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# scipy.fft.idct

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

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

  Parameters:
    x array_like

      The input array.

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

      Type of the DCT (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 idct 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 IDCT variant (see Notes). Defaults to `True` when `norm="ortho"` and `False` otherwise.

      New in version 1.8.0.

  Returns:
    idct ndarray of real

      The transformed input array.

  See also

  `dct`

    Forward DCT

  Notes

  For a single dimension array x, `idct(x, norm='ortho')` is equal to MATLAB `idct(x)`.

  Warning

  For `type in {1, 2, 3}`, `norm="ortho"` breaks the direct correspondence with the inverse direct Fourier transform. To recover it you must specify `orthogonalize=False`.

  For `norm="ortho"` both the `dct` and `idct` are scaled by the same overall factor in both directions. By default, the transform is also orthogonalized which for types 1, 2 and 3 means the transform definition is modified to give orthogonality of the IDCT matrix (see `dct` for the full definitions).

  ‘The’ IDCT is the IDCT-II, which is the same as the normalized DCT-III.

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

  Examples

  The Type 1 DCT is equivalent to the DFT for real, even-symmetrical inputs. The output is also real and even-symmetrical. Half of the IFFT input is used to generate half of the IFFT output:

      >>> from scipy.fft import ifft, idct
      >>> import numpy as np
      >>> ifft(np.array([ 30.,  -8.,   6.,  -2.,   6.,  -8.])).real
      array([  4.,   3.,   5.,  10.,   5.,   3.])
      >>> idct(np.array([ 30.,  -8.,   6.,  -2.]), 1)
      array([  4.,   3.,   5.,  10.])