Compute the onedimensional inverse discrete Fourier Transform.
This function computes the inverse of the onedimensional npoint 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 positivefrequency terms, and a[n/2+1:] should contain the negativefrequency terms, in order of decreasingly negative frequency. See numpy.fft for details.
Parameters:  a : array_like
n : int, optional
axis : int, optional


Returns:  out : complex ndarray

Raises:  IndexError :

See also
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 bandlimited 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')
>>> plt.legend(('real', 'imaginary'))
>>> plt.show()
Output