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bundles / scipy latest / scipy / fft / _realtransforms / idct

_Function

scipy.fft._realtransforms:idct

source: build-install/usr/lib/python3.14/site-packages/scipy/fft/_realtransforms.py:425

Signature

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

Summary

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.

Returns

idct : ndarray of real

The transformed input array.

Notes

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

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
idct(np.array([ 30.,  -8.,   6.,  -2.]), 1)
✗
array([ 4.,  3.,  5., 10.])

See also

dct

Forward DCT

Aliases

  • scipy.fft.idct