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bundles / scipy 1.17.1 / scipy / fft / _realtransforms / idct

_Function

scipy.fft._realtransforms:idct

source: /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.

Array API Standard Support

idct has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

====================  ====================  ====================
Library               CPU                   GPU
====================  ====================  ====================
NumPy                 ✅                     n/a                 
CuPy                  n/a                   ⛔                   
PyTorch               ✅                     ⛔                   
JAX                   ✅                     ⛔                   
Dask                  ⚠️ computes graph     n/a                 
====================  ====================  ====================

See dev-arrayapi for more information.

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)
✗

See also

dct

Forward DCT

Aliases

  • scipy.fft.idct