2.1
a=[1 2 2];b=[1 0];sys=tf(b,a); td=0.1;t=0:td:25;
f=1.*(t>=0);y=lsim(sys,f,t);
subplot(311);plot(t,y);xlabel('t(sec)');ylabel('y(t)');
h=impulse(sys,t);subplot(312);plot(t,h); xlabel('t(sec)');ylabel('h(t)');
g=step(sys,t);subplot(313);plot(t,g); xlabel('t(sec)');ylabel('g(t)'); 2.2
function[f,k]=dconv(f1,f2,k1,k2) f=conv(f1,f2);
k_start=k1(1)+k2(1);
k_end=length(f1)+length(f2)-2; k=k_start:(k_start+k_end); k1=-4:4; k2=-4:4;
f1=1.*(k1==-1)+2.*(k1==0)+1.*(k1==1); f2=1.*(k2>=-2)&(k2<3);
[f,k]=dconv(double(f1),double(f2),k1,k2); subplot(311);stem(k1,f1); subplot(312);stem(k2,f2); subplot(313);stem(k,f); 2.3
function[f,k]=cconv(f1,f2,k1,k2,td) f=td*conv(f1,f2); k_start=k1(1)+k2(1);
k_end=length(f1)+length(f2)-2; k=k_start:td:(k_start+k_end*td)； td=0.01;k1=-4:td:4;k2=-4:td:4; f1=2.*(((k1+1)>=0)-((k1-1)>=0)); f2=((k2+2)>=0)-((k2-2)>=0);
[f,k]=cconv(double(f1),double(f2),k1,k2,td); subplot(311); plot(k1,f1); subplot(312);plot(k2,f2);
subplot(313);plot(k,f); 3.1
T=4;w=2*pi/T;
a0=quadl(@singrect,0,2)*2/T;
N=10;an=zeros(1,N);bn=zeros(1,N); for k=1:N
an(k)=quadl(@rectcos,0,2,[],[],k,w)*2/T;
bn(k)=quadl(@rectsin,0,2,[],[],k,w)*2/T; end;
n=1:1:N; figure(1);
subplot(1,2,1);plot(n,an,'-o');axis([0,10,-0.45,0.1]); grid on;
subplot(1,2,2);plot(n,bn,'-o');axis([0,10,-0.35,0.05]); grid on;
t=-6:0.01:6;
x=pulstran(t-0.5,-10:2:10,'tripuls',1,1); figure(2);subplot(6,2,1);plot(t,x); axis([-4,4,-1,2]);grid on;
subplot(6,2,2);plot(t,a0/2);grid on; wave=a0/2; for k=1:10
wave=wave+an(k)*cos(k)+bn(k)*sin(k*w*t);
subplot(6,2,k+2);plot(t,wave);grid on; end
function y=singrect(t); y=sawtooth(pi*t,1);
function y=rectcos(t,n,w);
y=sawtooth(pi*t,1).*cos(n*w*t); function y=rectsin(t,n,w);
y=sawtooth(pi*t,1).*sin(n*w*t); 3.2
R=0.005;t=-2:R:2; f=cos((pi/2)*t);
w1=40;N=1000;k=-N:N;w=k*w1/N; F=f*exp(-j*t'*w)*R; Fudu=real(F);
figure(1);
subplot(2,1,1);plot(t,f);
xlabel('t');ylabel('f(t)');grid on; subplot(2,1,2);plot(w,Fudu);
xlabel('w');ylabel('F(jw)');grid on; sf=cos((pi/2)*t*1/2);
w1=40;N=1000;k=-N:N;w=k*w1/N; SF=f*exp(-j*t'*w)*R; SFudu=real(SF); figure(2);
subplot(2,1,1);plot(t,sf);
xlabel('t');ylabel('sf(t)');grid on; subplot(2,1,2);plot(w,SFudu);
xlabel('w');ylabel('SF(jw)');grid on; mf=f.*cos(10*2*pi*t); figure(3);
subplot(3,1,1);plot(t,cos(10*pi*t)); ylabel('y(t)=cos(10*pi*t)');grid on; subplot(3,1,2);plot(t,mf);
ylabel('f1(t)=f(t)*cos(10*pi*t)');grid on;
MF=mf*exp(-j*t'*w)*R; MFudu=real(MF);
subplot(3,1,3);plot(w,MFudu);
xlabel('w');ylabel('MF(jw)');grid on; 3.3
R=0.005;t=-2:0.001:2; f=tripuls(t,2,0);
w1=40;N=1000;k=-N:N;w=k*w1/N; F=f*exp(-j*t'*w)*R; Fudu=real(F); figure(1);
subplot(2,1,1);plot(t,f);
xlabel('t');ylabel('f(t)');grid on; subplot(2,1,2);plot(w,Fudu);
xlabel('w');ylabel('F(jw)');grid on; mf=f.*cos(10*2*pi*t);figure(3);
subplot(3,1,1);plot(t,cos(10*2*pi*t)); ylabel('y(t)=cos(10*2*pi*t)');grid on; subplot(3,1,2);plot(t,mf);
ylabel('f1(t)=f(t)*cos(10*2*pi*t)');grid on;
MF=mf*exp(-j*t'*w)*R; MFudu=real(MF);
subplot(3,1,3);plot(w,MFudu);
xlabel('w');ylabel('MF(jw)');grid on; 3.4
b=[1 0];a=[1 3 2];w=linspace(0,5,200); H=freqs(b,a,w); figure(1);
subplot(2,1,1);plot(w,abs(H));
xlabel('\\omega');ylabel('|H(j\\omega)');
grid on;
subplot(2,1,2);plot(w,angle(H));
xlabel('\\omega');ylabel('\\phi');grid on; 1.5
k1=-1:4;k2=-5:1; f1=k1+1;f2=-k2+1;
[f1_new,f2_new,k]=duiqi(f1,k1,f2,k2); add_f=f1_new-f2_new; pro_f=f1_new.*f2_new;
subplot(221);stem(k1,f1);
axis([-1,4,0,6]);xlabel('k1');ylabel('f1=k1+1'); subplot(222);stem(k2,f2);
axis([-5,1,0,6]);xlabel('k2');ylabel('f2=-k2+1'); subplot(223);stem(k,add_f);
axis([-5,4,-6,6]);xlabel('k');ylabel('add_f'); subplot(224);stem(k,pro_f);
axis([-5,4,0,1]);xlabel('k');ylabe('pro_f'); 4.2
num=[1 0 -4];den=[1 2 -3 2 1]; zs=roots(num);ps=roots(den); figure(1);
plot(real(zs),imag(zs),'o',real(ps),imag(ps),'ks','markersize',12); axis([-2 2 -2 2]);grid on;
sys=tf(num,den);figure(2);pzmap(sys);axis([-2 2 -2 2]);
4.3
num=[1 4];den=[1 3 2];sys=tf(num,den); poles=roots(den);figure(1);pzmap(sys); t=0:0.02:10;h=impulse(num,den,t);
figure(2);plot(t,h);xlabel('t(s)');ylabel('h(s)');
[H,w]=freqs(num,den);
figure(3);plot(w,abs(H));
xlabel('\\omega(rad/s)');ylabel('|H(j\\omega))');
title('Magenitude Response');