# scipy.fftpack.idct¶

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

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. axis : int, optional Axis over which to compute the transform. norm : {None, ‘ortho’}, optional Normalization mode (see Notes). Default is None. overwrite_x : bool, optional If True the contents of x can be destroyed. (default=False) idct : ndarray of real The transformed input array.

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:

```>>> ifft(array([ 30.,  -8.,   6.,  -2.,   6.,  -8.])).real
array([  4.,   3.,   5.,  10.,   5.,   3.])
>>> idct(array([ 30.,  -8.,   6.,  -2.]), 1) / 6
array([  4.,   3.,   5.,  10.])
```

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