Blackman window : It is a taper formed by using the first three terms of a summation of cosines. It was designed to have close to the minimal leakage possible. It is close to optimal, only slightly worse than a Kaiser window.
Parameters(numpy.blackman):
M : int Number of points in the output window.
If zero or less, an empty array is returned.
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.blackman(12)) |
Output:
[ -1.38777878e-17 3.26064346e-02 1.59903635e-01 4.14397981e-01 7.36045180e-01 9.67046769e-01 9.67046769e-01 7.36045180e-01 4.14397981e-01 1.59903635e-01 3.26064346e-02 -1.38777878e-17]
Plotting the window and its frequency response (requires SciPy and matplotlib):
Code : For Window:
import numpy as np import matplotlib.pyplot as plt from numpy.fft import fft, fftshift   window = np.blackman(51)   plt.plot(window) plt.title("Blackman window") plt.ylabel("Amplitude") plt.xlabel("Sample") plt.show() |
Output:
Code : For frequency:
import numpy as np import matplotlib.pyplot as plt from numpy.fft import fft, fftshift   window = np.blackman(51)   plt.figure()   A = fft(window, 2048) / 25.5mag = 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 Blackman window") plt.ylabel("Magnitude [dB]") plt.xlabel("Normalized frequency [cycles per sample]") plt.axis('tight') plt.show() |
Output:
