MatLab:

1，终端中输入 fdatool

2，选择参数，如下

3，【Edit】→\rightarrow→【convert structure…】

4，【Edit】→\rightarrow→【convert to Single section】
5，【File】→\rightarrow→【Generate MATLAB code 】→\rightarrow→【Filter Design Function】 保存 我这里选择的是 Lowpass.m
6，【File】→\rightarrow→【Export…】

Butterworth 时域滤波公式
y[i]=∑j=0N+1(b[j]×x[i−j])−∑j=1N+1(a[j]×y[i−j])y[i]=\sum_{j=0}^{N+1}(b[j]\times x[i-j])-\sum_{j=1}^{N+1}(a[j]\times y[i-j])y[i]=j=0∑N+1​(b[j]×x[i−j])−j=1∑N+1​(a[j]×y[i−j])
其中 b为Num、a为Den、N为阶数

将Num Den 导出
编写c++语言代码：
产生频率为 50、300的正弦波
改变printf 生成 x和y

code :

#include <bits/stdc++.h>
using namespace std;
#define pi 3.1415926
#define S 1000
typedef struct {double InPut;double OutPut;double x[11];double y[11];double b[11]={0.00049945,0.0049945,0.022475,0.059934,0.10489,0.12586,0.10489,0.059934,0.022475,0.0049945,0.00049945};double a[11]={1,-1.9924,3.0195,-2.8185,2.0387,-1.0545,0.41445,-0.11572,0.022499,-0.0026689,0.00014876};int Begin=0;int End=0;int M=0;int N=11;
}IIR;void IIRCalc(IIR &Lowpass){Lowpass.x[Lowpass.Begin]=Lowpass.InPut;Lowpass.y[Lowpass.Begin]=Lowpass.OutPut=0;Lowpass.End=(Lowpass.Begin)%Lowpass.N;for(int i=0;i<Lowpass.N;i++){if(Lowpass.End<0){Lowpass.End=(Lowpass.End+Lowpass.N)%Lowpass.N;}Lowpass.OutPut+=Lowpass.b[i]*Lowpass.x[Lowpass.End];Lowpass.OutPut-=Lowpass.a[i]*Lowpass.y[Lowpass.End];--Lowpass.End;}Lowpass.y[Lowpass.Begin]=Lowpass.OutPut;++Lowpass.Begin;if(Lowpass.Begin>=Lowpass.N){Lowpass.Begin=0;}
}
IIR Lowpass;
int main(){freopen("out.txt", "w", stdout);for(int i=0;i<S;i++){if(sin(2*pi*100*i/1000)>0) Lowpass.InPut=5;else Lowpass.InPut=0;IIRCalc(Lowpass);printf("%lf ,", Lowpass.OutPut);}
}

将 x y的数据复制到 MATLAB中，查看结果

MATLAB code:

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,2.830208 ,0.877728 ,-0.459678 ,-0.666516 ,0.340372 ,2.169177 ,4.121656 ,5.459063 ,5.665901 ,4.659012 ,2.830208 ,0.877728 ,-0.459678 ,-0.666516 ,0.340372 ,2.169177 ,4.121656 ,5.459063 ,5.665901 ,4.659012 ,2.830208 ,0.877728 ,-0.459678 ,-0.666516 ,0.340372 ,2.169177 ,4.121656 ,5.459063 ,5.665901 ,4.659012 ,2.830208 ,0.877728 ,-0.459678 ,-0.666516 ,0.340372 ,2.169177 ,4.121656 ,5.459063 ,5.665901 ,4.659012 ,2.830208 ,0.877728 ,-0.459678 ,-0.666516 ,0.340372 ,2.169177 ,4.121656 ,5.459063 ,5.665901 ,4.659012 ,2.830208 ,0.877728 ,-0.459678 ,-0.666516 ,0.340372 ,2.169177 ,4.121656 ,5.459063 ,5.665901 ,4.659012 ,2.830208 ,0.877728 ,-0.459678 ,-0.666516 ,0.340372 ,2.169177 ,4.121656 ,5.459063 ,5.665901 ,4.659012 ,2.830208 ,0.877728 ,-0.459678 ,-0.666516 ,0.340372 ,2.169177 ,4.121656 ,5.459063 ,5.665901 ,4.659012 ,2.830208 ,0.877728 ,-0.459678 ,-0.666516 ,0.340372 ,2.169177 ,4.121656 ,5.459063 ,5.665901 ,4.659012 ,2.830208 ,0.877728 ,-0.459678 ,-0.666516 ,0.340372 ,2.169177 ,4.121656 ,5.459063 ,5.665901 ,4.659012 ,2.830208 ,0.877728 ,-0.459678 ,-0.666516 ,0.340372 ,2.169177 ,4.121656 ,5.459063 ,5.665901 ,4.659012 ,2.830208 ,0.877728 ,-0.459678 ,-0.666516 ,0.340372 ,2.169177 ,4.121656 ,5.459063 ,5.665901 ,4.659012 ,2.830208 ,0.877728 ,-0.459678 ,-0.666516 ,0.340372 ,2.169177 ,4.121656 ,5.459063 ,5.665901 ,4.659012 ,2.830208 ,0.877728 ,-0.459678 ,-0.666516 ,0.340372 ,2.169177 ,4.121656 ,5.459063 ,5.665901 ,4.659012 ,2.830208 ,0.877728 ,-0.459678 ,-0.666516 ,0.340372 ,2.169177 ,4.121656 ,5.459063 ,5.665901 ,4.659012 ,2.830208 ,0.877728 ,-0.459678 ,-0.666516 ,0.340372 ,2.169177 ,4.121656 ,5.459063 ,5.665901 ,4.659012 ,2.830208 ,0.877728 ,-0.459678 ,-0.666516 ,0.340372 ,2.169177 ,4.121656 ,5.459063 ,5.665901 ,4.659012 ,2.830208 ,0.877728 ,-0.459678 ,-0.666516 ,0.340372 ,2.169177 ,4.121656 ,5.459063 ,5.665901 ,4.659012 ,2.830208 ,0.877728 ,-0.459678 ,-0.666516 ,0.340372 ,2.169177 ,4.121656 ,5.459063 ,5.665901 ,4.659012 ,2.830208 ,0.877728 ,-0.459678 ,-0.666516 ,0.340372 ,2.169177 ,4.121656 ,5.459063 ,5.665901 ,4.659012 ,2.830208 ,0.877728 ,-0.459678 ,-0.666516 ,0.340372 ,2.169177 ,4.121656 ,5.459063 ,5.665901 ,4.659012 ,2.830208 ,0.877728 ,-0.459678 ,-0.666516 ,0.340372 ,2.169177 ,4.121656 ,5.459063 ,5.665901 ,4.659012 ,2.830208 ,0.877728 ,-0.459678 ,-0.666516 ,0.340372 ,2.169177 ,4.121656 ,5.459063 ,5.665901 ,4.659012 ,2.830208 ,0.877728 ,-0.459678 ,-0.666516 ,0.340372 ,2.169177 ,4.121656 ,5.459063 ,5.665901 ,4.659012 ,2.830208 ,0.877728 ,-0.459678 ,-0.666516 ,0.340372 ,2.169177 ,4.121656 ,5.459063 ,5.665901 ,4.659012 ,2.830208 ,0.877728 ,-0.459678 ,-0.666516 ,0.340372 ,2.169177 ,4.121656 ,5.459063 ,5.665901 ,4.659012 ,2.830208 ,0.877728 ,-0.459678 ,-0.666516 ,0.340372 ,2.169177 ,4.121656 ,5.459063 ,5.665901 ,4.659012 ,2.830208 ,0.877728 ,-0.459678 ,-0.666516 ,0.340372 ,2.169177 ,4.121656 ,5.459063 ,5.665901 ,4.659012 ,2.830208 ,0.877728 ,-0.459678 ,-0.666516 ,0.340372 ,2.169177 ,4.121656 ,5.459063 ,5.665901 ,4.659012 ,2.830208 ,0.877728 ,-0.459678 ,-0.666516 ,0.340372 ,2.169177 ,4.121656 ,5.459063 ,5.665901 ,4.659012 ,2.830208 ,0.877728 ,-0.459678 ,-0.666516 ,0.340372 ,2.169177 ,4.121656 ,5.459063 ,5.665901 ,4.659012 ,2.830208 ,0.877728 ,-0.459678 ,-0.666516 ,0.340372 ,2.169177 ,4.121656 ,5.459063 ,5.665901 ,4.659012 ,2.830208 ,0.877728 ,-0.459678 ,-0.666516 ,0.340372 ,2.169177 ,4.121656 ,5.459063 ,5.665901 ,4.659012 ,2.830208 ,0.877728 ,-0.459678 ,-0.666516 ,0.340372 ,2.169177 ,4.121656 ,5.459063 ,5.665901 ,4.659012 ,2.830208 ,0.877728 ,-0.459678 ,-0.666516 ,0.340372 ,2.169177 ,4.121656 ,5.459063 ,5.665901 ,4.659012 ,2.830208 ,0.877728 ,-0.459678 ,-0.666516 ,0.340372 ,2.169177 ,4.121656 ,5.459063 ,5.665901 ,4.659012 ,2.830208 ,0.877728 ,-0.459678 ,-0.666516 ,0.340372 ,2.169177 ,4.121656 ,5.459063 ,5.665901 ,4.659012 ,2.830208 ,0.877728 ,-0.459678 ,-0.666516 ,0.340372 ,2.169177 ,4.121656 ,5.459063 ,5.665901 ,4.659012 ,2.830208 ,0.877728 ,-0.459678 ,-0.666516 ,0.340372 ,2.169177 ,4.121656 ,5.459063 ,5.665901 ,4.659012 ,2.830208 ,0.877728 ,-0.459678 ,-0.666516 ,0.340372 ,2.169177 ,4.121656 ,5.459063 ,5.665901 ,4.659012 ,2.830208 ,0.877728 ,-0.459678 ,-0.666516 ,0.340372 ,2.169177 ,4.121656 ,5.459063 ,5.665901 ,4.659012 ,2.830208 ,0.877728 ,-0.459678 ,-0.666516 ,0.340372 ,2.169177 ,4.121656 ,5.459063 ,5.665901 ,4.659012 ,2.830208 ,0.877728 ,-0.459678 ,-0.666516 ,0.340372 ,2.169177 ,4.121656 ,5.459063 ,5.665901 ,4.659012 ,2.830208 ,0.877728 ,-0.459678 ,-0.666516 ,0.340372 ,2.169177 ,4.121656 ,5.459063 ,5.665901 ,4.659012 ,2.830208 ,0.877728 ,-0.459678 ,-0.666516 ,0.340372 ,2.169177 ,4.121656 ,5.459063 ,5.665901 ,4.659012 ,2.830208 ,0.877728 ,-0.459678 ,-0.666516 ,0.340372 ,2.169177 ,4.121656 ,5.459063 ,5.665901 ,4.659012 ,2.830208 ,0.877728 ,-0.459678 ,-0.666516 ,0.340372 ,2.169177 ,4.121656 ,5.459063 ,5.665901 ,4.659012 ,2.830208 ,0.877728 ,-0.459678 ,-0.666516 ,0.340372 ,2.169177 ,4.121656 ,5.459063 ,5.665901 ,4.659012 ,2.830208 ,0.877728 ,-0.459678 ,-0.666516 ,0.340372 ,2.169177 ,4.121656 ,5.459063 ,5.665901 ,4.659012 ,2.830208 ,0.877728 ,-0.459678 ,-0.666516 ,0.340372 ,2.169177 ,4.121656 ,5.459063 ,5.665901 ,4.659012 ,2.830208 ,0.877728 ,-0.459678 ,-0.666516 ,0.340372 ,2.169177 ,4.121656 ,5.459063 ,5.665901 ,4.659012 ,];
subplot(6,1,1);
plot(x);subplot(6,1,2);
y1=abs(fft(x)).*2/1000;
plot(y1);y3 = filter(loss,x);
subplot(6,1,3);
plot(y3);subplot(6,1,4);
y4=abs(fft(y3)).*2/1000;
plot(y4);subplot(6,1,5);
plot(y);subplot(6,1,6);
y5=abs(fft(y)).*2/1000;
plot(y5);

同样 带阻滤波器如下：

code

#include <bits/stdc++.h>
using namespace std;
#define pi 3.1415926
#define S 50000
double x[200000];
double y[200000];
double b[20]={ 0.36979, -1.1967, 3.3981,-5.7896,8.6699,-9.2278,8.6699,-5.7896,3.3981,-1.1967,0.36979};
double a[20]={1,-2.6071, 5.8006,-7.9918,9.6486,-8.442,6.5155,-3.631,1.7741,-0.52858,0.13674};int main(){freopen("out.txt", "w", stdout);for(int i=15;i<S;i++){x[i]=sin(2*pi*5000*i/S)+sin(2*pi*6000*i/S)+sin(2*pi*7000*i/S)+sin(2*pi*8000*i/S)+sin(2*pi*9000*i/S)+sin(2*pi*10000*i/S)+sin(2*pi*15000*i/S);for(int j=0;j<11;j++)y[i]+=b[j]*x[i-j];for(int j=1;j<11;j++)y[i]-=a[j]*y[i-j];printf("%lf ,", y[i]);}
}

MATLAB 显示 同上

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