利用Matlab工具箱设计FIR和IIR滤波器

发布于 2023-09-21 16:05:50 浏览：548 订阅该版

[tocm]

## 生成系数
截止频率：65Hz
```matlab
SOS Matrix:                                                 
1  2  1  1  -1.9483812279206605  0.95235504547143668        
1  2  1  1  -1.8848795046449112  0.88872380736622714        
                                                            
Scale Values:                                               
0.0009934543876940359                                       
0.00096107568032897277   
```
截止频率：75Hz
```matlab
SOS Matrix:                                                 
1  2  1  1  -1.9399670771829454  0.94523778322684693        
1  2  1  1  -1.867646689657416   0.8727209080865993         
                                                            
Scale Values:                                               
0.0013176765109754376                                       
0.0012685546072958092  
```
截止频率：85Hz                                                   
```matlab
SOS Matrix:                                                 
1  2  1  1  -1.9314328304904613  0.93817732047303393        
1  2  1  1  -1.8505362037561721  0.85699820579506891        
                                                            
Scale Values:                                               
0.001686122495643158                                        
0.0016155005097241886 
```
截止频率：95Hz
```matlab
SOS Matrix:                                                 
1  2  1  1  -1.9227805373301849  0.93117365861042944        
1  2  1  1  -1.8335462899281088  0.84154989516829737        
                                                            
Scale Values:                                               
0.002098280320061078                                        
0.0020009013100471622     
```
截止频率：105Hz
```matlab
SOS Matrix:                                                 
1  2  1  1  -1.9140122208955201  0.92422678970950123        
1  2  1  1  -1.8166752155117512  0.82637032288824241        
                                                            
Scale Values:                                               
0.0025536422034952134                                       
0.0024237768441227759   
```
## 生成IIR滤波器调用函数

```matlab
function Hd = iir_designer
%IIR_DESIGNER Returns a discrete-time filter object.

% MATLAB Code
% Generated by MATLAB(R) 9.1 and the DSP System Toolbox 9.3.
% Generated on: 19-Aug-2023 21:26:11

% Butterworth Lowpass filter designed using FDESIGN.LOWPASS.

% All frequency values are in Hz.
Fs = 6400;  % Sampling Frequency

N  = 4;   % Order
Fc = 65;  % Cutoff Frequency

% Construct an FDESIGN object and call its BUTTER method.
h  = fdesign.lowpass('N,F3dB', N, Fc, Fs);
Hd = design(h, 'butter');

% [EOF]
```

# 滤波器验证比较
       
```matlab
%%
close all;
clc;
clear;
f = 50;
fs = 6400; %采样频率
time = 1 / fs;
t = 0:time:0.1;
y1 = sin(2 * pi * f * t) + sin(2 * pi * 13 * f * t);
figure('color',[1,1,1]);
subplot(3,1,1);
plot(t,y1);
title('滤波前波形（基波50Hz+13次谐波）');
%%
y2 = filter(fir_designer,y1);  % 直接使用设计好的滤波器进行滤波，fir_designer函数是滤波函数
subplot(3,1,2);
plot(t,y2);
title('FIR滤波后波形');

%%
y3 = filter(iir_designer,y1);  % 直接使用设计好的滤波器进行滤波，iir_designer函数是滤波函数
subplot(3,1,3);
plot(t,y3);
title('IIR滤波后波形');

```