信號(hào)與系統(tǒng)實(shí)驗(yàn)

信號(hào)與系統(tǒng)實(shí)驗(yàn)實(shí)驗(yàn)一持續(xù)時(shí)間信號(hào)的產(chǎn)生與運(yùn)算編制程序,生成以下持續(xù)信號(hào):ε(t-3),cos3t+sin2tt=-2:0.01:6;u=(t>=3);plot(t,u);axis([-2,6,0,1.2]);xlabel('時(shí)間（t）');ylabel('幅值（f)');title('單位階躍信號(hào)');t=-0:0.001:3;y=sin(2*t);plot(t,y,'k');xlabel('時(shí)間（t）');ylabel('幅值（f)');title('單位階躍信號(hào)');t=-0:0.001:3;y=sin(3*t+pi/2);plot(t,y,'k');xlabel('時(shí)間（t）');ylabel('幅值（f)');title('單位階躍信號(hào)');t1=-10;t2=10;dt=0.01;t=t1:dt:t2;f1=sin(2*t);f2=cos(3*t);f=f1+f2;plot(t,f);axis([t1,t2,-1.5,1.5]);title('f(t)函數(shù)');xlabel('時(shí)間(t)');ylabel('幅值(f)');設(shè)計(jì)一種程序，選擇一種信號(hào)f(t),完畢信號(hào)f(t)到f(2t+2)的轉(zhuǎn)化symst;f=sym('sin(t)');f1=subs(f,t,t+2);f2=subs(f1,t,2*t);subplot(2,2,1);ezplot(f,[-8,8]);gridon;subplot(2,2,2);ezplot(f1,[-8,8]);gridon;subplot(2,2,3);ezplot(f2,[-8,8]);gridon;3.若f1(t)=sin(t),f2(t)=ε(t),f(t)=ε(t)-ε(t-4),證明卷積滿足：f1(t)*[f2(t)+f3(t)]=f1(t)*f2(t)+f1(t)*f3(t)t=-10:0.01:10;f1=sin(t);f2=heaviside(t);f3=heaviside(t)-heaviside(t-4);s1=conv(f1,f2+f3);s2=conv(f1,f2)+conv(f1,f3);t1=-20:0.01:20;subplot(2,1,1);plot(t1,s1);subplot(2,1,2);plot(t1,s2);實(shí)驗(yàn)二：離散時(shí)間信號(hào)的產(chǎn)生與運(yùn)算編制程序,生成以下持續(xù)信號(hào):sqrt(a*k)u(k-3),δ(k+5)k=(1:10);n=3;u=[(k-n)>=0];a=sqrt(2*k);stem(k,a.*u);title('sqrt(2*k)u(k?3)的圖像');xlabel('時(shí)間(k)');ylabel('幅值f(k)');k1=-10;k2=0;k=k1:k2;n=-5;f=[(k-n)==0];stem(k,f,'filled');title('δ(k+5)序列的圖像');xlabel('時(shí)間(k)');ylabel('幅值f(k)');2.設(shè)計(jì)一種程序，選擇一種信號(hào)f(k),完畢信號(hào)f(k)到f(2k+2)的轉(zhuǎn)化k1=-20;k2=20;k=k1:k2;d=k+1;f1=sin(0.2*pi*d);stem(k,f1,'filled');title('正弦序列');xlabel('時(shí)間(k)');ylabel('幅值f(2k+2)');3.若f1(k)=δ(t),f2(k)=u(k),f3(k)=u(k)+u(k-4),證明卷積滿足：f1(k)*[f2(k)+f3(k)]=f1(k)*f2(k)+f1(k)*f3(k)k=-10:10;fk1=[zeros(1,10),1,zeros(1,10)];fk2=[zeros(1,10),ones(1,11)];fk3=[zeros(1,10),ones(1,11)]+[zeros(1,14),ones(1,7)];fk4=fk2+fk3;hk1=conv(fk1,fk4);hk2=conv(fk1,fk2)+conv(fk1,fk3);n=-20:(length(hk1)-1-20);subplot(2,1,1);stem(n,hk1);subplot(2,1,2);stem(n,hk2);實(shí)驗(yàn)三：持續(xù)LTI系統(tǒng)的時(shí)域分析計(jì)算下述系統(tǒng)在指數(shù)函數(shù)激勵(lì)下的零狀態(tài)響應(yīng)H(s)=1.65*s^4-0.331*s^3-576*s^2+90.6s+19080/s^6+0.996*s^5+463*s^4+97.8*s^3+1213*s^2+8.11*sa=[1,0.996,463,97.8,12131,8.11,0];b=[1.65,-0.331,-576,90.6,19080];sys=tf(b,a);t=0:0.1:10;x=exp(t);y=lsim(sys,x,t);plot(t,y);xlabel('t');ylabel('y(t)');計(jì)算下列系統(tǒng)在沖激階躍斜坡和正弦激勵(lì)下的零狀態(tài)響應(yīng)y(t)(4)+0.6363*y(t)(3)+0.9396*y(t)(2)+0.5123*y(t)(1)+0.0037y(t)=-0.475*f(t)(3)-0.248*f(t)(2)-0.1189*f(1)-0.0564*f(t)b=[-0.475,-0.248,-0.1189,-0.0564];a=[1,0.6363,0.9396,0.5123,0.0037;sys=tf(b,a);t=0:0.1:10;y1=impulse(sys,t);y2=step(sys,t);x1=t;x2=sin(t);y3=lsim(sys,x1,t);y4=lsim(sys,x2,t);subplot(2,2,1);plot(t,y1);title('impulse,zero,state,response');subplot(2,2,2);plot(t,y2);title('step,zero,state,response');subplot(2,2,3);plot(t,y3);title('slope,zero,state,respons');subplot(2,2,4);plot(t,y4);title('sin(t),zero,state,response');已知某線性時(shí)不變系統(tǒng)的動(dòng)態(tài)方程式為Y(t)(2+4y(t)(1)+4y(t)=2*f(t)(1)+3f(t),t>0系統(tǒng)的初始狀態(tài)為y(0)=2,y(0)=1,求系統(tǒng)的零輸入響應(yīng)y(t)eq='D2y+4*Dy+4*y=0';cond='y(0)=2,Dy(0)=1';yx=dsolve(eq,cond);ezplot(yx,[0,10]);xlabel('t');ylabel('yx(t)');title('系統(tǒng)的零輸入響應(yīng)');gridon;axis{[0,5,0,2.5]};實(shí)驗(yàn)四：離散LTI系統(tǒng)的時(shí)域分析規(guī)定寫(xiě)出下列各實(shí)驗(yàn)內(nèi)容的完整程序描LTI離散系統(tǒng)的差分方程以下，繪出該系統(tǒng)在0~50單位時(shí)間范疇內(nèi)單位序列響應(yīng)的波形，并求出其數(shù)值解2y(k)-2y(k-1)+y(k-2)=f(k)+3f(k-1)+2f(k-2))a=[2,-2,1];b=[1,3,2];impz(b,a,0:50);y=impz(b,a,0:50);實(shí)驗(yàn)五：持續(xù)系統(tǒng)的頻域分析方波的合成實(shí)驗(yàn)。用5項(xiàng)諧波合成一種頻率為50Hz，幅值為3的方波，寫(xiě)出MATLAB程序，給出實(shí)驗(yàn)的成果clearall;fs=10000;t=[0:1/fs:0.1];f0=50;sum=0;subplot(211)forn=1:2:9;plot(t,4/pi*3/n*sin(2*pi*n*f0*t),'k');holdon;endtitle('信號(hào)疊加前');subplot(212)forn=1:2:9;sum=sum+4/pi*3/n*sin(2*pi*n*f0*t);endplot(t,sum,'k');title('信號(hào)疊加后');2.編寫(xiě)程序，畫(huà)出信號(hào)f(t)=e^-3tε(t),f(t-4)以及信號(hào)f(t)e^-j4t的頻譜圖r=0.02;t=-5:r:5;N=200;W=2*pi;k=-N:N;w=k*W/N;f1=1*exp(-3*t).*stepfun(t,0);F=r*f1*exp(-j*t'*w);F1=abs(F);p1=angle(F);subplot(3,1,1),plot(t,f1);gridxlabel('t');ylabel('f(t)');title('f(t)');subplot(3,1,2);plot(w,F1);xlabel('w');grid;ylabel('F(jw)');subplot(3,1,3);plot(w,p1*180/pi);grid;xlabel('w');ylabel('相位(度)');r=0.02;t=0:r:10;N=200;W=2*pi;k=-N:N;w=k*W/N;f1=1*exp(-3*(t-4)).*stepfun(t,4);F=r*f1*exp(-j*t'*w);F1=abs(F);p1=angle(F);subplot(3,1,1),plot(t,f1);gridxlabel('t');ylabel('f(t)');title('f(t-4)');subplot(3,1,2);plot(w,F1);xlabel('w');grid;ylabel('F(jw)的模');subplot(3,1,3);plot(w,p1*180/pi);grid;xlabel('w');ylabel('相位(度)');R=0.02;t=-5:R:5;f=exp(-3*t).*stepfun(t,0);f1=f.*exp(-1j*4*t);W1=2*pi*5;N=500;k=-N:N;W=k*W1/N;F=f1*exp(-1j*t'*W)*R;F=real(F);subplot(1,1,1);plot(W,F);xlabel('W');ylabel('F1(W)');title('頻譜F1(jw)');實(shí)驗(yàn)六：持續(xù)系統(tǒng)的復(fù)頻域分析系統(tǒng)傳遞函數(shù)為：F(s)=s^2-4/s^3+5*s^2+16s+30,編寫(xiě)程序，完畢下列任務(wù)繪制系統(tǒng)的零極點(diǎn)圖，闡明系統(tǒng)的穩(wěn)定性求上述系統(tǒng)的沖激響應(yīng)clear;b=[1,-4];a=[1,5,16,30];zs=roots(b);ps=roots(a);subplot(2,1,1);plot(real(zs),imag(zs),'go',real(ps),imag(ps),'mx','markersize',12);grid;title('零極點(diǎn)分布圖');legend('零點(diǎn)','極點(diǎn)');sys=tf(b,a);t=0:0.1:10;y=step(sys,t);subplot(2,1,2);plot(t,y);grid;xlabel('時(shí)間(t)');ylabel('y(t)');title('單位沖激響應(yīng)');求當(dāng)系統(tǒng)的輸入為Ug=cos(20t)u(t)的穩(wěn)定響應(yīng)clearall;symsst;Hs=('(s^2-4)/(s^3+5*s^2+16*s+30)');Vs=laplace(cos(20*t));Vos=Hs*Vs;Vo=ilaplace(Vos);Vo=vpa(Vo,4);ezplot(Vo,[1,3]);holdon;ezplot('cos(20*t)',[1,3]);axis([1,3,-2,2]);Vos=Hs*Vs;實(shí)驗(yàn)七：離散持續(xù)的Z域分析系統(tǒng)傳遞函數(shù)為：H(z)=3*z^3-5*z^2+10z/z^3-3*z^2+7*z-5,編寫(xiě)程序，繪制系統(tǒng)的零極點(diǎn)圖，并闡明系統(tǒng)的穩(wěn)定性clear;b=[3,-5,10];a=[1,-3,7,-5];zs=roots(b);ps=roots(a);plot(real(zs),imag(zs