input is longer than this, it is cropped. If it is shorter than this, it is padded with zeros. If `n` is not given, it is taken to be ``2*(m-1)``, where ``m`` is the length of the input along the axis specified by `axis`. axis : int, optional Axis over which to compute the inverse FFT. If not given, the last axis is used. norm : {"backward", "ortho", "forward"}, optional Normalization mode (see `fft`). Default is "backward". overwrite_x : bool, optional If True, the contents of `x` can be destroyed; the default is False. See :func:`fft` for more details. workers : int, optional Maximum number of workers to use for parallel computation. If negative, the value wraps around from ``os.cpu_count()``. See :func:`~scipy.fft.fft` for more details. plan : object, optional This argument is reserved for passing in a precomputed plan provided by downstream FFT vendors. It is currently not used in SciPy. .. versionadded:: 1.5.0 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 larger than the last axis of `x`. See Also -------- rfft : The 1-D FFT of real input, of which `irfft` is inverse. fft : The 1-D FFT. irfft2 : The inverse of the 2-D FFT of real input. irfftn : The inverse of the N-D FFT of real input. Notes ----- Returns the real valued `n`-point inverse discrete Fourier transform of `x`, where `x` 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 default value of `n` assumes an even output length. By the Hermitian symmetry, the last imaginary component must be 0 and so is ignored. To avoid losing information, the correct length of the real input *must* be given. Examples -------- >>> import scipy.fft >>> scipy.fft.ifft([1, -1j, -1, 1j]) array([0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j]) # may vary >>> scipy.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