added:: 2.0.0

Returns
-------
out : ndarray
    The truncated or zero-padded input, transformed along the axis
    indicated by `axis`, or the last one if `axis` is not specified.
    The length of the transformed axis is `n`, or, if `n` is not given,
    ``2*(m-1)`` where ``m`` is the length of the transformed axis of the
    input. To get an odd number of output points, `n` must be specified.

Raises
------
IndexError
    If `axis` is not a valid axis of `a`.

See Also
--------
numpy.fft : For definition of the DFT and conventions used.
rfft : The one-dimensional FFT of real input, of which `irfft` is inverse.
fft : The one-dimensional FFT.
irfft2 : The inverse of the two-dimensional FFT of real input.
irfftn : The inverse of the *n*-dimensional FFT of real input.

Notes
-----
Returns the real valued `n`-point inverse discrete Fourier transform
of `a`, where `a` contains the non-negative frequency terms of a
Hermitian-symmetric sequence. `n` is the length of the result, not the
input.

If you specify an `n` such that `a` must be zero-padded 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)``.

The correct interpretation of the hermitian input depends on the length of
the original data, as given by `n`. This is because each input shape could
correspond to either an odd or even length signal. By default, `irfft`
assumes an even output length which puts the last entry at the Nyquist
frequency; aliasing with its symmetric counterpart. By Hermitian symmetry,
the value is thus treated as purely real. To avoid losing information, the
correct length of the real input **must** be given.

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

r