大连理工大学时间序列作业 - 图文

plot(f(1:N/2),sarw(1:N/2)); xlabel('频率(Hz)'); ylabel('功率谱值'); title('AR谱图'); grid on;

运行matlab程序，可得AR谱图如下：

AR模型的AR谱图

六、进行周期图谱（FFT）分析

PESxx? AR模型的周期图谱的公式为：

12?N?xeit?0N?12?i?t

?12X(?)2?NMatlab程序如下：

%进行周期图谱（FFT）分析

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% clear clc

close all hidden

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %读入原始数据 s=1;

fid=fopen(['yuanshixushujubiao',num2str(s),'.txt'],'r'); h=fscanf(fid,'%f'); fclose(fid);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%计算周期图谱 N=length(h);

fs=6400; %采样频率

spews=fft(h,N); %原信号的FFT变换 spew=2*abs(spews).^2/(2*pi*N); f=0:fs/N:(fs-fs/N);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %绘制周期图谱 figure;

plot(f(1:N/2),spew(1:N/2)); xlabel('频率(Hz)'); ylabel('周期图谱值');

title('原始数据的周期图谱'); grid on;

运行matlab程序，得AR模型的周期图谱如下：

AR模型的周期图谱

比较：从AR谱和周期图谱两图中可以看出，AR谱比周期图谱平滑，且无毛刺，谱峰突出。

七、程序流程图

采集原始数据 读入到matlab程序去均值 利用最小二乘法估计AR模型的参数 利用BIC准则对AR模型进行适应性检建立AR模型 AR谱分析 AR周期图谱（FFT）分析 计算AR模型的Green函数

八、计算Green函数

利用递推算式计算Green函数：

G0?1G1??1G0G2??1G1??2G0G3??1G2??2G1??3G0?Gn??1Gn?1??2Gn?2????nG0?Gj??1Gj?1??2Gj?2????nGj?n(j?n) Matlab程序如下： %计算Green函数

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% clear clc

close all hidden

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %AR(n)模型的初始参数 s=1;

fid=fopen(['D:\\matlab2009\\work\\AR模型参数',num2str(s),'.txt'],'r'); h=fscanf(fid,'%f'); fclose(fid); n=h(1);

b=h(3:(n+2));

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %利用递推法算式计算Green函数 G0=1;

G1=b(1)*G0; G(1:40)=0; G(1)=G0; G(2)=G1; for j=3:40

for i=1:j-1 if j<=n

G(j)=G(j)+b(i)*G(j-i); end end if j>n

for i=1:n

G(j)=G(j)+b(i)*G(j-i); end end

end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %绘制Green函数 stem(G);

xlabel('n的值');ylabel('G的值'); title('Green函数'); grid on

运行matlab程序，可得Green函数如下：

AR模型的Green函数

Green函数为G=

1.0000 0.2352 0.1097 0.0081 0.1857 -0.0002 -0.1859 -0.1014 0.0034 -0.0391 -0.1374 -0.1705 0.0051 -0.1080 0.0072 0.1855 0.1682 0.0930 0.0552 0.1248 0.0553 -0.0423 -0.0399 0.0029 -0.0022 -0.0982 -0.0943 -0.0411

-0.0569 -0.0443 0.0076 0.0601 0.0475 0.0361 0.0601 0.0536 0.0207 -0.0007 0.0152 0.0107