在實現(xiàn)多級CIC濾波器前我們先來了解滑動平均濾波器、微分器、積分器以及梳狀濾波器原理。CIC濾波器在通信信號處理中有著重要的應用。

1滑動平均濾波器

圖1 8權值滑動平均濾波器結構

滑動平均濾波器(Moving Average Filter)的所有權值系數(shù)均為1，實現(xiàn)對信號的平滑作用，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

%滑動平均濾波器

b =[1,1,1,1,1,1,1,1];

a =1;

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

圖2 滑動平均濾波器的幅頻特征

2 微分器

圖3 微分器結構

微分器有1和-1兩個權值系數(shù)的濾波器，該濾波器具有簡單的高通幅頻響應特性。

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

%微分濾波器

b =[1,-1];

a =1;

sf=filter(b,a,sc);

圖4 微分器幅頻響應特征

3 積分器

圖5 數(shù)字積分器結構

數(shù)字積分器是只有一個系數(shù)的IIR濾波器該濾波器具有低通的濾波器的幅頻響應特性。

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

%積分濾波器

b =1;

a =[1,-1];

sf=filter(b,a,sc);

圖6 積分器幅頻響應特征