numpy.hamming#
- numpy.hamming(M)[源代码]#
返回 Hamming 窗.
Hamming 窗是通过使用加权余弦形成的锥形.
- 参数:
- Mint
输出窗口中的点数. 如果为零或更小,则返回一个空数组.
- 返回:
- outndarray
该窗口的最大值已归一化为 1(仅当样本数为奇数时,值才为 1).
注释
Hamming 窗定义为
\[w(n) = 0.54 - 0.46\cos\left(\frac{2\pi{n}}{M-1}\right) \qquad 0 \leq n \leq M-1\]Hamming 窗以 J. W. Tukey 的同事 R. W. Hamming 的名字命名,并在 Blackman 和 Tukey 中进行了描述.建议用于平滑时域中的截断自协方差函数.大多数对 Hamming 窗的引用来自信号处理文献,在信号处理文献中,它被用作许多用于平滑值的窗函数之一.它也称为保迹函数(意思是“去除足部”,即平滑采样信号开始和结束处的不连续性)或逐渐变细函数.
参考
[1]Blackman, R.B. and Tukey, J.W., (1958) The measurement of power spectra, Dover Publications, New York.
[2]E.R. Kanasewich, “Time Sequence Analysis in Geophysics”, The University of Alberta Press, 1975, pp. 109-110.
[3]Wikipedia, “Window function”, https://en.wikipedia.org/wiki/Window_function
[4]W.H. Press, B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling, “Numerical Recipes”, Cambridge University Press, 1986, page 425.
示例
>>> import numpy as np >>> np.hamming(12) array([ 0.08 , 0.15302337, 0.34890909, 0.60546483, 0.84123594, # may vary 0.98136677, 0.98136677, 0.84123594, 0.60546483, 0.34890909, 0.15302337, 0.08 ])
绘制窗口和频率响应.
import matplotlib.pyplot as plt from numpy.fft import fft, fftshift window = np.hamming(51) plt.plot(window) plt.title("Hamming 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)) response = 20 * np.log10(mag) response = np.clip(response, -100, 100) plt.plot(freq, response) plt.title("Frequency response of Hamming window") plt.ylabel("Magnitude [dB]") plt.xlabel("Normalized frequency [cycles per sample]") plt.axis('tight') plt.show()
