随机工程matlab实验.docx
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随机工程matlab实验.docx
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随机工程matlab实验
自动化学院
随机过程课程设计
学号:
S3*******1
专业:
导航、制导与控制
学生姓名:
任课教师:
赵希人教授
2008年12月
第一题、
源程序:
x=rand(1,2000)
EX=mean(x)%均质检验
DX=var(x)%方差检验
subplot(2,1,1),hist(x,10);
y=linspace(-10,10,21);
form=-10:
10
mAbs=abs(m);
s=0;
forn=1:
2000-mAbs
s=s+(x(n+mAbs)-EX)*(x(n)-EX);
end
y(m+11)=(1/(2000-mAbs))*s;
end
x2=[-15:
30/20:
15];
subplot(2,1,2),plot(x2,y);
1.打印前50个数:
Columns1through12
0.33290.51890.54350.90380.24510.13240.09770.69750.37070.19850.57700.4111
Columns13through24
0.15700.71280.34450.64340.47110.31070.96100.22360.06070.26570.38610.3220
Columns25through36
0.39330.30220.71590.43120.59410.90340.13900.11190.81270.17620.51750.0592
Columns37through48
0.45350.71520.16390.16610.24400.22960.97260.54980.79010.35000.28990.8619
Columns49through50
0.99370.3002
2.分布检验:
3.均值检验:
EX=
0.5038
4.方差检验:
DX=
0.0827
5.计算相关函数:
第二题、
源程序:
clearall;
forn=1:
2000
xt(n)=normrnd(0,1);%产生2000个N(0,1)分布的独立序列
end
plot(xt),title('2000个N(0,1)分布的独立序列');
figure
fori=1:
5
forj=1:
10
sc(j,i)=xt((i-1)*5+j);
end;
end;
disp([sc]);
EX=mean(xt)%求平均数并输出
DX=cov(xt)%求方差并输出
subplot(2,1,1);
p=hist(xt,20);%将产生的2000个随机数分为20组
p=p/100;t=-2.85:
0.3:
2.85;%求概率密度
bar(t,p,1),title('N(0,1)分布的独立序列的直方图');
xlabel('x');ylabel('f(x)');
[tx,i]=xcov(xt,10);%τ取-10到10
Tx=tx/2000;%求自相关函数Γx(τ)
subplot(2,1,2)
plot(i,Tx,'.-'),title('自相关函数Γx(τ)分布图');
xlabel('τ');ylabel('Γx(τ)');
1.打印前50个数:
0.35990.75621.00201.37470.0046
0.63071.1306-0.45530.0294-0.5836
-0.6737-0.8743-0.0972-1.62000.5674
0.7104-0.80680.7932-0.39710.4200
0.6455-0.0149-1.1756-0.0226-0.3667
0.75621.00201.37470.00460.5132
1.1306-0.45530.0294-0.58361.6777
-0.8743-0.0972-1.62000.5674-0.5122
-0.80680.7932-0.39710.42000.4997
-0.0149-1.1756-0.0226-0.36670.6410
程序运行产生的2000个N(0,1)分布的独立序列:
2.分布检验:
3.均值检验:
EX=
0.0069
4.方差检验:
DX=
0.9903
5.计算相关函数:
第三题、
源程序:
y=normrnd(0,1,1,2000);
x=zeros(1,2000);
fork=2:
2000
x(k)=y(k)+4*y(k-1);
end;
Ex=mean(x)%求EX(k)
Ex2=mean(x.^2)%EX.^2(k)
Dx=var(x)%DX(k)
Bm=zeros(1,11);
fori=0:
10
xy=zeros(1,2000-i);
forj=1:
(2000-i)
xy(j)=(x(j+i)-Ex)*(x(j)-Ex);
end;
Bm(i+1)=sum(xy)/(2000-i);%Bx(m)
end;
a=Bm(:
11:
-1:
1);
a=[a(1:
10),Bm];
Bm=a
q=-10:
10;
plot(q,Bm)
1.求均值EX:
Ex=
0.1767
2.求二阶矩EX2:
EX2=
16.6688
3.求方差:
Dx=
16.6459
4.BX(m):
Columns1through12
0.5104-0.1167-0.41100.17650.44230.12370.2300-0.3652-0.44334.065216.63764.0652
Columns13through21
-0.4433-0.36520.23000.12370.44230.1765-0.4110-0.11670.5104
第四题、
源程序:
y=normrnd(0,1,1,2000);
x=zeros(1,2000);
