# scipy.fft.idst

scipy.fft.idst(x, type=2, n=None, axis=-1, norm=None, overwrite_x=False, workers=None, orthogonalize=None)

  Return the Inverse Discrete Sine Transform of an arbitrary type sequence.

  Parameters:
    x array_like

      The input array.

    type{1, 2, 3, 4}, optional

      Type of the DST (see Notes). Default type is 2.

    n int, optional

      Length of the transform. If `n < x.shape[axis]`, x is truncated. If `n > x.shape[axis]`, x is zero-padded. The default results in `n = x.shape[axis]`.

    axis int, optional

      Axis along which the idst is computed; the default is over the last axis (i.e., `axis=-1`).

    norm{“backward”, “ortho”, “forward”}, optional

      Normalization mode (see Notes). Default is “backward”.

    overwrite_x bool, optional

      If True, the contents of x can be destroyed; the default is False.

    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.

    orthogonalize bool, optional

      Whether to use the orthogonalized IDST variant (see Notes). Defaults to `True` when `norm="ortho"` and `False` otherwise.

      New in version 1.8.0.

  Returns:
    idst ndarray of real

      The transformed input array.

  See also

  `dst`

    Forward DST

  Notes

  Warning

  For `type in {2, 3}`, `norm="ortho"` breaks the direct correspondence with the inverse direct Fourier transform.

  For `norm="ortho"` both the `dst` and `idst` are scaled by the same overall factor in both directions. By default, the transform is also orthogonalized which for types 2 and 3 means the transform definition is modified to give orthogonality of the DST matrix (see `dst` for the full definitions).

  ‘The’ IDST is the IDST-II, which is the same as the normalized DST-III.

  The IDST is equivalent to a normal DST except for the normalization and type. DST type 1 and 4 are their own inverse and DSTs 2 and 3 are each other’s inverses.