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# numpy.fft.ifft

`numpy.fft.``ifft`(a, n=None, axis=-1)

  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+1]` should contain the positive-frequency terms, and `a[n/2+1:]` should contain the negative-frequency terms, in order of decreasingly negative frequency. 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.
  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 axes is larger than the last 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

      >>> np.fft.ifft([0, 4, 0, 0])
      array([ 1.+0.j,  0.+1.j, -1.+0.j,  0.-1.j])

  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, 'b-', t, s.imag, 'r--')
      [<matplotlib.lines.Line2D object at 0x...>, <matplotlib.lines.Line2D object at 0x...>]
      >>> plt.legend(('real', 'imaginary'))
      <matplotlib.legend.Legend object at 0x...>
      >>> plt.show()

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