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# numpy.fft.ifft

fft.ifft(a, n=None, axis=-1, norm=None, out=None)

  Compute the one-dimensional inverse discrete Fourier Transform.

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

  The input should be ordered in the same way as is returned by `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. See `numpy.fft` for details.

  Parameters:
    a array_like

      Input array, can be complex.

    n 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. See notes about padding issues.

    axis int, optional

      Axis over which to compute the inverse DFT. If not given, the last axis is used.

    norm{“backward”, “ortho”, “forward”}, optional

      Normalization mode (see `numpy.fft`). Default is “backward”. Indicates which direction of the forward/backward pair of transforms is scaled and with what normalization factor.

      Added in version 1.20.0: The “backward”, “forward” values were added.

    out complex ndarray, optional

      If provided, the result will be placed in this array. It should be of the appropriate shape and dtype.

      Added in version 2.0.0.

  Returns:
    out complex ndarray

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

  Raises:
    IndexError

      If axis is not a valid axis of a.

  See also

  `numpy.fft`

    An introduction, with definitions and general explanations.

  `fft`

    The one-dimensional (forward) FFT, of which `ifft` is the inverse

  `ifft2`

    The two-dimensional inverse 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 `ifft`.

  Examples

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

  Create and plot a band-limited signal with random phases:

      >>> import matplotlib.pyplot as plt
      >>> t = np.arange(400)
      >>> n = np.zeros((400,), dtype=complex)
      >>> n[40:60] = np.exp(1j*np.random.uniform(0, 2*np.pi, (20,)))
      >>> s = np.fft.ifft(n)
      >>> plt.plot(t, s.real, label='real')
      [<matplotlib.lines.Line2D object at ...>]
      >>> plt.plot(t, s.imag, '--', label='imaginary')
      [<matplotlib.lines.Line2D object at ...>]
      >>> plt.legend()
      <matplotlib.legend.Legend object at ...>
      >>> plt.show()