scipy.signal.windows.

kaiser_bessel_derived#

scipy.signal.windows.kaiser_bessel_derived(M, beta, *, sym=True, xp=None, device=None)[source]#

Return a Kaiser-Bessel derived window.

Parameters:

Mint: Number of points in the output window. If zero, an empty array is returned. An exception is thrown when it is negative. Note that this window is only defined for an even number of points.
betafloat: Kaiser window shape parameter.
symbool, optional: This parameter only exists to comply with the interface offered by the other window functions and to be callable by get_window. When True (default), generates a symmetric window, for use in filter design.
xparray_namespace, optional: Optional array namespace. Should be compatible with the array API standard, or supported by array-api-compat. Default: numpy
device: any: optional device specification for output. Should match one of the supported device specification in xp.

Returns:

wndarray: The window, normalized to fulfil the Princen-Bradley condition.

See also

kaiser

Notes

It is designed to be suitable for use with the modified discrete cosine transform (MDCT) and is mainly used in audio signal processing and audio coding.

Added in version 1.9.0.

Array API Standard Support

kaiser_bessel_derived 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	✅	n/a

See Support for the array API standard for more information.

References

[1]

Bosi, Marina, and Richard E. Goldberg. Introduction to Digital Audio Coding and Standards. Dordrecht: Kluwer, 2003.

[2]

Wikipedia, “Kaiser window”, https://en.wikipedia.org/wiki/Kaiser_window

Examples

Plot the Kaiser-Bessel derived window based on the wikipedia reference [2]:

>>> import numpy as np
>>> from scipy import signal
>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots()
>>> N = 50
>>> for alpha in [0.64, 2.55, 7.64, 31.83]:
...     ax.plot(signal.windows.kaiser_bessel_derived(2*N, np.pi*alpha),
...             label=f"{alpha=}")
>>> ax.grid(True)
>>> ax.set_title("Kaiser-Bessel derived window")
>>> ax.set_ylabel("Amplitude")
>>> ax.set_xlabel("Sample")
>>> ax.set_xticks([0, N, 2*N-1])
>>> ax.set_xticklabels(["0", "N", "2N+1"])  
>>> ax.set_yticks([0.0, 0.2, 0.4, 0.6, 0.707, 0.8, 1.0])
>>> fig.legend(loc="center")
>>> fig.tight_layout()
>>> fig.show()

../../_images/scipy-signal-windows-kaiser_bessel_derived-1.png