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Module « scipy.fft »

Fonction idct - module scipy.fft

Signature de la fonction idct

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

Description

help(scipy.fft.idct)

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 :func:`~scipy.fft.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.

    .. versionadded:: 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.])

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