简单的滤波算法

import numpy as np
import math
import matplotlib.pyplot as plt


###############################
#一维滤波
###############################


start_X = -np.pi
end_x = np.pi
slice_num = 200 #切分
X = np.linspace(start_X,end_x,slice_num,endpoint=True) #X轴向
wave1 = 10*np.sin(X) + 5*np.append(np.random.rand(len(X)-100),np.zeros(100))
#使用复数代表波形，实部代表时间轴，虚部代表幅度
wave1 = X + wave1 * 1j

wave1_real=np.real(wave1)
wave1_imag=np.imag(wave1)
#将波形旋转90度
#wave1 = wave1 * 1j


plt.title('original data')
plt.plot(np.real(wave1), np.imag(wave1))
plt.show()



# 卷积滤波 使用复数
wave2 = []
filter1 = [0.2,0.3,0.5]
for i in range(len(wave1) - len(filter1) + 1):
    point = 0
    for j in range(len(filter1)):
        point += wave1[i+j] * filter1[j]
    wave2.append(point)
wave2 = np.array(wave2)

fig=plt.figure()
plt.title('Convolution filtering consider the time axis')
plt.plot(np.real(wave2), np.imag(wave2))
plt.show()




# 卷积滤波 不使用复数
wave2 = []
for i in range(len(wave1_imag) - len(filter1) + 1):
    point = 0
    for j in range(len(filter1)):
        point += wave1_imag[i+j] * filter1[j]
    wave2.append(point)
for j in range(len(filter1) - 1):
    wave2.append(0)
wave2 = np.array(wave2)

fig=plt.figure()
plt.title('Convolution filtering does not consider the time axis')
plt.plot(np.real(wave1),wave2)
plt.show()




# 普通平滑滤波 
#老数据加权和
wave2 = []
#注意此处的滤波器是老数据的各个加权和
filter2 = [0.4,0.4,0.5]
last = [0,0]#保存老数据
for i in range(len(wave1_imag)):
    k=0
    for j in range(len(filter2)-1):#先加权老数据
        k += last[j] * filter2[j]
    #再加权新数据
    k += wave1_imag[i] * filter2[-1]
    #删除最老的一个数据
    del last[0]
    #添加新数据
    last.append(k)
    wave2.append(last[-1])
wave2 = np.array(wave2)

fig=plt.figure()
plt.title('Ordinary smoothing filter')
plt.plot(X,wave2)
plt.show()

import numpy as np
import math
import matplotlib.pyplot as plt
import cv2

###############################
# 二维滤波
###############################

start_X = -np.pi
end_x = np.pi
slice_num = 200  # 切分
X = np.linspace(start_X, end_x, slice_num, endpoint=True)  # X轴向
wave1 = 10*np.sin(X) + np.append(np.random.rand(len(X)-100), np.zeros(100))
wave1 = X + wave1 * 1j
wave1_real = np.real(wave1)
wave1_imag = np.imag(wave1)

wave2 = 10*np.sin(X) + np.append(np.random.rand(len(X)-100), np.zeros(100))
wave2 = X + wave2 * 1j
wave2_real = np.real(wave1)
wave2_imag = np.imag(wave1)


plt.title('original data1')
plt.plot(np.real(wave1), np.imag(wave1))
fig = plt.figure()
plt.title('original data2')
plt.plot(np.real(wave2), np.imag(wave2))
plt.show()


# 二维卷积滤波,常用于2个或多个传感器滤波减少误差
wave = [wave1, wave2]
wave3 = []
filter1 = [[0.5,0.5],
           [0.5,0.5]]
for i in range(len(wave1) - len(filter1) + 1):
    point = 0
    for j in range(len(filter1)):  # 2行
        for k in range(len(filter1[0])):  # 2列
            point += filter1[j][k] * wave[j][i+k]
    wave3.append(point)
wave3 = np.array(wave3)
fig = plt.figure()
plt.title('filter data')
plt.plot(np.real(wave3), np.imag(wave3))
plt.show()

# 二维图像滤波，这里是直接调opencv库
fig = plt.figure()
plt.title('original image')
img = plt.imread("0.jpg")
plt.imshow(img)

# 卷积核
kernel = np.array([ [1, -2, 1], 
                    [1, -2, 1], 
                    [1, -2, 1]])

res =  cv2.filter2D(img, -1, kernel)
fig = plt.figure()
plt.title('filter image')
plt.imshow(res)

import numpy as np
import math
import matplotlib.pyplot as plt


###############################
#离散傅里叶变换 时域转频域
###############################


start_X = -2*np.pi
end_x = 2*np.pi
slice_num = 200 #切分
X = np.linspace(start_X,end_x,slice_num,endpoint=True) #X轴向
#在原始波形的基础上添加噪点
wave1 = 10*np.sin(X) + 5*np.append(np.random.rand(len(X)-100),np.zeros(100))
wave1 = X + wave1 * 1j
wave1_real=np.real(wave1)
wave1_imag=np.imag(wave1)

# wave1 = wave1

plt.title('original data')
plt.plot(np.real(wave1), np.imag(wave1))
plt.show()


pi = 3.1415926
def DFT(origin):  # 计算给定序列的离散傅里叶变换结果
    N= len(origin)
    output = []
    for i in range(N):
        temp = 0
        for j in range(N):
            temp += origin[j] * ( 
                    (math.cos(2 * math.pi * i * j / N) - math.sin(2 * math.pi * i * j / N) * 1j)
                ) 
        output.append(temp)
    return output


def IDFT(origin): #逆变换
    N= len(origin)
    output = []
    for i in range(N):
        temp = 0
        for j in range(N):
            temp += origin[j] * ( 
                    (math.cos(2 * math.pi * i * j / N) + math.sin(2 * math.pi * i * j / N) * 1j)
                ) 
        output.append(temp / N)
    return output

#dft输出 , 对波形1做傅里叶变换
dft_wave = DFT(wave1_imag)
#idft输出 逆变换
idft_wave = IDFT(dft_wave)

fig = plt.figure()
plt.title('DFT abs data')
plt.plot(np.real(wave1), np.abs(dft_wave))
plt.show()


fig = plt.figure()
plt.title('IDFT data')
plt.plot(np.real(wave1), np.real(idft_wave))
plt.show()

#傅里叶滤波
dft_new_wave = dft_wave.copy()
#过滤杂波，将频谱图上的杂波过滤
for i in range(len(dft_new_wave)):
    if(dft_new_wave[i].__abs__() <= 200):
        dft_new_wave[i]=0
#逆变换得到无杂波的波形
idft_wave = IDFT(dft_new_wave)


fig = plt.figure()
plt.title('DFT filter data')
plt.plot(np.real(wave1), np.real(idft_wave))
plt.show()