fork=2:
2000
x(k)=y(k)-0.707*x(k-1);
end;
M=zeros(1,901);
fork=101:
1001
x(k)=x(k)+x(k-1);
M(k-100)=x(k-1);
end;
Ex=x(k)/900%EX(k)
Ex2=sum(M.^2)/900%EX.^2(k)
Dx=Ex2-(Ex).^2%DX(k)
Bm=zeros(1,11);
fori=0:
10
xy=zeros(1,1900-i);
forj=100:
(2000-i)
xy(j-99)=(x(j+i)-Ex)*(x(j)-Ex);
end;
Bm(i+1)=sum(xy)/1900%Bx(m)
end;
a=Bm(:
11:
-1:
1);
a=[a(1:
10),Bm];
q=-10:
10;
plot(q,a)%Bx(m)二维分布曲线
1.求EX:
Ex=
-0.0025
2.求Ex2:
Ex2=
39.8177
3.求DX:
Dx=
39.8177
4.求Bx(m):
Bm=
19.859317.743619.024318.024518.457418.015918.086317.838117.772517.591917.4769
第五题、
源程序:
f='sin(x)';%画出符号函数
subplot(3,2,1);
ezplot(f)
subplot(3,2,2);
ezplot(f)
n=-20:
20;
y=sin(n*pi/2);
subplot(3,2,3);
k=-10:
10;
plot(k,sin(k*pi/2),'--rs','MarkerEdgeColor','k','MarkerFaceColor','g','MarkerSize',5)
title('采样信号(±10点)');
subplot(3,2,4);
k=-20:
20;
plot(k,sin(k*pi/2),'--rs','MarkerEdgeColor','k','MarkerFaceColor','g','MarkerSize',5)
title('采样信号(±20点)');
D=0.05;
z1=1;
fort1=-5*pi:
D:
5*pi;
s1=0;
form1=-10:
10
s1=s1+y(m1+11)*sinc((1/pi)*(t1-pi*m1/2));
%sinc函数内插恢复,重建信号过程
end
fa(z1)=s1;z1=z1+1;
end
subplot(3,2,5)
xlab1=linspace(-5*pi,5*pi,length(fa));
plot(xlab1,fa);title('内插恢复信号(±10点)');
z2=1;
fort1=-10*pi:
D:
10*pi;
s2=0;
form2=-20:
20
s2=s2+y(m2+21)*sinc((1/pi)*(t1-pi*m2/2));
%sinc函数内插恢复,重建信号过程
end
fb(z2)=s2;z2=z2+1;
end
subplot(3,2,6)
xlab2=linspace(-10*pi,10*pi,length(fb));
plot(xlab2,fb);title('内插恢复信号(±20点)');
运行结果:
说明:
图中第一行两图为sin函数的符号函数示意图,区间-2π~2π。
图中第二行两图为sin函数的采样函数示意图,左图区间-5π~5π(±10点),右图区间-10π~10π(±20点)。
图中第三行两图为sin函数的恢复函数示意图,右图比左图更加接近原函数,但是由于是有限采样点恢复,并且,内插sinc函数本身是非因果的连续信号,物理上不可实现,故只能用大样本离散值模拟,程序中取步长D=0.05。
所以,可以看到两图在函数边缘有较大过冲。
这是由于sinc函数被截断而引起的。
第六题、
源程序:
A=zeros(40,21);
k=zeros(1,20);
fori=1:
21
A(1,i)=2*i-1;
end
forj=1:
20
ifmod(j,2)==1;
A(2,j)=A(1,j+1);
else
A(2,j)=0;
end;
end;
k
(1)=A(1,1)/A(2,1);
fori=3:
40
ifmod(i,2)==1;
forj=(i+1)/2:
2:
20;
A(i,j)=A(i-2,j);
ifj~=20;
A(i,j+1)=A(i-2,j+1)-A(i-1,j+1)*k((i-1)/2);
else
A(i,j+1)=41;
end;
end
else
forj=i/2:
2:
20
A(i,j)=A(i-1,j+1);
end;
k(i/2)=A(i-1,i/2)/A(i,i/2);
end;
end;
disp(A)
disp(k)
1.奥斯特姆表:
A=
Columns1through12
1.00003.00005.00007.00009.000011.000013.000015.000017.000019.000021.000023.0000
3.000007.0000011.0000015.0000019.0000023.00000
03.00002.66677.00005.333311.00008.000015.000010.666719.000013.333323.0000
02.666705.333308.0000010.6667013.3333016.0000
002.66671.00005.33332.00008.00003.000010.66674.000013.33335.0000
001.000002.000003.000004.000005.00000
0001.000002.00000.00003.00000.00004.000005.0000
000000.000000.00000000.0000
00000-Inf0.0000-Inf0.0000NaN0-Inf
0000-Inf0-Inf0NaN0-Inf0
