长江大学信号与系统matlab实验答案

1、word实验1 信号变换与系统非时变性质的波形绘制l 用MATLAB画出习题1-8的波形。l 用MATLAB画出习题1-10的波形。Eg 1.8代码如下：function y=zdyt(t) %定义函数zdyty=-2/3*(t-3).*(heaviside(-t+3)-heaviside(-t);endt0=-10;t1=4;dt=0.02;t=t0:dt:t1;f=zdyt(t);y=zdyt(t+3);x=zdyt(2*t-2);g=zdyt(2-2*t);h=zdyt(-0.5*t-1);fe=0.5*(zdyt(t)+zdyt(-t);fo=0.5*(zdyt(t)-zdyt(-t)

2、;subplot(7,1,1),plot(t,f);title('信号波形的变化')ylabel('f(t)')grid;line(t0 t1,0 0);subplot(7,1,2),plot(t,y);ylabel('y(t)')grid;line(t0 t1,0 0);subplot(7,1,3),plot(t,x);ylabel('x(t)')grid;line(t0 t1,0 0);subplot(7,1,4),plot(t,g);ylabel('g(t)')grid;line(t0 t1,0 0);sub

3、plot(7,1,5),plot(t,h);ylabel('h(t)')grid;line(t0 t1,0 0);subplot(7,1,6),plot(t,fe);ylabel('fe(t)')grid;line(t0 t1,0 0);subplot(7,1,7),plot(t,fo);ylabel('fo(t)')grid;line(t0 t1,0 0);xlabel('Time(sec)')结果：Eg1.10代码如下：function u=f(t) %定义函数f(t)u= heaviside(t)-heaviside(t-2

4、);endfunction u =y(t) %定义函数y(t)u=2*(t.*heaviside(t)-2*(t-1).*heaviside(t-1)+(t-2).*heaviside(t-2);endt0=-2;t1=5;dt=0.01;t=t0:dt:t1;f1=f(t);y1=y(t);f2=f(t)-f(t-2);y2=y(t)-y(t-2);f3=f(t)-f(t+1);y3=y(t)-y(t+1);subplot(3,2,1),plot(t,f1);title('鼓励响应波形图')ylabel('f1(t)')grid;line(t0 t1,0 0)

5、;subplot(3,2,2),plot(t,y1);ylabel('y1(t)')grid;line(t0 t1,0 0);subplot(3,2,3),plot(t,f2);ylabel('f2(t)')grid;line(t0 t1,0 0);subplot(3,2,4),plot(t,y2);ylabel('y2(t)')grid;line(t0 t1,0 0);subplot(3,2,5),plot(t,f3);ylabel('f3(t)')grid;line(t0 t1,0 0);subplot(3,2,6),plot

6、(t,y3);ylabel('y3(t)')grid;line(t0 t1,0 0);xlabel('Time(sec)')结果：实验2 微分方程的符号计算和波形绘制上机内容l 用MATLAB计算习题2-1，并画出系统响应的波形。注：由于MATLAB版本的不同，求齐次通解和非齐次通解中的常数C可能不同，这时可令C1=1；C2=1；C3=1；C4=1；yht=subs(yht); yt=subs(yt); 那么特解可求出 yp=yt-yhtl 用MATLAB计算习题2-3，并画出系统响应的波形。Eg2.1代码如下：C5=1;C6=1;C8=1;C9=1;y=dso

7、lve('D2y+3*Dy+2*y=4*exp(-3*t)','y(0)=3,Dy(0)=4')yht=dsolve('D2y+3*Dy+2*y=0')yt=dsolve('D2y+3*Dy+2*y=4*exp(-3*t)')yp=yt-yhtyh=y-ypyzi=dsolve('D2y+3*Dy+2*y=0','y(0)=3,Dy(0)=4')yzs=dsolve('D2y+3*Dy+2*y=4*exp(-3*t)','y(0)=0,Dy(0)=0')t=linsp

