信号与系统matlab实验.doc

实验一：常用信号的时域分析与MATLAB实现实验内容：1、用MATLAB实现常用连续时间信号，如抽样信号、阶跃信号、冲激信号、正弦信号、单边指数信号、复指数信号。2、用MATLAB实现常用离散时间信号，如阶跃序列、单位序列、正弦序列、单边实指数序列、虚指数序列、复指数序列。3、用MATLAB编程实现连续信号变换。如：1、设信号，用MATLAB求f (t + 2)，f (t - 2), f (-t ), f (2t),- f (t)，并绘出其时域波形。2、已知如图所示信号，信号tf1(t)044求：（1）（2）（3）（4）附：参考程序一、常用连续时间信号1、抽样信号t=-10:1:10；f=sin(t)./t；plot(t,f)；title(f(t)=Sa(t)；xlabel(t)；axis(-10,10,-0.4,1.1)；t=-10:0.02:10；f=sin(t)./t；plot(t,f)；title(f(t)=Sa(t)；xlabel(t)；axis(-10,10,-0.4,1.1)；2、阶跃信号function jieyao(t1,t2,t0)t=t1:0.01:-t0; %t0时刻前时间样本向量tt=-t0:0.01:t2; %t0时刻后时间样本向量n=length(t); %t0前时间样本点向量长度nn=length(tt) %t0后样本点向量长度u=zeros(1,n); %t0前各样本点信号值赋值为零uu=ones(1,nn); %t0后各样本点信号值赋值为一plot(tt,uu) %绘出t0时刻后波形hold on %允许在同一坐标系中添加图形plot(t,u) %绘出t0时刻前波形plot(-t0,-t0,0,1) %添加直线hold off %关闭添加命令title(单位阶跃信号) %图形标题axis(t1,t2,-0.2,1.5) %限制坐标范围jieyue(-1,4,0)%实现画图f(t)=u(t+3)-2u(t)f=sym(heaviside(t+3)-2*heaviside(t)ezplot(f,-5,4),hold on,plot(0,0,-1,1),axis(-5,4,-1.1,1.1),hold off3、冲激信号function chongji(t1,t2,t0)dt=0.01;t=t1:dt:t2;n=length(t); %时间样本点的向量长度x=zeros(1,n); %各样本点信号值赋为零x(1,(-t0-t1)/dt+1)=1/dt; %在时间t=-t0处，给样本点赋值为1/dtstairs(t,x);axis(t1,t2,0,1.2/dt)title(单位冲激信号d(t)chongji(-1,5,0)4、正弦信号f=sym(3*sin(w)*t)f1=subs(f,w,pi/2)ezplot(f1,0,4*pi)f2=subs(f,w,pi)ezplot(f2,0,4*pi)f3=subs(f,w,3*pi/2)ezplot(f3,0,4*pi)5、单边指数信号t=0:0.05:3;f=exp(-1.5*t);plot(t,f)axis(0,3,0,1.2)title(单边指数信号)text(3.1,0.05,t)f=sym(exp(a*t)f1=subs(f,a,-1)ezplot(f1,-2,2)f2=subs(f,a,1)ezplot(f2,-2,2)f3=subs(f,a,0)ezplot(f3,-2,2)6、虚指数信号下面是用MATLAB绘制虚指数信号的实用子函数：function xzsu(w,n1,n2,a)%n1:绘制波形的起始时间%n1:绘制波形的终止时间%w:虚指数信号角频率%a: 虚指数信号的幅度t=n1:0.01:n2;X=a*exp(i*w*t);Xr=real(X);Xi=imag(X);Xa=abs(X);Xn=angle(X);subplot(2,2,1),plot(t,Xr),axis(n1,n2,-(max(Xa)+0.5),max(Xa)+0.5),title(实部);subplot(2,2,3),plot(t,Xi),axis(n1,n2,-(max(Xa)+0.5),max(Xa)+0.5),title(虚部);subplot(2,2,2), plot(t,Xa),axis(n1,n2,0,max(Xa)+1),title(模);subplot(2,2,4),plot(t,Xn),axis(n1,n2,-(max(Xn)+1),max(Xn)+1),title(相角);xzsu(pi/4,0,15,2)7、复指数信号t=0:0.01:3a=-1;b=10;z=exp(a+i*b)*t)subplot(2,2,1),plot(t,real(z),title(实部)subplot(2,2,3),plot(t,imag(z),title(虚部)subplot(2,2,2),plot(t,abs(z),title(模)subplot(2,2,4),plot(t,angle(z),title(相角)二、常用离散时间信号1、离散时间信号function