the calculated terms. The symmetry is highest when n is a power of 2, and the transform is therefore most efficient for these sizes.

Examples

>>> import dpnp as np
>>> a = np.exp(2j * np.pi * np.arange(8) / 8)
>>> np.fft.fft(a)
array([-3.44509285e-16+1.14423775e-17j,  8.00000000e+00-8.52069395e-16j,
        2.33486982e-16+1.22464680e-16j,  0.00000000e+00+1.22464680e-16j,
        9.95799250e-17+2.33486982e-16j, -8.88178420e-16+1.17281316e-16j,
        1.14423775e-17+1.22464680e-16j,  0.00000000e+00+1.22464680e-16j])