kaiser in Numpy – Python

Kaiser window is a taper formed by using a Bessel function.

Syntax : numpy.kaiser(M, beta)

Parameters :
M : [int] Number of points in the output window. If zero or less, an empty array is returned.
beta : [float] Shape parameter for window.

Returns:
out : [array] The window, with the maximum value normalized to one (the value one appears only if the number of samples is odd).

Example:

import numpy as np

print(np.kaiser(12, 14))

Output:

[  7.72686684e-06   3.46009194e-03   4.65200189e-02   2.29737120e-01
   5.99885316e-01   9.45674898e-01   9.45674898e-01   5.99885316e-01
   2.29737120e-01   4.65200189e-02   3.46009194e-03   7.72686684e-06]

Plotting the window and its frequency response –

For Window :

import numpy as np
import matplotlib.pyplot as plt
from numpy.fft import fft, fftshift

window = np.kaiser(51, 14)

plt.plot(window)
plt.title("Kaiser window")
plt.ylabel("Amplitude")
plt.xlabel("Sample")
plt.show()

Output:

For frequency :

import numpy as np
import matplotlib.pyplot as plt
from numpy.fft import fft, fftshift

window = np.kaiser(51, 14)
plt.figure()

A = fft(window, 2048) / 25.5
mag = np.abs(fftshift(A))
freq = np.linspace(-0.5, 0.5, len(A))
response = 20 * np.log10(mag)
response = np.clip(response, -100, 100)

plt.plot(freq, response)
plt.title("Frequency response of Kaiser window")
plt.ylabel("Magnitude [dB]")
plt.xlabel("Normalized frequency [cycles per sample]")
plt.axis("tight")
plt.show()

Output: