python - 时间序列中的降噪保持锐利的边缘

Question

在来自功率计的时间序列中，过程和传感器都会产生噪声。为了识别步骤，我想在不牺牲边缘陡峭度的情况下过滤噪声。

想法是做一个rolling(window).mean()=> 杀死边缘或rolling(window).median()=> 但如果窗口大小需要小，这会产生谐波噪声问题。

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

# create a reference signal
xrng = 50
sgn = np.zeros(xrng)
sgn[10:xrng//2] = 1
sgn[xrng//2:xrng-10]=0.5

fig = plt.figure(figsize=(10,6))
plt.plot(sgn, label='raw') 

T=3    # period of the sine like noise (random phase shifts not modeled)
noise1 = (np.random.rand(xrng)-0.5)*0.2          # sensor noise
noise2 = np.sin(np.arange(xrng)*2*np.pi/T)*0.1   # harmonic noise 
sg_n = sgn + noise1 + noise2                     # noised signal 
plt.plot(sg_n, label='noised')

# 1. filter mean (good for hamonic)
mnfltr = np.ones(7)/7             
sg_mn = np.convolve(mnfltr,sg_n, 'same')
plt.plot(sg_mn, label='roll_mean')

# 2. filter median (good for edges)  
median = pd.Series(sg_n).rolling(9).median().shift(-4) 
plt.plot(median, label='roll_med') 

plt.legend()
plt.show()

输出看起来像：

有没有办法结合两个过滤器来获得两种好处或任何其他方法？

标签： pythontime-seriesnoise

Answer 1

如果噪声的幅度没有掩盖步长，则可以使用完全不同的方法重建步进信号。

您的设置：

import numpy as np
import matplotlib.pyplot as plt

xrng = 50
sgn = np.zeros(xrng)
sgn[10:xrng//2] = 1
sgn[xrng//2:xrng-10]=0.5

fig = plt.figure(figsize=(10,6))
plt.plot(sgn, label='raw') 

T=3    # period of the sine like noise (random phase shifts not modeled)
noise1 = (np.random.rand(xrng)-0.5)*0.2          # sensor noise
noise2 = np.sin(np.arange(xrng)*2*np.pi/T)*0.1   # harmonic noise 
sg_n = sgn + noise1 + noise2                     # noised signal 
plt.plot(sg_n, label='noised')

噪声信号可以被数字化

bins = np.arange(-.25, 2, .5)
plt.plot((np.digitize(sg_n, bins)-1)/2, '.', markersize=8, label='reconstructed from noiced')
plt.legend();

结果：