numpy.hanning

numpy.hanning(M)

返回 Hanning 窗.

Hanning 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,形状为(M,)

该窗口,最大值已标准化为 1(仅当 M 为奇数时,才会出现值 1).

参见

bartlett , blackman , hamming , kaiser

注释

Hanning 窗定义为

\[w(n) = 0.5 - 0.5\cos\left(\frac{2\pi{n}}{M-1}\right) \qquad 0 \leq n \leq M-1\]

Hanning 窗以奥地利气象学家 Julius von Hann 的名字命名.它也被称为 Cosine Bell.有些作者更希望将其称为 Hann 窗,以帮助避免与非常相似的 Hamming 窗混淆.

大多数对 Hanning 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. 106-108.

[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

Try it in your browser!

>>> import numpy as np
>>> np.hanning(12)
array([0.        , 0.07937323, 0.29229249, 0.57115742, 0.82743037,
       0.97974649, 0.97974649, 0.82743037, 0.57115742, 0.29229249,
       0.07937323, 0.        ])

绘制窗口及其频率响应图.

import matplotlib.pyplot as plt
from numpy.fft import fft, fftshift
window = np.hanning(51)
plt.plot(window)
plt.title("Hann 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 the Hann window")
plt.ylabel("Magnitude [dB]")
plt.xlabel("Normalized frequency [cycles per sample]")
plt.axis('tight')
plt.show()

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