`scipy.fft._realtransforms:idst`

source: build-install/usr/lib/python3.14/site-packages/scipy/fft/_realtransforms.py:656

Signature

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

Summary

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

Parameters

x : array_like: The input array.
type : {1, 2, 3, 4}, optional: Type of the DST (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 idst 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 IDST variant (see Notes). Defaults to True when norm="ortho" and False otherwise.
versionadded 1.8.0

Returns

idst : ndarray of real: The transformed input array.

Notes

For norm="ortho" both the dst and idst are scaled by the same overall factor in both directions. By default, the transform is also orthogonalized which for types 2 and 3 means the transform definition is modified to give orthogonality of the DST matrix (see dst for the full definitions).

'The' IDST is the IDST-II, which is the same as the normalized DST-III.

The IDST is equivalent to a normal DST except for the normalization and type. DST type 1 and 4 are their own inverse and DSTs 2 and 3 are each other's inverses. For an example that demonstrates the relation between the DST and ISDT, consult the DST and IDST section of the user_guide.

Examples

The following example calculates the signal from a spectrum `X` where only the first bin has a non-zero value. The signal for all four DST types is plotted:

import numpy as np
import matplotlib.pyplot as plt
from scipy.fft import idst
N = 15
X = np.array([0, N])  # the last `N-2` bin zero-valued bins are not needed
_, ax = plt.subplots()

✓

ax.set(title=f"Inverse of one component DST ({N} samples)",
       xlim=(0, N), xlabel="k", ylabel="x[k]")
for t_ in range(1, 5):
    x = idst(X, type=t_, n=N)  # parameter `n` pads `X` to length `N`.
    ax.plot(x, '.-', alpha=0.5, label=f"Type {t_}")

✗

[<matplotlib.lines.Line2D object at 0x7f3f60d6b770>]
[<matplotlib.lines.Line2D object at 0x7f3f60d6b8c0>]
[<matplotlib.lines.Line2D object at 0x7f3f60d6ba10>]
[<matplotlib.lines.Line2D object at 0x7f3f60d6bb60>]

ax.grid(True)

✓

ax.legend()

✗

<matplotlib.legend.Legend object at 0x7f3f60d6b4d0>

plt.show()

✓

The resulting signals are sines with their period and their phase determined by the used DST type. The following table shows those, with `N` being the number of signal samples and `n` is the index of the non-zero bin (here: ``N, n = 15, 1``): +------+------------------------------+------------------------+ | Type | period in samples | phase shift in samples | +======+==============================+========================+ | 1 | :math:`2 (N+1) / (n+1) = 16` | :math:`-1` | +------+------------------------------+------------------------+ | 2 | :math:`2 N / (n+1) = 15` | :math:`-1/2` | +------+------------------------------+------------------------+ | 3 | :math:`2 N / (n+1/2) = 20` | :math:`-1` | +------+------------------------------+------------------------+ | 4 | :math:`2 N / (n+1/2) = 20` | :math:`-1/2` | +------+------------------------------+------------------------+

Aliases

scipy.fft.idst

Signature

Summary

Parameters

Returns

Notes

Examples

See also

Aliases