Python实现数据滤波的示例详解

import numpy as np
import scipy.signal as ss

t = np.linspace(-1, 1, 201)
PI = 2*np.pi
x = (np.sin(PI*0.75*t*(1-t) + 2.1) +
     0.1*np.sin(PI*1.25*t + 1) +
     0.18*np.cos(PI*3.85*t))

# 原始数据添加噪声
np.random.seed(42)
xn = x + np.random.rand(len(t))

w = ss.wiener(xn, 9) # 维纳滤波

plt.scatter(t, xn, marker='.', label="original")
plt.plot(t, w, c = 'r', label="wiener")
plt.legend()
plt.show()

import scipy.signal as ss
import matplotlib.pyplot as plt

b, a = ss.butter(3, 0.05)
z = ss.lfilter(b, a, xn)
z2 = ss.lfilter(b, a, z)
z3 = ss.filtfilt(b, a, xn)

# 下面为绘图代码
plt.plot(t, z, 'r--', label="lfilter, once")
plt.plot(t, z2, 'g--', label="lfilter, twice")
plt.plot(t, z3, 'b', label="filtfilt")
plt.scatter(t, xn, marker='.', alpha=0.75)

plt.grid()
plt.legend()
plt.show()

import numpy as np
import scipy.signal as ss
x = [1,3,2,4]
ss.medfilt(x,3) # [1, 2, 3, 2]

from scipy.misc import ascent
import matplotlib.pyplot as plt

img = ascent()
img = img[:256, :256]
r = np.random.rand(*img.shape)
img[r>0.96] = 255
img[r<0.04] = 0

plt.subplot(121)
plt.imshow(img, cmap='gray')
plt.axis('off')

plt.subplot(122)
imFilt = ss.medfilt2d(img, [3,3])
plt.imshow(imFilt, cmap='gray')
plt.axis('off')

plt.show()

x = np.arange(25).reshape(5, 5).astype(float)
I = np.identity(3)

mats = {"original":x}
for i in range(3):
    mats[f"order_filter:{i}"] = ss.order_filter(x, I, i)

def drawMat(x, ax=None):
    M, N = x.shape
    if not ax:
        ax = plt.subplot()
    arrM, arrN = np.arange(M), np.arange(N)
    plt.yticks(arrM+0.5, arrM)
    plt.xticks(arrN+0.5, arrN)
    ax.pcolormesh(x)
    ax.invert_yaxis()
    for i,j in product(range(M),range(N)):
        ax.text(j+0.2, i+0.6, f"{x[i,j]}")

for i,key in enumerate(mats,1):
    ax = plt.subplot(2,2,i)
    drawMat(mats[key], ax)
    plt.title(key)

plt.show()