8、ace(0,4,300);figure(1)y_n=subs(y);yh_n=subs(yh);yp_n=subs(yp);plot(t,y_n,t,yh_n,'m:',t,yp_n,'r-.','linewidth',2)xlabel('Time(sec)'),title('全响应，自由响应，强迫响应')legend('全响应','自由响应','强迫响应',0)figure(2)yzi_n=subs(yzi);yzs_n=subs(yzs);plot(t,y_n,t

9、,yzi_n,'m:',t,yzs_n,'r-.','linewidth',2)xlabel('Time(sec)'),title('全响应，零输入响应，零状态响应')legend('全响应','零输入响应','零状态响应',0)结果：>> eg2_1 y =12*exp(-t) - 11*exp(-2*t) + 2*exp(-3*t) yht =C5*exp(-t) + C6*exp(-2*t) yt =2*exp(-3*t) + C8*exp(-t)

10、+ C9*exp(-2*t) yp =2*exp(-3*t) - C5*exp(-t) - C6*exp(-2*t) + C8*exp(-t) + C9*exp(-2*t)yh =12*exp(-t) - 11*exp(-2*t) + C5*exp(-t) + C6*exp(-2*t) - C8*exp(-t) - C9*exp(-2*t) yzi =10*exp(-t) - 7*exp(-2*t) yzs =2*exp(-t) - 4*exp(-2*t) + 2*exp(-3*t)Eg2.3代码如下：y1zi=dsolve('D2y+5*Dy+6*y=0','y(0)

11、=2,Dy(0)=-1')y2zi=dsolve('D2y+4*Dy+4*y=0','y(0)=3,Dy(0)=-4')y3zi=dsolve('D2y+4*Dy+13*y=0','y(0)=5,Dy(0)=8')y4zi=dsolve('D3y+D2y=0','y(0)=4,Dy(0)=3,D2y(0)=-1')y1zi_n=subs(y1zi);y2zi_n=subs(y2zi);y3zi_n=subs(y3zi);y4zi_n=subs(y4zi);t=linspace(0,6,300

12、);subplot(4,1,1),plot(t,y1zi_n);title('D2y+5*Dy+6*y=Df+f的零输入响应')subplot(4,1,2),plot(t,y2zi_n);title('D2y+4*Dy+4*y=Df的零输入响应')subplot(4,1,3),plot(t,y3zi_n);title('D2y+4*Dy+13*y=D2f的零输入响应')subplot(4,1,4),plot(t,y4zi_n);title('D3y+D2y=D2f+2*f的零输入响应')xlabel('Time(sec)&

13、#39;)结果如下：eg2_3 y1zi = 5*exp(-2*t) - 3*exp(-3*t) y2zi =3*exp(-2*t) + 2*t*exp(-2*t) y3zi =5*cos(3*t)*exp(-2*t) + 6*sin(3*t)*exp(-2*t) y4zi =2*t - exp(-t) + 5实验3 绘制连续系统的四幅图上机内容l 用MATLAB计算习题3-283。画出四幅图l 用MATLAB计算习题3-29a。画出四幅图Eg3.28(3)代码如下：num=1 0 0;a=1 1;b=1 4 16;c=conv(a,b);den=c;subplot(3,1,1);pzmap(

14、num,den);t=0:0.02:5;subplot(3,1,2);impulse(num,den,t);subplot(3,1,3);step(num,den,t);figure(2)freqs(num,den);figure(3)bode(num,den);结果：Eg3.29(a)代码如下：b=0 1;n=1 3;m=1 6;c=conv(n,m);a=c;figure(1)w=linspace(0,200,200);zpplot(b,a)freresp(b,a,w)figure(2)t=0:0.02:5;subplot(1,2,1);impulse(b,a,t);subplot(1,2

