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# scipy.fftpack.idct

`scipy.fftpack.``idct`(x, type=2, n=None, axis=-1, norm=None, overwrite_x=False)

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

  Parameters: | x : array_like The input array. type : {1, 2, 3}, 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 : {None, ‘ortho’}, optional Normalization mode (see Notes). Default is None. overwrite_x : bool, optional If True, the contents of x can be destroyed; the default is False.
  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)`.

  ‘The’ IDCT is the IDCT of type 2, which is the same as DCT of type 3.

  IDCT of type 1 is the DCT of type 1, IDCT of type 2 is the DCT of type 3, and IDCT of type 3 is the DCT of type 2. For the definition of these types, see `dct`.

  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.fftpack import ifft, idct
      >>> 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) / 6
      array([  4.,   3.,   5.,  10.])