bartlett(M, sym=True)
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.
The Bartlett window is defined as
$$w(n) = \frac{2}{M-1} \left(\frac{M-1}{2} - \left|n - \frac{M-1}{2}\right| \right)$$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.
Number of points in the output window. If zero or less, an empty array is returned.
When True (default), generates a symmetric window, for use in filter design. When False, generates a periodic window, for use in spectral analysis.
The triangular window, with the first and last samples equal to zero and the maximum value normalized to 1 (though the value 1 does not appear if M is even and :None:None:`sym` is True).
Return a Bartlett window.
triang
A triangular window that does not touch zero at the ends
Plot the window and its frequency response:
>>> from scipy import signal
... from scipy.fft import fft, fftshift
... import matplotlib.pyplot as plt
>>> window = signal.windows.bartlett(51)
... plt.plot(window)
... plt.title("Bartlett window")
... plt.ylabel("Amplitude")
... plt.xlabel("Sample")
>>> plt.figure()See :
... A = fft(window, 2048) / (len(window)/2.0)
... freq = np.linspace(-0.5, 0.5, len(A))
... response = 20 * np.log10(np.abs(fftshift(A / abs(A).max())))
... plt.plot(freq, response)
... plt.axis([-0.5, 0.5, -120, 0])
... plt.title("Frequency response of the Bartlett window")
... plt.ylabel("Normalized magnitude [dB]")
... plt.xlabel("Normalized frequency [cycles per sample]")
The following pages refer to to this document either explicitly or contain code examples using this.
scipy.signal.bartlett
scipy.signal.windows._windows.bartlett
scipy.signal.windows._windows.get_window
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