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

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


The input array.

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

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

nint, 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].

axisint, 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_xbool, optional

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

workersint, 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.

orthogonalizebool, optional

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

Added in version 1.8.0.

idctndarray of real

The transformed input array.

See also


Forward DCT


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


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.


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.])