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b=0.5;
a=0.8;
t=0:0.001:5;
x=b*exp(-a*t).*sin(pi*t);
plot(t,x)   % 绘制波形

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c=2;
d=0.8;
k=-5:5;
y=c*d.^k;
stem(k,y);  % 绘制波形

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sys=tf(b, a)

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sys=tf([1],[1,2,77]); %　tf函数获得系统模型sys
t=0:0.01:5;           % 对时间t进行离散取样
f=10*sin(2*pi*t);     
y=lsim(sys,f,t);      % 求系统的零状态响应
plot(t,y)
xlabel('Time(sec)')
ylabel('y(t)')

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impulse(b, a)

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step(b, a)

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a=[7,4,6];
b=[1,1];
subplot(2,1,1)
impulse(b,a);
subplot(2,1,2)
step(b,a)

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t11=0;t12=1;t21=0;t22=2;
%f1(t)
t1=t11:0.001:t12;
ft1=2*rectpuls(t1-0.5,1); %幅值为1，宽度为1，t1=0.5点对称的方波信号
%f2(t)
t2=t21:0.001:t22;
ft2=t2;
t3=t11+t21:0.001:t12+t22;
ft3=conv(ft1,ft2);
ft3=ft3*0.001;  % 取1000个样点之和，因此需要*0.001
plot(t3,ft3)
title('ft1(t)*ft2(t)')

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y=filter(b,a,f)

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R=51;
d=rand(1,R)-0.5;
k=0:R-1;
s=2*k.*(0.9.^k);
f=s+d;
figure(1);
stem(k,f,'.');
M=5;
b=ones(M,1)/M;
a=1;
y=filter(b,a,f);
figure(2)
stem(k,y,'.')

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h=impz(b,a,k)

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k=0:10;
a=[1,3,2];  
b=[1];
h=impz(b,a,k);
stem(k,h,'.')

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conv(x1,x2)

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k1=0:10;
x1=sin(k1);
k2=0:15;
x2=0.8.^k2;
y=conv(x1,x2);
subplot(3,1,1)
stem(k1,x1,'o')
title('x1')
subplot(3,1,2)
stem(k2,x2,'o')
title('x2')
subplot(3,1,3)
stem(0:25,y,'o')
title('y')

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t=0:pi/100:4*pi;
b=[-1,1]; %频率响应函数的分子系数
a=[1 1]; %频率响应函数的分母系数
ft=sin(t)+sin(3*t); % 激励
yt=lsim(b,a,ft,t); %求解响应
plot(t,ft,t,yt)
legend('激励','响应')

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f=sym('cos(a*k)');
F=ztrans(f)

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F=sym('1/(1+z)^2');
fInver=iztrans(F)