kaiser_bessel_derived#, beta, *, sym=True)[source]#

Return a Kaiser-Bessel derived window.


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.


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.


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

See also



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.



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


Wikipedia, “Kaiser window”,


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(*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()