15、,2);step(b,a,t);figure(3)bode(b,a);结果：实验4 离散信号波形绘制和迭代法计算上机内容l 用MATLAB计算习题4-4。用MATLAB计算习题4-6。并显示前15项数值，画出其波形。Eg4.4代码如下：function y=f(k) %定义函数f(k)y=-(k-3)/3).*(u(k)-u(k-4)+delta(k+1)+delta(k+2);endk=-5:6;y=f(k);y1=f(k+2);y2=f(k+2).*u(-k-2);y3=f(-k+2);y4=f(-k+2).*u(k-1);subplot(5,1,1),ylabel('f(k)&#

16、39;)mystem(k,y),title('信号f(k)的波形图');subplot(5,1,2),ylabel('f(k+2)')mystem(k,y1),title('信号f(k+2)的波形图');subplot(5,1,3),ylabel('f(k+2) (-k-2)')mystem(k,y2),title('信号f(k+2)(-k-2)的波形图');subplot(5,1,4),ylabel('f(-k+2)')mystem(k,y3),title('信号f(-k+2)的波形图&#

17、39;);subplot(5,1,5),ylabel('f(-k+2) (k-1)')mystem(k,y4),title('信号f(-k+2)(k-1)的波形图');结果：Eg4.6代码如下：k=-2:20;n=length(k)-2;y=2,3,zeros(1,n);f=(3.k).*u(k);for i=1:n y(i+2)=-3*y(i+1)-2*y(i)+f(i+2)+3*f(i+1)+3*f(i);endclf;stem(k,y);xlabel('y');ylabel('y(k)');disp('k y'

18、;);disp(num2str(k',y');结果：实验5 绘制离散系统的四幅图上机内容l 用MATLAB计算习题5-8。画出四幅图l 用MATLAB计算习题5-18。画出四幅图注：四幅图为：零极点图，冲激响应和阶跃响应图两个响应竖排，零输入响应和零状态响应图两个响应竖排，频率响应幅频响应和相频响应竖排。Eg5.8代码如下：a=2 -3 1;b=4 -3 0;k=0:20;x=zeros(1,21);f=(4.-k).*u(k);zi=filtic(b,a,0 -1,0 0);yzi=filter(b,a,x,zi)figure(1),subplot(2,1,1),mystem

19、(0:20),yzi)xlabel('k'),title('零输入响应')yzs=filter(b,a,f);subplot(2,1,2),mystem(k,yzs)xlabel('k'),title('零状态响应')figure(2),subplot(2,1,1),impz(b,a,21);xlabel('k'),title('冲激响应')subplot(2,1,2),stepz(b,a,21);xlabel('k'),title('阶跃响应')figure(3),

20、zplane(b,a);figure(4),H,w=freqz(b,a);subplot(2,1,1),myplot(w/pi,abs(H)xlabel('频率omega(xpi rad/sample'),title('幅度响应')subplot(2,1,2),myplot(w/pi,unwrap(angle(H)*180/pi)xlabel('频率omega(xpi rad/sample'),title('频率')结果：Eg5.18(1)代码如下：b=1 0;a=1 0.9;figure(1);zplane(b,a);n=0:4

21、0;figure(2);subplot(2,1,1)h=impz(b,a,n);mystem(n,h)xlabel('k')title('冲激响应')subplot(2,1,2)g=stepz(b,a,n);mystem(n,g)xlabel('k')title('阶跃响应')H,w=freqz(b,a);figure(3);subplot(2,1,1)myplot(w/pi,abs(H);xlabel('频率omega(xpi rad/sample)')title('幅度响应')subplot(2

22、,1,2)myplot(w/pi,unwrap(angle(H)*180/pi)xlabel('频率omega(xpi rad/sample)')title('相位响应')结果：Eg5.18(2)代码如下：b=1 0;a=1 -0.9;figure(1);zplane(b,a);n=0:40;figure(2);subplot(2,1,1)h=impz(b,a,n);mystem(n,h)xlabel('k')title('冲激响应')subplot(2,1,2)g=stepz(b,a,n);mystem(n,g)xlabel(&

