Skip to main content
`Ctrl`+`K`
scipy.fft.

# ihfft

scipy.fft.ihfft(x, n=None, axis=-1, norm=None, overwrite_x=False, workers=None, *, plan=None)

  Compute the inverse FFT of a signal that has Hermitian symmetry.

  Parameters:
    x array_like

      Input array.

    n int, optional

      Length of the inverse FFT, the number of points along transformation axis in the input to use. If n is smaller than the length of the input, the input is cropped. If it is larger, the input is padded with zeros. If n is not given, the length of the input along the axis specified by axis is used.

    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 `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 `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.

      Added in version 1.5.0.

  Returns:
    out complex 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//2 + 1`.

  See also

  `hfft`, `irfft`

  Notes

  `hfft`/`ihfft` are a pair analogous to `rfft`/`irfft`, but for the opposite case: here, the signal has Hermitian symmetry in the time domain and is real in the frequency domain. So, here, it’s `hfft`, for which you must supply the length of the result if it is to be odd: * even: `ihfft(hfft(a, 2*len(a) - 2) == a`, within roundoff error, * odd: `ihfft(hfft(a, 2*len(a) - 1) == a`, within roundoff error.

  Array API Standard Support

  `ihfft` has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable `SCIPY_ARRAY_API=1` and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

  Library | CPU | GPU
  --- | --- | ---
  NumPy | ✅ | n/a
  CuPy | n/a | ✅
  PyTorch | ✅ | ✅
  JAX | ✅ | ✅
  Dask | ⚠️ computes graph | n/a

  > See Support for the array API standard for more information.

  Examples

      >>> from scipy.fft import ifft, ihfft
      >>> import numpy as np
      >>> spectrum = np.array([ 15, -4, 0, -1, 0, -4])
      >>> ifft(spectrum)
      array([1.+0.j,  2.+0.j,  3.+0.j,  4.+0.j,  3.+0.j,  2.+0.j]) # may vary
      >>> ihfft(spectrum)
      array([ 1.-0.j,  2.-0.j,  3.-0.j,  4.-0.j]) # may vary