基于FPGA的多级CIC滤波器实现四倍抽取一

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。

1滑动平均滤波器

图1 8权值滑动平均滤波器结构

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。

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);

图2 滑动平均滤波器的幅频特征

2 微分器

图3 微分器结构

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。

y(k) = x(k)-x(k-1)

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);

图4 微分器幅频响应特征

3 积分器

图5 数字积分器结构

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。

q(k)=p(k) +q(k-1)

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);

图6 积分器幅频响应特征