numpy bartlett() in Python

The Bartlett window is very similar to a triangular window, except that the endpoints are at zero. It is often used in signal processing for tapering a signal, without generating too much ripple in the frequency domain.

Parameters(numpy.bartlett(M)): 
M : int Number of points in the output window. 
     If zero or less, an empty array is returned.

Returns: 
out : array

The triangular window, with the maximum value normalized to one (the value one appears only if the number of samples is odd), with the first and last samples equal to zero. Example: Python3 1==

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

Output:

[ 0.          0.18181818  0.36363636  0.54545455  0.72727273  0.90909091
  0.90909091  0.72727273  0.54545455  0.36363636  0.18181818  0.        ]

Plotting the window and its frequency response (requires SciPy and matplotlib): For Window: Python3 1==

import numpy as np
import matplotlib.pyplot as plt
from numpy.fft import fft, fftshift
window = np.bartlett(51)
plt.plot(window)
plt.title("Bartlett window")
plt.ylabel("Amplitude")
plt.xlabel("Sample")
plt.show()

Output: For frequency: Python3 1==

import numpy as np
import matplotlib.pyplot as plt
from numpy.fft import fft, fftshift
window = np.bartlett(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 Bartlett window")
plt.ylabel("Magnitude [dB]")
plt.xlabel("Normalized frequency [cycles per sample]")
plt.axis('tight')
plt.show()

Output: