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南通大学罗开元

t=[t1,t2,t3];

f=[zeros(1,length(t1)),ones(1,length(t2)),zeros(1,length(t3))]; m0=5;

f1=[zeros(1,m0),f];f2=f1(1:length(f)) w=-2*pi:0.1:2*pi; F=f*exp(-j*t'*w)*dt;

subplot(2,2,1);plot(w,abs(F));grid; subplot(2,2,2);plot(w,angle(F));grid; F2=f2*exp(-j*t'*w)*dt;

subplot(2,2,3);plot(w,abs(F2));grid; subplot(2,2,4);plot(w,angle(F2));grid; 仿真结果:

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南通大学罗开元

频移性质:

Command Window

dt=0.1; N=500; door__width=10; tao=door__width/2; t1=-(N-1):dt:-tao+1; t2=-tao:dt:tao; t3=tao-1:dt:N-1; t=[t1,t2,t3];

f=[zeros(1,length(t1)),ones(1,length(t2)),zeros(1,length(t3))]; w1=0.5*pi;

f2=f.*exp(-j*w1*t); w=-2*pi:0.1:2*pi; F=f*exp(-j*t'*w)*dt;

subplot(2,2,1);plot(w,abs(F));grid; subplot(2,2,2);plot(w,angle(F));grid; F2=f2*exp(-j*t'*w)*dt;

subplot(2,2,3);plot(w,abs(F2));grid; subplot(2,2,4);plot(w,angle(F2));grid; 仿真结果:

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南通大学罗开元

(3)画出g(*g(的频谱图,验证时域卷积定理。 ?t)?t)Command Window

dt=0.1;N=50; door__width=8; tao=door__width/2; t1=-(N-1):dt:-tao+dt; t2=-tao:dt:tao; t3=tao-dt:dt:N-1; t=[t1,t2,t3];

f=[zeros(1,length(t1)),ones(1,length(t2)),zeros(1,length(t3))]; [k,f2]=myconv(f,f,t,t,dt) subplot(2,2,1);stairs(t,f); subplot(2,2,2);plot(k,f2); w=-2*pi:0.1:2*pi;

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南通大学罗开元

F=f*exp(-j*t'*w)*dt;

subplot(2,2,3);plot(w,abs(F));grid; F2=f2*exp(-j*t'*w)*dt;

subplot(2,2,4);plot(w,abs(F2));grid; 得到波形如下图所示:

(4)画出g(和?Sa(? t/2)的频谱图,比较两者的联系,验证傅里叶变换的对?t)称性;

Command Window

dt=0.03;N=10; door__width=10; tao=door__width/2; t1=-(N-1):dt:-tao-dt; t2=-tao:dt:tao; t3=tao-dt:dt:N-1; t=[t1,t2,t3];

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南通大学罗开元

f=[zeros(1,length(t1)),ones(1,length(t2)),zeros(1,length(t3))]; subplot(2,2,1);stairs(t,f);grid;title('门函数波形'); f2=10*sin(5*t)./(5*t);

subplot(2,2,2); plot(t,f2);grid;title('Sa函数波形'); w=-2*pi:0.1:2*pi; F=f*exp(-j*t'*w)*dt;

subplot(2,2,3);plot(w,real(F));grid;title('门函数频谱'); F2=f2*exp(-j*t'*w)*dt;

subplot(2,2,4);plot(w,real(F2));grid;title('Sa函数频谱'); 仿真结果:

(5)画sin(2?t)和g?(t)sin(2?t)的振幅频谱图,验证频域卷积定理。

Command Window

dt=0.01;N=20; door_width=5; tao=door_width/2;

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