Python | Blackman in numpy

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:



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import numpy as np 
print(np.blackman(12))

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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:

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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() 

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Output:

blackman_window

.

Code : For frequency:

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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) / 25.5
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 Blackman window")
plt.ylabel("Magnitude [dB]")
plt.xlabel("Normalized frequency [cycles per sample]")
plt.axis('tight')
plt.show()

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Output:

blackman_window

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