(1)t=-2:0.001:4;T=2;xt=rectpuls(t-1,T); plot(t,xt)axis([-2,4,-0.5,1.5]) 图象为：(2)t=sym('t');y=Heaviside(t); ezplot(y,[-1,1]); grid onaxis([-1 1 -0.1 1.1]) 图象为：A=10;a=-1;B=5;b=-2;t=0:0.001:10;xt=A*exp(a*t)-B*exp(b*t); plot(t,xt)图象为：(4)t=sym('t');y=t*Heaviside(t);ezplot(y,[-1,3]);grid onaxis([-1 3 -0.1 3.1])图象为：A=2;w0=10*pi;phi=pi/6;t=0:0.001:0.5;xt=abs(A*sin(w0*t+phi)); plot(t,xt)图象为：(6)A=1;w0=1;B=1;w1=2*pi;t=0:0.001:20;xt=A*cos(w0*t)+B*sin(w1*t); plot(t,xt)图象为：A=4;a=-0.5;w0=2*pi;t=0:0.001:10;xt=A*exp(a*t).*cos(w0*t); plot(t,xt)图象为：(8)w0=30;t=-15:0.001:15;xt=cos(w0*t).*sinc(t/pi); plot(t,xt)axis([-15,15,-1.1,1.1])图象为：（1）function yt=x2_3(t)yt=(t).*(t>=0&t<=2)+2*(t>=2&t<=3)-1*(t>=3&t<=5); （2）function yt=x2_3(t)yt=(t).*(t>=0&t<=2)+2*(t>=2&t<=3)-1*(t>=3&t<=5);t=0:0.001:6;subplot(3,1,1)plot(t,x2_3(t))title('x(t)')axis([0,6,-2,3])subplot(3,1,2)plot(t,x2_3(0.5*t))title('x(0.5t)')axis([0,11,-2,3])subplot(3,1,3)plot(t,x2_3(2-0.5*t))title('x(2-0.5t)')axis([-6,5,-2,3])图像为：M2-9（1）k=-4:7;xk=[-3,-2,3,1,-2,-3,-4,2,-1,4,1,-1];stem(k,xk,'file')（2）k=-12:21;x=[-3,0,0,-2,0,0,3,0,0,1,0,0,-2,0,0,-3,0,0,-4,0,0,2,0,0,-1,0,0,4,0,0,1,0,0,-1]; subplot(2,1,1)stem(k,x,'file')title('3倍内插')t=-1:2;y=[-2,-2,2,1];subplot(2,1,2)stem(t,y,'file')title('3倍抽取')axis([-3,4,-4,4])k=-4:7;x=[-3,-2,3,1,-2,-3,-4,2,-1,4,1,-1]; subplot(2,1,1)stem(k+2,x,'file')title('x[k+2]')subplot(2,1,2)stem(k-4,x,'file')title('x[k-4]')（4）k=-4:7;x=[-3,-2,3,1,-2,-3,-4,2,-1,4,1,-1]; stem(-fliplr(k),fliplr(x),'file') title('x[-k]')（1）ts=0;te=5;dt=0.01;sys=tf([2 1],[1 3 2]);t=ts:dt:te;x=exp(-3*t);y=lsim(sys,x,t);plot(t,y)xlabel('Time(sec)')ylabel('y(t)')（2）ts=0;te=5;dt=1;sys=tf([2 1],[1 3 2]);t=ts:dt:te;x=exp(-3*t);y=lsim(sys,x,t)y =0.6649-0.0239-0.0630-0.0314-0.0127从（1）（2）对比我们当抽样间隔越小时数值精度越高。

x=[0.85,0.53,0.21,0.67,0.84,0.12]; kx=-2:3;h=[0.68,0.37,0.83,0.52,0.71];kh=-1:3;y=conv(x,h);k=kx(1)+kh(1):kx(end)+kh(end); stem(k,y,'file');M3-8k=0:30;a=[1 0.7 -0.45 -0.6];b=[0.8 -0.44 0.36 0.02];h=impz(b,a,k);stem(k,h,'file')（1）对于周期矩形信号的傅里叶级数cn =-1/2j*sin(n/2*pi)*sinc(n/2) n=-15:15;X=-j*1/2*sin(n/2*pi).*sinc(n/2);subplot(2,1,1);stem(n,abs(X),'file');title('幅度谱')xlabel('nw');subplot(2,1,2);stem(n,angle(X),'file');title('相位谱')（2）对于三角波信号的频谱是：Cn=-++n=-15:15;X=sinc(n)-0.5*((sinc(n/2)).^2);subplot(2,1,1);stem(n,abs(X),'file');title('幅度谱')xlabel('nw');subplot(2,1,2);stem(n,angle(X),'file');title('相位谱')M4-6(4)x=[1,2,3,0,0];X=fft(x,5);subplot(2,1,1);m=0:4;stem(m,real(X),'file'); title('X[m]实部') subplot(2,1,2);stem(m,imag(X),'file'); title('X[m]虚部')M4-7（3）k=0:10;x=0.5.