让我们假设我们有一个数据集，它大概是
import numpy as np
x = np.linspace(0,2*np.pi,100)
y = np.sin(x) + np.random.random(100) * 0.2
Therefore we have a variation of 20% of the dataset. My first idea was to use the UnivariateSpline function of scipy, but the problem is that this does not consider the small noise in a good way. If you consider the frequencies, the background is much smaller than the signal, so a spline only of the cutoff might be an idea, but that would involve a back and forth fourier transformation, which might result in bad behaviour.
Another way would be a moving average, but this would also need the right choice of the delay.
有什么提示/书籍或链接可以解决这个问题吗?
我喜欢Savitzky-Golay滤镜。它使用最小二乘将数据的一个小窗口回归到一个多项式上，然后使用多项式来估计窗口中心的点。最后，窗口向前移动一个数据点，然后重复这个过程。这一直持续到每个点都相对于它的邻居进行了最佳调整。即使是非周期和非线性源的噪声样本，它也能很好地工作。
下面是一个完整的食谱示例。请参阅下面的代码，了解它使用起来有多简单。注意:我省略了定义savitzky_golay()函数的代码，因为您可以从上面链接的烹饪书示例中复制/粘贴它。
import numpy as np
import matplotlib.pyplot as plt
x = np.linspace(0,2*np.pi,100)
y = np.sin(x) + np.random.random(100) * 0.2
yhat = savitzky_golay(y, 51, 3) # window size 51, polynomial order 3
plt.plot(x,y)
plt.plot(x,yhat, color='red')
plt.show()
更新:我注意到我链接的食谱例子已经被撤下了。幸运的是，正如@dodohjk(感谢@bicarlsen提供的更新链接)指出的那样，Savitzky-Golay过滤器已经被合并到SciPy库中。
要使用SciPy源代码调整上面的代码，输入:
from scipy.signal import savgol_filter
yhat = savgol_filter(y, 51, 3) # window size 51, polynomial order 3
