如何平滑曲线作为距离的函数

Question

我有一个模拟结果曲线，它是 y = f(x)，它在某个距离间隔之间有一些振荡。我喜欢通过沿 x 应用一些移动平均线来平滑振荡。怎么做？

我知道的移动平均是时间平均。距离平均呢？谢谢

Answer 1

如果您使用的是 python，那么有很多选择：

Savitzky-Golay Filter:

import numpy as np
import matplotlib.pyplot as plt
from scipy.signal import savgol_filter

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()

B-spline:

from scipy.interpolate import make_interp_spline, BSpline

#create data
x = np.array([1, 2, 3, 4, 5, 6, 7, 8])
y = np.array([4, 9, 12, 30, 45, 88, 140, 230])

#define x as 200 equally spaced values between the min and max of original x 
xnew = np.linspace(x.min(), x.max(), 200) 

#define spline
spl = make_interp_spline(x, y, k=3)
y_smooth = spl(xnew)

#create smooth line chart 
plt.plot(xnew, y_smooth)
plt.show()

polynomial approximation:

import numpy as np
import matplotlib.pyplot as plt

plt.figure()
poly = np.polyfit(list_x,list_y,5)
poly_y = np.poly1d(poly)(list_x)
plt.plot(list_x,poly_y)
plt.plot(list_x,list_y)
plt.show()