numpy.bartlett()

Return the Bartlett window.

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

Notes

The Bartlett window is defined as

Most references to the Bartlett window come from the signal processing literature, where it is used as one of many windowing functions for smoothing values. Note that convolution with this window produces linear interpolation. It is also known as an apodization (which means?removing the foot?, i.e. smoothing discontinuities at the beginning and end of the sampled signal) or tapering function. The fourier transform of the Bartlett is the product of two sinc functions. Note the excellent discussion in Kanasewich.

References

Examples

>>> np.bartlett(12)
array([ 0.        ,  0.18181818,  0.36363636,  0.54545455,  0.72727273,
        0.90909091,  0.90909091,  0.72727273,  0.54545455,  0.36363636,
        0.18181818,  0.        ])

Plot the window and its frequency response (requires SciPy and matplotlib):

>>> from numpy.fft import fft, fftshift
>>> window = np.bartlett(51)
>>> plt.plot(window)
[<matplotlib.lines.Line2D object at 0x...>]
>>> plt.title("Bartlett window")
<matplotlib.text.Text object at 0x...>
>>> plt.ylabel("Amplitude")
<matplotlib.text.Text object at 0x...>
>>> plt.xlabel("Sample")
<matplotlib.text.Text object at 0x...>
>>> plt.show()

>>> plt.figure()
<matplotlib.figure.Figure object at 0x...>
>>> 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)
[<matplotlib.lines.Line2D object at 0x...>]
>>> plt.title("Frequency response of Bartlett window")
<matplotlib.text.Text object at 0x...>
>>> plt.ylabel("Magnitude [dB]")
<matplotlib.text.Text object at 0x...>
>>> plt.xlabel("Normalized frequency [cycles per sample]")
<matplotlib.text.Text object at 0x...>
>>> plt.axis('tight')
(-0.5, 0.5, -100.0, ...)
>>> plt.show()