跳转到主要内容

基于FPGA的多级CIC滤波器实现四倍抽取一

由 judy 提交于

<font color="#F30">作者：lee</font>

在实现多级CIC滤波器前我们先来了解滑动平均滤波器、微分器、积分器以及梳状滤波器原理。CIC滤波器在通信信号处理中有着重要的应用。

<font color="red"><strong>1、滑动平均滤波器</strong></font>

<center><img width="600" src="http://xilinx.eetrend.com/files/2019-06/wen_zhang_/100043821-72881-1.jp…; alt=""></center><center><font color="#9a9a9a"><i>图1 8权值滑动平均滤波器结构</i></font></center><br>

滑动平均滤波器(Moving Average Filter)的所有权值系数均为1，实现对信号的平滑作用，具有低通特性。

<pre>Matlab ：
close all
clear all
clc

%set system parameter
fs = 1000; %The frequency of the local oscillator signal
Fs = 44100; %sampling frequency
N = 24; %Quantitative bits
L = 8192;

%Generating an input signal
t =0:1/Fs:(1/Fs)*(L-1); %Generating the time series of sampling frequencies
sc =sin(2*pi*fs*t); %a sinusoidal input signal that produces a random starting phase

%滑动平均滤波器
b =[1,1,1,1,1,1,1,1];
a =1;

sf=filter(b,a,sc).*(1/8);</pre>

<center><img width="600" src="http://xilinx.eetrend.com/files/2019-06/wen_zhang_/100043821-72882-2.jp…; alt=""></center><center><font color="#9a9a9a"><i>图2 滑动平均滤波器的幅频特征</i></font></center><br>

<font color="red"><strong>2、微分器</strong></font>

<center><img src="http://xilinx.eetrend.com/files/2019-06/wen_zhang_/100043821-72883-3.jp…; alt=""></center><center><font color="#9a9a9a"><i>图3 微分器结构</i></font></center><br>

微分器有1和-1两个权值系数的滤波器，该滤波器具有简单的高通幅频响应特性。

<center>y( k ) = x( k ) - x( k - 1 )</center>

<pre>Matlab :
close all
clear all
clc

%set system parameter
fs = 1000; %The frequency of the local oscillator signal
Fs = 44100; %sampling frequency
N = 24; %Quantitative bits
L = 8192;

%Generating an input signal
t =0:1/Fs:(1/Fs)*(L-1); %Generating the time series of sampling frequencies
sc =sin(2*pi*fs*t); %a sinusoidal input signal that produces a random starting phase

%微分滤波器
b =[1,-1];
a =1;

sf=filter(b,a,sc);</pre>

<center><img width="600" src="http://xilinx.eetrend.com/files/2019-06/wen_zhang_/100043821-72884-4.jp…; alt=""></center><center><font color="#9a9a9a"><i>图4 微分器幅频响应特征</i></font></center><br>

<font color="red"><strong>3、积分器</strong></font>

<center><img src="http://xilinx.eetrend.com/files/2019-06/wen_zhang_/100043821-72885-5.jp…; alt=""></center><center><font color="#9a9a9a"><i>图5 数字积分器结构</i></font></center><br>

数字积分器是只有一个系数的IIR滤波器该滤波器具有低通的滤波器的幅频响应特性。

<center>q( k ) = p (k) + q( k - 1)</center>

<pre>Matlab :
close all
clear all
clc

%set system parameter
fs = 1000; %The frequency of the local oscillator signal
Fs = 44100; %sampling frequency
N = 24; %Quantitative bits
L = 8192;

%Generating an input signal
t =0:1/Fs:(1/Fs)*(L-1); %Generating the time series of sampling frequencies
sc =sin(2*pi*fs*t); %a sinusoidal input signal that produces a random starting phase

%积分滤波器
b =1;
a =[1,-1];

sf=filter(b,a,sc);</pre>

<center><img width="600" src="http://xilinx.eetrend.com/files/2019-06/wen_zhang_/100043821-72886-6.jp…; alt=""></center><center><font color="#9a9a9a"><i>图6 积分器幅频响应特征</i></font></center><br>

由图3，图4，和图5分析，1khz基本未发生改变，44.1khz相对于352.8khz采样率1khz点变得疏松。

文章转载自： <a href="https://mp.weixin.qq.com/s/aRqsnzxuS6UnV8SlOYPCIA">FPGA开源工作室</a&gt;（leezym0317）
*本文由作者授权转发，如需转载请联系作者本人