23、#39;k')title('阶跃响应')H,w=freqz(b,a);figure(3);subplot(2,1,1)myplot(w/pi,abs(H);xlabel('频率omega(xpi rad/sample)')title('幅度响应')subplot(2,1,2)myplot(w/pi,unwrap(angle(H)*180/pi)xlabel('频率omega(xpi rad/sample)')title('相位响应')结果： 实验6 周期信号的分解与合成上机内容l 用MATLAB画出图1的频

24、谱和谐波次数N=20时合成的波形。观察N变化时合成波形和吉布斯现象。其中图1是一个周期的波形。图1Eg6代码如下：function An=ZQXHFS(x,T0,T,N)%UNTITLED 计算连续周期信号的频谱% x为周期信号的第一周期的字符串表达式，T0为第一周期的起始时间，T为周期，N为最高谐波次数t=linspace(T0,T0+T,10000);w=2*pi/T;fm=eval(x);for k=0:N a(k+1)=2/T*trapz(t,fm.*cos(k*w*t); b(k+1)=2/T*trapz(t,fm.*sin(k*w*t);endAn=a-1i*b;An(1)=a(1

25、)/2;f=abs(An);A=angle(An)*180/pi;A(1)=A(1)/2;fm_max=max(f);fm_min=min(f);f_max=max(f);f_min=min(f);df=(f_max-f_min)/10;A_max=max(A);A_min=min(A);dA=(A_max-A_min)/10;t1=t,t+T,t+2*T;ft=fm,fm,fm;subplot(3,1,1);plot(t1,ft,'LineWidth',2);ylabel('f(t)');title('周期信号的波形','FontSiz

26、e',8)axis(t1(1) t1(end) 0 3);grid,set(gca,'FontSize',8)subplot(3,1,2);h=stem(0:N,f,'.');title('单边幅度频谱','FontSize',8);ylabel('An的模','FontSize',8);set(h(2),'color','r','LineWidth',2),set(h(1),'color','r','L

27、ineWidth',2)axis(0 N -0.2 1.5);grid,set(gca,'FontSize',8)subplot(3,1,3);h=stem(0:N,A,'.');title('单边相位频谱','FontSize',8)set(h(2),'color','r','LineWidth',2),set(h(1),'color','r','LineWidth',2)grid,set(gca,'FontSize&

28、#39;,8);ylabel('An的相位度');w=2/T;xw=strcat('nOmega, Omega=',num2str(w),'pi');xlabel(xw);endT=4;N=20;y='t.*(heaviside(t)-heaviside(t-3)'figure(1)A_n=ZQXHFS(y,0,T,N);t=linspace(0,3*T,400);n=0:N;omega_0=2*pi/T;y1=A_n*exp(1i*omega_0*n'*t);yt=real(y1);figure(2),plot(t,yt

29、,'linewidth',2);title('周期信号合成前20项的局部和',8)结果：实验7 滤波器频域分析与卷积分析上机内容滤波器为RC低通滤波器，输入信号为周期锯齿波如图1所示。当RC=0.5、2时，用MATLAB分析系统的输入频谱、输出频谱以及系统的时域响应。再用卷积分析的方法画出滤波器输出波形。Eg7局部代码如下不会做，没做完t=linspace(0,4,400);w=linspace(-15,15,30);f=sym('t*(Heaviside(t)-Heaviside(t-3)') F=fourier(f), F=simple(F)

30、 f1=subs(f); Fv=subs(F); F1=abs(Fv); P1=angle(Fv)*180/pi; subplot(3,1,1),plot(t,f1,'linewidth',2); grid;ylabel('f(t)');subplot(3,1,2),stem(w,F1,'.'); grid;ylabel('|F(jomega)|');结果：以下局部非实验相关内容RC频率特性：f0=0;f1=10000;f=f0:20:f1;RC=2;fc1=round(1./(RC*2*pi);H=1./(1+j*2*pi*f*RC);Hw1=abs(H);P1=angle(H);RC=0.1;fc2=round(1./(RC*