求解$H(z)=\frac{0.1321-0.3963z^{-2}+0.3963z^{-4}-0.1321z^{-6}}{1+0.34319z^{-2}+0.60439z^{-4}+0.20407z^{-6}}$
初始状态：$y(-1)=7,x(-1)=-3$

$\text{方法一：}使用\text{impz()}\text{dstep()}求冲激和阶跃响应$

注意只能求解无初始状态的

%% impz()求离散系统单位冲激响应，dstep()求离散系统单位阶跃响应

b = [0.1321 0 -0.3963 0 0.3963 0 -0.1321];
a = [1 0 0.34319 0 0.60439 0 0.20407];

N = 32;
n = 0:N-1;

h = impz(b,a,n);
g = dstep(b,a,n);

figure("color",'w');
subplot(121)
stem(n,h,"filled");title('impz()求解系统单位冲激');
subplot(122)
stem(n,g,"filled");title('dstep()求解系统单位阶跃');

$\text{方法二：}使用\text{filtic()}\text{filter()}求冲激和阶跃响应$

可以求解有初始状态的

%% filtic()和filter()求解离散系统单位冲激响应
clear;

b = [0.1321 0 -0.3963 0 0.3963 0 -0.1321];
a = [1 0 0.34319 0 0.60439 0 0.20407];

N = 32;
n = 0:N-1;

%建立单位冲激信号
x1 = [n==0];
%建立单位阶跃信号
x2 = [n>=0];

x01 = -3;y01 = 7;%初始条件：x(-1)=0,y(-1)=0

xi = filtic(b,a,y01,x01);

h = filter(b,a,x1,xi);
g = filter(b,a,x2,xi);

figure("color",'w');
subplot(221)
stem(n,h,"filled");title('filtic()filter()求解系统单位冲激');
subplot(222)
stem(n,g,"filled");title('filtic()filter()求解系统单位阶跃');

h2 = impz(b,a,n);
g2 = dstep(b,a,n);
subplot(223)
stem(n,h2,"filled");title('impz()求解系统单位冲激');
subplot(224)
stem(n,g2,"filled");title('dstep()求解系统单位阶跃');