dpnp.fft.ifft

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

Compute the one-dimensional inverse discrete Fourier Transform.

This function computes the inverse of the one-dimensional n-point discrete Fourier transform computed by dpnp.fft.fft. In other words, ifft(fft(a)) == a to within numerical accuracy. For a general description of the algorithm and definitions, see dpnp.fft.

The input should be ordered in the same way as is returned by dpnp.fft.fft, i.e.,

  • a[0] should contain the zero frequency term,

  • a[1:n//2] should contain the positive-frequency terms,

  • a[n//2 + 1:] should contain the negative-frequency terms, in increasing order starting from the most negative frequency.

For an even number of input points, A[n//2] represents the sum of the values at the positive and negative Nyquist frequencies, as the two are aliased together.

For full documentation refer to numpy.fft.ifft.

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 inverse FFT. If not given, the last axis is used. Default: -1.

  • norm ({"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 (consistent with the choice of n) 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.fft

The one-dimensional (forward) FFT, of which dpnp.fft.ifft is the inverse.

dpnp.fft.ifft2

The two-dimensional inverse FFT.

dpnp.fft.ifftn

The N-dimensional inverse FFT.

Notes

If the input parameter n is larger than the size of the input, the input is padded by appending zeros at the end. Even though this is the common approach, it might lead to surprising results. If a different padding is desired, it must be performed before calling dpnp.fft.ifft.

Examples

>>> import dpnp as np
>>> a = np.array([0, 4, 0, 0])
>>> np.fft.ifft(a)
array([ 1.+0.j,  0.+1.j, -1.+0.j,  0.-1.j]) # may vary