信号与信号实验

信号与信号实验MATLAB部分实验一：基本信号在MATLAB中的表示和运算一、实验目的;1、学会用MATLAB表示常用连续信号的方法；2、学会用MATLAB进行信号基本运算的方法；3、学会用MATLAB实现连续时间信号的卷积的方法。二、实验内容：1、绘出下列信号的时域波形(1)f(t)=(2-e-2t)u(t)(2)f(t)=cos(πt)[u(t)-u(t-1)](3)f(t)=u(-3t+2)(4)f(t)=-(1/2)tu(t+2)解：t1=0:0.01:5;y1=(2-exp(-2*t1)).*(t10);subplot(221);plot(t1,y1);grid;title('f(t)=(2-e-2t)u(t)');t2=0:0.01:5;y2=cos(pi*t2).*((t20)-(t21));subplot(222);plot(t2,y2);grid;title('f(t)=cos(πt)[u(t)-u(t-1)]');t3=-2:0.01:5;y3=(-3*t3+20);subplot(223);plot(t3,y3);grid;title('f(t)=u(-3t+2)');t4=-3:0.01:5;y4=(-1/2)*t4.*(t4-2);subplot(224);plot(t4,y4);grid;title('f(t)=-(1/2)tu(t+2)');024600.511.52f(t)=(2-e-2t)u(t)图1-10246-1-0.500.51f(t)=cos(πt)[u(t)-u(t-1)]图1-2-2024600.51f(t)=u(-3t+2)图1-3-505-3-2-101f(t)=-(1/2)tu(t+2)图1-42、用MATLAB绘出下列信号的卷积积分f1(t)*f2(t)的时域波形(1)f1(t)=tu(t),f2(t)=u(t)(2)f1(t)=u(t)-u(t-4),f2(t)=sin(πt)u(t)(3)f1(t)=e-2tu(t),f2(t)=e-tu(t)(4)f1(t)=e-tu(t),f2(t)=u(t)解：（1）fs=1000;t=-1:1/fs:4;x1=stepfun(t,0);x2=x1.*t;y=conv(x1,x2)/fs;n=length(y1);tt=(0:n-1)/fs-2;subplot(311),plot(t,x1),grid;title('f1(t)=tu(t)');subplot(312),plot(t,x2),grid;title('f2(t)=u(t)');subplot(313),plot(tt,y),gridon;title('f1(t)*f2(t)');（2）fs=1000;t=-1:1/fs:4;x1=(t0)-(t4);x2=sin(pi*t).*(t0);x=conv(x1,x2)/fs;n=length(x);tt=(0:n-1)/fs-2;subplot(311);plot(t,x1);grid;title('f1(t)=u(t)-u(t-4))');subplot(312);plot(t,x2);grid;title('f2(t)=sin(πt)u(t)');subplot(313);plot(tt,x);grid;title('f1(t)*f2');（3）t=0:1/fs:4;x1=exp(-2*t).*(t0);x2=exp(-t).*(t0);x=conv(x1,x2)/fs;n=length(x);tt=(0:n-1)/fs-0;subplot(311);plot(t,x1);grid;title('f1(t)=e-2tu(t)');subplot(312);plot(t,x2);grid;title('f2(t)=e-tu(t)');subplot(313);plot(tt,x);grid;title('f1(t)*f2(t)');（4）t=0:1/fs:2;x1=exp(-2*t).*(t0);x2=(t0);x=conv(x1,x2)/fs;n=length(x);tt=(0:n-1)/fs-0;subplot(311);plot(t,x1);grid;title('f1(t)=e-tu(t))');subplot(312);plot(t,x2);grid;title('f2(t)=u(t)');subplot(313);plot(tt,x);grid;title('f1(t)*f2(t)');00.511.522.533.5400.51f1(t)=e-2tu(t)00.511.522.533.5400.51f2(t)=e-tu(t)01234567800.20.4f1(t)*f2(t)-1-0.500.511.522.533.5400.51f1(t)=tu(t)?2-1-1-0.500.511.522.533.54024f2(t)=u(t)?2-2-2-10123456780510f1(t)*f2(t)?2-3实验二：连续时间LTI系统的时域分析一、实验目的：学会用MATLAB求解连续系统的零状态响应、冲击响应和阶跃响应。二、实验内容：1、已知描述系统的微分方程和激励信号f(t)如下，用MATLAB绘出系统的零状态响应的时域仿真波形。(1)y’’(t)+4y’(t)+3y(t)=f(t)，f(t)=u(t)(2)y’’(t)+4y’(t)+4y(t)=f’(t)+3f(t)，f(t)=e-tu(t)解：(1)t=0:0.01:5;sys=tf([1],[1,4,3]);f=stepfun(t,0);y=lsim(sys,f,t);plot(t,y),grid;title('（1）的零状态响应');(2)t=0:0.01:5;sys=tf([13],[144]);f=exp(-t).*(t0);y=lsim(sys,f,t);plot(t,y),grid;title('（2）的零状态响应');-10123400.51f1(t)=u(t)-u(t-4))-101234-101f2(t)=sin(?t)u(t)-202468-101f1(t)*f200.20.40.60.811.21.41.61.8200.51f1(t)=e-tu(t))00.20.40.60.811.21.41.61.8200.51f2(t)=u(t)00.511.522.533.5400.5f1(t)*f2(t)00.511.522.533.544.5500.050.10.150.20.250.30.35（1）的零状态响应00.511.522.533.544.5500.050.10.150.20.250.30.35（2）的零状态响应2、已知描述系统的微分方程如下，用MATLAB绘出系统在0~10秒范围内冲激响应和阶跃响应的时域波形。(1)y’’(t)+3y’(t)+2y(t)=f(t)(2)y’’(t)+2y’(t)+2y(t)=f’(t)解：(1)t=0:0.01:10;sys=tf([1],[132]);h=impulse(sys,t);subplot(211);plot(t,h);grid;title('冲激响应');g=step(sys,t);subplot(212);plot(t,g);grid;title('阶跃响应');(2)t=0:0.01:10;sys=tf([1],[122]);h=impulse(sys,t);subplot(211);plot(t,h);grid;title('冲激响应');g=step(sys,t);subplot(212);plot(t,g);grid;title('阶跃响应');012345678910-0.200.20.40.6冲激响应01234567891000.20.40.60.8阶跃响应01234567891000.10.20.30.4冲激响应01234567891000.20.40.60.8阶跃响应实验三：傅里叶、系统的频域分析及滤波器设计一、实验目的：1、学会用MATLAB实现连续时间信号傅里叶变换；2、学会用MATLAB分析LTI系统的频率特性；3、学会用MATLAB分析LTI系统的输出响应。二、实验内容：1、试用MATLAB求单边指数信号f(t)=e-atu(t)的傅里叶变换，并画出其幅度谱。2、设H(w)=1/[0.08(jw)^2+0.4jw+1]，试用MATLAB画出该系统的幅频特性和相频特性。1、解：ft=sym('exp(-2*t)*Heaviside(t)');Fw=simplify(fourier(ft));Ff=subs(Fw,'2*pi*f','w');Ff_conj=conj(Ff);GF=sqrt(Ff*Ff_conj);ezplot(GF);gridon;-3-2-101230.050.10.150.20.250.30.350.40.45f(1/(2+2if)/(2-2iconj(f)))1/22、解：w=0:0.025:5;b=[1];a=[0.080.41];H=freqs(b,a,w);subplot(211);plot(abs(H));gridon;xlabel('\omega(rad/s)');ylabel('|H(j\omega)|');title('H(jw)的幅频特性');subplot(212);plot(w,angle(H));grid;xlabel('\omega(rad/s)');ylabel('\phi(\omega)');title('H(jw)的相频特性');0501001502002500.40.60.81(rad/s)|H(j)|H(jw)的幅频特性00.511.522.533.544.55-3-2-10(rad/s)()H(jw)的相频特性实验四：信号抽样与重建及调制一、实验目的：学会用MATLAB实现连续信号的采样和重建二、实验内容：1、设f(t)=e-1000|t|，由于不是严格的带限信号，但其带宽Wm可根据一定的精度要求做一些近似。试根据以下三种情况用MATLAB实现由f(t)的抽样信号fs(t)重建f(t)并求两者误差，分析三种情况的结果。（1）Wm=5000π，Wc=Wm，Ts=π/Wm；（2）Wm=10000π，Wc=1.1Wm，Ts=π/Wm；（3）Wm=2500π，Wc=0.9Wm，Ts=π/Wm；解：（1）、wm=5000*pi;wc=1*wm;Ts=pi/wm;ws=2*pi/Ts;n=-100:100;nTs=n*Ts;f=exp(-1000.*abs(nTs));Dt=0.005;t=-15:Dt:15;fa=f*Ts*wc/pi*sinc((wc/pi)*(ones(length(nTs),1)*t-nTs'*ones(1,length(t))));error=abs(fa-exp(-1000.*abs(t)));t1=-15:0.5:15;f1=exp(-1000.*abs(t1));subplot(311);stem(t1,f1);ylabel('f(kTs)');title('exp(-1000.*abs(t))的采样信号');subplot(312);plot(t,fa);ylabel('fa(t)');title('由exp(-1000.*abs(t))的采样信号重构)');subplot(313);plot(t,error);ylabel('error(t)');title('采样信号与原信号的误差error(t)');（2）、wm=10000*pi;wc=1.1*wm;Ts=pi/wm;ws=2*pi/Ts;n=-100:100;nTs=n*Ts;f=exp(-1000.*abs(nTs));Dt=0.005;t=-15:Dt:15;fa=f*Ts*wc/pi*sinc((wc/pi)*(ones(length(nTs),1)*t-n