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