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发布网友 发布时间：2022-04-20 08:32

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热心网友 时间：2022-07-12 00:47

当采样频率ws=2wm时，称为临界采样。据此可知：下列程序实现对信号Sa(t)的临界采样及由采样信号恢复Sa(t):

程序如下:

wm=1; wc=wm;  

Ts=pi/wm; ws=2*pi/Ts;

n=-170:170; nTs=n*Ts f=sinc(nTs/pi);

Dt=0.005;t=-45:Dt:45; 

fa=f*Ts*wc/pi*sinc((wc/pi)*(ones(length(nTs),1)*t-nTs'*ones(1,length(t))));

t1=-25:0.5:25;

f1=sinc(t1/pi); subplot(211); stem(t1,f1); xlabel('kTs');

ylabel('f(kTs)'); 

title('sa(t)=sinc(t/pi)的临界采样信号');

subplot(212); plot(t,fa) xlabel('t'); ylabel('fa(t)'); 

title('由sa(t)=sinc(t/pi)的临界采样信号重构sa(t)'); grid;

过采样及其重构 ,当ws>2wm时则称采样为过采样，所以令wm=1，wc=1.1*wm，Ts=0.8*pi/wm，ws=2*pi/Ts则下列程序实现对信号Sa(t)的临界采样及由采样信号恢复Sa(t):

wm=1; wc=1.1*wm;

 Ts=0.8*pi/wm; ws=2*pi/Ts;

n=-170:170; nTs=n*Ts f=sinc(nTs/pi);

Dt=0.005;t=-45:Dt:45; 

fa=f*Ts*wc/pi*sinc((wc/pi)*(ones(length(nTs),1)*t-nTs'*ones(1,length(t))));

error=abs(fa-sinc(t/pi));

t1=-25:0.5:25;

f1=sinc(t1/pi); subplot(311); stem(t1,f1); xlabel('kTs');

ylabel('f(kTs)'); 

title('sa(t)=sinc(t/pi)的采样信号');

subplot(312); plot(t,fa) xlabel('t'); ylabel('fa(t)'); 

      title('由sa(t)=sinc(t/pi)的过采样信号重构sa(t)');

     grid;  subplot(313); plot(t,error); xlabel('t'); ylabel('error(t)'); 

     title('过采样信号与原信号的误差error(t)');

3、欠采样及其重构 令wm=1，wc=wm，ws=1.3*pi/wm，这种采样信号被称为欠采样信号，这种信号的重构被称为欠采样信号的重构，具体程序如下： 

 wm=1; wc=wm;

  Ts=1.3 *pi/wm; ws=2*pi/Ts;

 n=-170:170; nTs=n*Ts f=sinc(nTs/pi);

 Dt=0.005;t=-45:Dt:45; 

fa=f*Ts*wc/pi*sinc((wc/pi)*(ones(length(nTs),1)*t-nTs'*ones(1,length(t))));

 error=abs(fa-sinc(t/pi));

 t1=-25:0.5:25; 

f1=sinc(t1/pi); subplot(311);

stem(t1,f1);

xlabel('kTs'); ylabel('f(kTs)'); 

title('sa(t)=sinc(t/pi)的采样信号'); subplot(312); plot(t,fa) xlabel('t'); ylabel('fa(t)'); 

title('由sa(t)=sinc(t/pi)的欠采样信号重构sa(t)'); grid; subplot(313); plot(t,error); xlabel('t'); ylabel('error(t)'); 

title('欠采样信号与原信号的误差error(t)');