Compute the inverse of the npoint DFT for real input.
This function computes the inverse of the onedimensional npoint discrete Fourier Transform of real input computed by rfft. In other words, irfft(rfft(a), len(a)) == a to within numerical accuracy. (See Notes below for why len(a) is necessary here.)
The input is expected to be in the form returned by rfft, i.e. the real zerofrequency term followed by the complex positive frequency terms in order of increasing frequency. Since the discrete Fourier Transform of real input is Hermitesymmetric, the negative frequency terms are taken to be the complex conjugates of the corresponding positive frequency terms.
Parameters:  a : array_like
n : int, optional
axis : int, optional


Returns:  out : ndarray

Raises:  IndexError :

See also
Notes
Returns the real valued npoint inverse discrete Fourier transform of a, where a contains the nonnegative frequency terms of a Hermitesymmetric sequence. n is the length of the result, not the input.
If you specify an n such that a must be zeropadded or truncated, the extra/removed values will be added/removed at high frequencies. One can thus resample a series to m points via Fourier interpolation by: a_resamp = irfft(rfft(a), m).
Examples
>>> np.fft.ifft([1, 1j, 1, 1j])
array([ 0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j])
>>> np.fft.irfft([1, 1j, 1])
array([ 0., 1., 0., 0.])
Notice how the last term in the input to the ordinary ifft is the complex conjugate of the second term, and the output has zero imaginary part everywhere. When calling irfft, the negative frequencies are not specified, and the output array is purely real.