MATLAB——Z transformation and Z inverse transformation

Topic 1:
Use the partial fraction method to find the inverse z-transformation of the system function, and compare the result obtained by impz with the graph.
Known system function:
$$X（z）=\frac{0.1321-0.3963z{\_}^{-2}+0.3962z{\_}^{-4}}{1+0.34319z^{-2}+0.60439z^{-4}}(|z|>1)$$
residueez:
residueez is a function in MATLAB that solves the poles and zeros of a system function of one or more order discrete or continuous systems. With it, it can be disassembled into partial fractions.
[r, p, c] = residueez(b, a)
residueez is a function in MATLAB that solves for the poles and zeros of a system function of one or more order discrete or continuous systems. Its syntax is:
[r, p, c] = residueez(b, a)
where b and a are respectively the numerator and denominator polynomial coefficient vectors of the system function. r is the vector of residuals at all poles of the system function, p is the vector of all poles of the system function, and c is the constant term of the system function (if present).
impz:
use the impz function to draw the unit impulse response of the discrete time series, the parameters are the numerator of the system function, the coefficient of the denominator and the discrete time series

b=[0.1321,0,-0.3963,0,0.3962]; % 分子多项式系数
a=[1,0,0.34319,0,0.60439]; % 分母多项式系数
[r,p,c]=residuez(b,a); % 使用residuez函数求解r、p、c
N=40; n=0:N-1; % 离散时间序列长度及其范围
% 利用部分分式分解的结果计算单位脉冲响应
h=r(1)*p(1).^n+r(2)*p(2).^n+r(3)*p(3).^n+r(4)p(4).^n+c(1).[n==0];
% 绘制单位脉冲响应与impz函数得到的结果
subplot(1,2,1); stem(n,real(h)) % 绘制离散时间序列的实部
subplot(1,2,2); impz(b,a,n) % 利用impz函数绘制离散时间序列的单位脉冲响应

operation result: