MA(n)模型识别

将要处理的数据放到

‘1.txt’文本中；

在Matlab中导入需要处理的数据：File-Import Data-添加数据文件-打开-Finish； 在Command Window下输入

plot(x1,'DisplayName','x1','YDataSource','x1');figure(gcf) 得到图如下：

43210-1-2-3-4020406080100120

求取自相关函数 autocorr(x1)

Sample Autocorrelation Function10.80.6Sample Autocorrelation0.40.20-0.2-0.4-0.6-0.80246810Lag1214161820A= autocorr(x1) A =

1.0000 -0.6831 0.2479 0.0384 -0.1498 0.2493 -0.2631 0.2057 -0.0956 -0.0403 0.1233 -0.1218 0.0134 0.13 -0.2274 0.1870 -0.1063 0.0007 0.0324 -0.0388

0.0363

求x1的偏相关函数 parcorr(x1)

Sample Partial Autocorrelation Function10.80.60.40.20-0.2-0.4-0.6-0.8Sample Partial Autocorrelations0246810Lag1214161820B=parcorr(x1) B =

1.0000 -0.6834 -0.4231 -0.0060 -0.0435 0.2531 0.0610 0.0715 0.0222 -0.1082 -0.0712 -0.0003 -0.1693 0.1483 -0.0041 -0.04 -0.0412

-0.1241 -0.2056 0.0424 -0.0296

%判断是MA（m）模型 a=mean(x1)%求均值 a =

0.1328 b=var(x1) %方差 b =

2.8245

c=std(x1) %标准差 c =

1.6806

2

%求取参数b1，b2和𝜎𝜀 p2 =

0.2479

>> p1=A(2,1); >> p1=A(2,1) p1 =

-0.6831

%p1和p2为自相关函数

2

%b2，b1为参数，b3为𝜎𝜀

b2=-0.5+1/(4*p2)+((p2+0.5)^2-p1^2)^0.5/(2*p2)-((0.5-1/(4*p2)-1/(2*p2)*((p2+0.5)^2-p1^2)^0.5)^2-1)^0.5

b2 =

0.6123

>> b1=p1*b2/(p2*(1+b2)) b1 =

-1.0466

>> b3=b*p2/b2 %b为样本方差，b3为噪声方差 b3 =

1.1434

所以所求的模型为：x(n)=w(n)+b1*w(n-1)+b2*w(n-2) %w（n）为纯随机过程

下面通过程序进行仿真：

clear

>> b1=-1.0466; b2= 0.6123; n=120;

x=zeros(1,n); w=randn(1,n); x(1)=w(1);

x(2)=w(2)+b1*w(1)+0; %信号序列的产生 for i=3:n

x(i)=w(i)+b1*w(i-1)+b2*w(i-2); end figure(1)

plot(1:n,x,'b:',1:n,w,'r-'); legend('信号序列','高斯白噪声')

title('基于MA（2）模型产生的信号x和高斯白噪声w'); xlabel('信号点数'); ylabel('x（n）n/w（）');

基于MA（2）模型产生的信号x和高斯白噪声w6信号序列高斯白噪声4 2x（n）n/w（）0-2-4-6 0204060信号点数80100120

C=x C =

Columns 1 through 10

-1.0667 2.0501 -1.2801 0.1761 0.4273 -1.7738 1.6652 0.7341 -1.6321 0.9205

Columns 11 through 20

-0.7173 0.7629 -0.1849 0.13 -0.6768 0.4148 2.0429 -4.5211 5.8321 -3.3786

Columns 21 through 30

2.0119 -2.5041 1.70 -0.6795 0.3525 -2.2829 2.4785 -2.7291 1.6243 -0.1595

Columns 31 through 40

-0.3152 1.1398 0.0733 -1.0410 1.53 -1.6120 -0.1760 1.7300 -1.7772 0.5113

Columns 41 through 50

0.9686 -0.3926 0.2858 1.2478 -0.13 0.0322 -0.3720 0.2178 1.4513 -3.2584

Columns 51 through 60

2.3924 -2.9102 3.0452 -1.3996 -0.2759 0.4556 -2.4114 3.1399 -4.3230 0.3312

Columns 61 through 70

1.19 -2.4522 1.4531 -0.3344 0.4012 -1.1743 0.9959 -0.2668

Columns 71 through 80

0.8425 -0.7434 0.07 1.0810 -3.2685 0.6383 0.2711 -0.0874

Columns 81 through 90

-1.4820 1.0968 0.0086 -0.7237 0.6912 -0.0947 -2.51 3.2685

Columns 91 through 100

-3.1333 0.1559 0.6208 -1.9000 1.31 -1.4136 -2.3550 3.7517

Columns 101 through 110

-3.38 1.4785 -0.4247 0.4195 -0.9550 2.3199 0.0275 -0.4100

Columns 111 through 120

1.1988 -0.66 -0.5830 -0.7868 3.2680 -3.6552 -0.4125 -0.6788

1.6979 2.3351 -1.1637 2.7518 -2.2979 1.8741 -0.7929 -2.0428 1.0413 -1.4841 1.7960 0.0848