numpy.
bartlett
返回巴特利特窗口。
巴特利特窗与三角形窗非常相似，只是端点为零。它通常用于信号处理，使信号逐渐变细，而不会在频域产生太多的纹波。
输出窗口中的点数。如果小于或等于零，则返回空数组。
三角形窗口，最大值归一化为1（只有当样本数为奇数时才显示值1），第一个和最后一个样本等于零。
参见
blackman
hamming
hanning
kaiser
笔记
Bartlett窗口定义为
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对bartlett窗口的大多数引用来自信号处理文献，在那里它被用作平滑值的许多窗口函数之一。注意，与此窗口的卷积产生线性插值。它也被称为变迹（意思是“消除脚”，即在采样信号的开始和结束处平滑不连续）或渐缩函数。巴特利特的傅立叶变换是两个sinc函数的乘积。注意Kanasewich的精彩讨论。
工具书类
M.S.Bartlett，“周期图分析和连续光谱”，Biometrika 37，1-16，1950年。
E.R.Kanasewich，“地球物理学中的时序分析”，阿尔伯塔大学出版社，1975年，第109-110页。
A.V.Oppenheim和R.W.Schafer，“离散时间信号处理”，普伦蒂斯·霍尔，1999年，第468-471页。
维基百科，“窗口函数”，https://en.wikipedia.org/wiki/window_function
W.H.Press、B.P.Flannery、S.A.Teukolsky和W.T.Vetterling，“数字食谱”，剑桥大学出版社，1986年，第429页。
实例
>>> 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. ])
绘制窗口及其频率响应（需要scipy和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') >>> plt.show()