dwxulie(k1,k2,k0)k=k1:k2;n=length(k);f=zeros(1,n);f(1,-k0-k1+1)=1; %在k0时刻，信号赋值为一stem(k,f,filled)axis(k1,k2,0,1.5)title(单位序列d(k)dwxulie(-5,5,0)2、单位阶跃信号function jyxulie(k1,k2,k0)k=k1:-k0-1;kk=-k0:k2;n=length(k);nn=length(kk)u=zeros(1,n); %k0前信号赋值为零uu=ones(1,nn);%k0后信号赋值为一stem(kk,uu,filled)hold onstem(k,u,filled)hold offtitle(单位阶跃序列)axis(k1 k2 0 1.5)jyxulie(-3,8,0)3、正弦序列k=0:40;subplot(2,1,1)stem(k,cos(k*pi/8),filled)title(cos(k*pi/8)subplot(2,1,2)stem(k,cos(2*k),filled)title(cos(2*k)4、离散时间实指数序列function dszsu(c,a,k1,k2)%c：指数序列的幅度%a：指数序列的底数%k1：绘制序列的起始序号%k2：绘制序列的终止序号k=k1:k2;x=c*(a.k);stem(k,x,filled)hold onplot(k1,k2,0,0)hold offdszsu(1,5/4,0,40)xlabel(k)title(f1(k)dszsu(1,-3/4,0,40)xlabel(k)title(f2(k)5、离散时间虚指数序列function=dxzsu(n1,n2,w)%n1:绘制波形的虚指数序列的起始时间序号%n2：绘制波形的虚指数序列的终止时间序号%w：虚指数序列的角频率k=n1:n2;f=exp(i*w*k);Xr=real(f)Xi=imag(f)Xa=abs(f)Xn=angle(f)subplot(2,2,1), stem(k,Xr,filled),title(实部);subplot(2,2,3), stem(k,Xi,filled),title(虚部);subplot(2,2,2), stem(k,Xa,filled),title(模);subplot(2,2,4), stem(k,Xn,filled),title(相角);dxzsu(0,20,pi/4)dxzsu(0,20,2 )6、复指数序列function dfzsu(n1,n2,r,w)%n1:绘制波形的虚指数序列的起始时间序号%n2：绘制波形的虚指数序列的终止时间序号%w：虚指数序列的角频率%r: 指数序列的底数k=n1:n2;f=(r*exp(i*w).k;Xr=real(f);Xi=imag(f);Xa=abs(f);Xn=angle(f);subplot(2,2,1), stem(k,Xr,filled),title(实部);subplot(2,2,3), stem(k,Xi,filled),title(虚部);subplot(2,2,2), stem(k,Xa,filled),title(模);subplot(2,2,4), stem(k,Xn,filled),title(相角);dfzsu(0,20,0.9,pi/4)三、连续时间信号操作1、设信号，用MATLAB求f (t + 2)，f (t - 2), f (-t ), f (2t),- f (t)，并绘出其时域波形。程序如下：syms tf=sym(t/2+1)*(heaviside(t+2)-heaviside(t-2)subplot(2,3,1),ezplot(f,-3,3)y1=subs(f,t,t+2)subplot(2,3,2),ezplot(y1,-5,1)y2=subs(f,t,t-2)subplot(2,3,3),ezplot(y2,-1,5)y3=subs(f,t,-t)subplot(2,3,4),ezplot(y3,-3,3)y4=subs(f,t,2*t)subplot(2,3,5),ezplot(y4,-2,2)y5=-fsubplot(2,3,6),ezplot(y5,-3,3)2、已知如图所示信号，信号tf1(t)044求：（1）（2）（3）（4）解：f1由图知为程序如下：syms tf1=sym(-1*t+4)*(heaviside(t)-heaviside(t-4)subplo