^k;subplot(3,1,1);stem(k,x,'file')title('x[k]')X=fft(x,10);subplot(3,1,2);m=0:9;stem(m,real(X),'file');title('X[m]实部')subplot(3,1,3);stem(m,imag(X),'file');title('X[m]虚部')M5-2t=0:0.05:2.5;T=1;xt1=rectpuls(t-0.5,T);subplot(2,2,1)plot(t,xt1)title('x(t1)')axis([0,2.5,0,2])xt2=tripuls(t-1,2);subplot(2,2,2)plot(t,xt2)title('x(t2)')axis([0,2.5,0,2])xt=xt1+xt2.*cos(50*t);subplot(2,2,[3,4])plot(t,xt)title('x(t)')figure;b=[10000];a=[1,26.131,341.42,2613.1,10000]; [H,w]=freqs(b,a,w);subplot(2,1,1)plot(w,abs(H));title('幅度曲线')subplot(2,1,2)plot(w,angle(H));title('相位曲线')figure;sys=tf([10000],[1 26.131 341.42 2613.1 10000]);yt1=lsim(sys,xt,t);subplot(2,1,1);plot(t,yt1);title('y(t1)')yt2=lsim(sys,xt.*cos(50*t),t);subplot(2,1,2);plot(t,yt2);title('y(t2)')M6-1（1）num=[41.6667];den=[1 3.7444 25.7604 41.6667];[r,p,k]=residue(num,den)r =-0.9361 - 0.1895i -0.9361 + 0.1895i 1.8722p =-0.9361 + 4.6237i -0.9361 - 4.6237i -1.8722k =[]（2）num=[16 0 0];den=[1 5.6569 816 2262.7 160000];[r,p,k]=residue(num,den)r =0.0992 - 1.5147i 0.0992 + 1.5147i -0.0992 + 1.3137i -0.0992 - 1.3137ip =-1.5145 +21.4145i -1.5145 -21.4145i -1.3140 +18.5860i -1.3140 -18.5860i k =[]（3）num=[1 0 0 0];den=conv([1 5],[1 5 25]);[r,p,k]=residue(num,den)r =-2.5000 - 1.4434i -2.5000 + 1.4434i -5.0000p =-2.5000 + 4.3301i -2.5000 - 4.3301i -5.0000k =1（4）num=[833.3025];den=conv([1 4.1123 28.867],[1 9.9279 28.867]);[r,p,k]=residue(num,den)r =-2.4819 + 1.0281i -2.4819 - 1.0281i 2.4819 - 5.9928i 2.4819 + 5.9928i p =-2.0562 + 4.9638i -2.0562 - 4.9638i -4.9640 + 2.0558i -4.9640 - 2.0558i k =[]M6-2sys=tf(b,a);x=1*(t>0)+0*(t<=0);y1=lsim(sys,x,t);plot(t,y1);title('零状态响应')figure;[A B C D]=tf2ss(b,a);sys=ss(A,B,C,D);x=1*(t>0)+0*(t<=0);zi=[1 2];y=lsim(sys,x,t,zi);plot(t,y);title('完全响应')figure;y2=y-y1;plot(t,y2);title('零输入响应')a=[1 2 2 1];b=[1 2];sys=tf(b,a); pzmap(sys)冲击响应a=[1 2 2 1];b=[1 2];sys=tf(b,a); impulse(sys)阶跃响应a=[1 2 2 1];b=[1 2];sys=tf(b,a);step(sys)频率响应a=[1 2 2 1];b=[1 2];w=linspace(-10,10,2 0000);H=freqs(b,a,w); plot(w,abs(H))（1）num=[2 16 44 56 32];den=[3 3 -15 18 -12];[r,p,k]=residuez(num,den)r =-0.0177 9.4914 -3.0702 + 2.3398i -3.0702 - 2.3398ip =-3.2361 1.2361 0.5000 + 0.8660i 0.5000 - 0.8660ik =-2.6667（2）num=[4 -8.86 -17.98 26.74 -8.04];den=[1 -2 10 6 65];[r,p,k]=residuez(num,den)r =1.0849 + 1.3745i 1.0849 - 1.3745i 0.9769 - 1.2503i 0.9769 + 1.2503i p =2.0000 + 3.0000i 2.0000 - 3.0000i -1.0000 + 2.0000i -1.0000 - 2.0000i k =-0.1237M7-2k=0:10;a=[2 -1 3];b=[2 -1];y1=filter(b,a,x);stem(k,y1)title('零状态响应')figure;h=impz(b,a,k);x=0.5.^k;y2=conv(x,h);N=length(y2);stem(0:N-1,y2)title('零输入响应')完全响应y=y1+y2(1)num=[2 16 44 56 32];den=[3 3 -15 18 -12];zplane(num,den)由图可知极点不是都在单位圆内，所以系统不是稳定系统。