numpy.bartlett#
- numpy.bartlett(M)[源代码]#
返回 Bartlett 窗口.
Bartlett 窗口与三角形窗口非常相似,只是端点为零.它通常用于信号处理中,用于对信号进行锥形处理,而不会在频域中产生太多的纹波.
- 参数:
- Mint
输出窗口中的点数.如果小于或等于零,则返回一个空数组.
- 返回:
- outarray
三角形窗口,最大值归一化为 1(仅当样本数为奇数时才出现值 1),第一个和最后一个样本等于零.
注释
Bartlett 窗口定义为
\[w(n) = \frac{2}{M-1} \left( \frac{M-1}{2} - \left|n - \frac{M-1}{2}\right| \right)\]大多数对 Bartlett 窗口的引用来自信号处理文献,它被用作平滑值的众多窗口函数之一. 请注意,与此窗口的卷积会产生线性插值. 它也称为apodization(意思是"去除脚",即平滑采样信号的开头和结尾处的不连续性)或锥形函数. Bartlett 窗口的傅里叶变换是两个 sinc 函数的乘积. 请注意 Kanasewich [2] 中的精彩讨论.
参考文献
[1]M.S. Bartlett, “Periodogram Analysis and Continuous Spectra”, Biometrika 37, 1-16, 1950.
[2]E.R. Kanasewich, “Time Sequence Analysis in Geophysics”, The University of Alberta Press, 1975, pp. 109-110.
[3]A.V. Oppenheim and R.W. Schafer, “Discrete-Time Signal Processing”, Prentice-Hall, 1999, pp. 468-471.
[4]Wikipedia, “Window function”, https://en.wikipedia.org/wiki/Window_function
[5]W.H. Press, B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling, “Numerical Recipes”, Cambridge University Press, 1986, page 429.
示例
>>> import numpy as np >>> 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).
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()
plt.figure() 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) plt.title("Frequency response of Bartlett window") plt.ylabel("Magnitude [dB]") plt.xlabel("Normalized frequency [cycles per sample]") plt.axis('tight') plt.show()
