bartlett(M)
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.
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.
Return the Bartlett window.
>>> import matplotlib.pyplot as plt
... np.bartlett(12) array([ 0. , 0.18181818, 0.36363636, 0.54545455, 0.72727273, # may vary 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") Text(0.5, 1.0, 'Bartlett window')
>>> plt.ylabel("Amplitude") Text(0, 0.5, 'Amplitude')
>>> plt.xlabel("Sample") Text(0.5, 0, 'Sample')
>>> plt.show()
>>> plt.figure() <Figure size 640x480 with 0 Axes>
>>> A = fft(window, 2048) / 25.5
... mag = np.abs(fftshift(A))
... freq = np.linspace(-0.5, 0.5, len(A))
... with np.errstate(divide='ignore', invalid='ignore'):
... 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") Text(0.5, 1.0, 'Frequency response of Bartlett window')
>>> plt.ylabel("Magnitude [dB]") Text(0, 0.5, 'Magnitude [dB]')
>>> plt.xlabel("Normalized frequency [cycles per sample]") Text(0.5, 0, 'Normalized frequency [cycles per sample]')
>>> _ = plt.axis('tight')See :
... plt.show()
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matplotlib.axes._axes.Axes.cohere
matplotlib.pyplot.psd
numpy.kaiser
matplotlib.pyplot.angle_spectrum
matplotlib.axes._axes.Axes.magnitude_spectrum
matplotlib.pyplot.cohere
numpy.hanning
matplotlib.mlab.cohere
matplotlib.mlab.specgram
numpy.blackman
matplotlib.pyplot.magnitude_spectrum
matplotlib.axes._axes.Axes.psd
matplotlib.pyplot.phase_spectrum
matplotlib.pyplot.csd
matplotlib.axes._axes.Axes.csd
numpy.hamming
matplotlib.mlab.csd
matplotlib.axes._axes.Axes.angle_spectrum
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