00000-InfNaN-InfNaNNaNNaN-Inf
Columns13through21
25.000027.000029.000031.000033.000035.000037.000039.000041.0000
27.0000031.0000035.0000039.000000
16.000027.000018.666731.000021.333335.000024.000039.000041.0000
018.6667021.3333024.0000041.00000
16.00006.000018.66677.000021.33338.000024.0000-7.12500
6.000007.000008.00000-7.125000
0.00006.00000.00007.000008.000043.0000-7.125041.0000
00.000000043.0000041.00000
0.0000-Inf0.0000NaN0-Inf43.0000-Inf0
-Inf0NaN0-Inf0-Inf00
NaN-InfNaNNaNNaN-InfNaN-Inf41.0000
Ak=0.3333,1.1250,2.6667,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN
B=
Columns1through12
000000000000
3.000007.0000011.0000015.0000019.0000023.00000
000000000000
02.666705.333308.0000010.6667013.3333016.0000
000000000000
001.000002.000003.000004.000005.00000
000000000000
000000.000000.000000.000000.0000
0000NaNNaNNaNNaNNaNNaNNaNNaN
0000-Inf0-Inf0NaN0-Inf0
00000NaNNaNNaNNaNNaNNaNNaN
Columns13through21
00000001.00000
27.0000031.0000035.0000039.000000
00000001.00000
018.6667021.3333024.0000041.00000
00000001.00000
6.000007.000008.00000-7.125000
00000001.00000
00.000000043.0000041.00000
NaNNaNNaNNaNNaNNaNNaNNaNNaN
-Inf0NaN0-Inf0-Inf00
NaNNaNNaNNaNNaNNaNNaNNaNNaN
Bk=0,0,0,NaN,NaNNaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN,NaN
2.由奥斯特姆表可以看出系统不稳定。
3.
第七题、
源程序:
n=7;
N=13;
x=[10.50.58-0.01-0.01210.000050.00006];
y=[10.5500000];
%x=[10.70.5-0.3];
%y=[10.30.20.1];
A=zeros(N,n);%分配内存空间
B=zeros(N,n);
a=zeros(n-1,1);
b=a;
fori=1:
n,%赋表的初始值,前两行及a
(1),b
(1);
A(1,i)=x(i);
B(1,i)=y(i);
end;
fori=1:
n,
A(2,i)=A(1,n-i+1);
end;
fori=1:
n,
B(2,i)=A(2,i);
end;
a
(1)=A(1,n)/A(2,n);
b
(1)=B(1,n)/B(2,n);
fori=2:
n,
forj=1:
n-i+1,
A(2*i-1,j)=A(2*i-3,j)-A(2*i-2,j)*a(i-1);
B(2*i-1,j)=B(2*i-3,j)-B(2*i-2,j)*b(i-1);
end;
ifi==n,
break;
end;
forj=1:
n-i+1,
A(2*i,j)=A(2*i-1,n-i+2-j);
end;
forj=1:
n,
B(2*i,j)=A(2*i,j);
end;
a(i)=A(2*i-1,n-i+1)/A(2*i,n-i+1);
b(i)=B(2*i-1,n-i+1)/B(2*i,n-i+1);
end;
A
B
1.奥斯特姆表:
A=
1.00000.50000.5800-0.0100-0.01210.00010.0001
0.00010.0001-0.0121-0.01000.58000.50001.0000
1.00000.50000.5800-0.0100-0.01210.00000
0.0000-0.0121-0.01000.58000.50001.00000
1.00000.50000.5800-0.0100-0.012100
-0.0121-0.01000.58000.50001.000000
0.99990.49990.5870-0.0039000
-0.00390.58700.49990.9999000
0.99980.50220.58900000
0.58900.50220.99980000
0.65280.206300000
0.20630.652800000
0.5876000000
B=
1.00000.550000000
0.00010.0001-0.0121-0.01000.58000.50001.0000
1.00000.550000000
0.0000-0.0121-0.01000.58000.50001.00000
1.00000.550000000
-0.0121-0.01000.58000.50001.000000
1.00000.550000000
-0.00390.58700.49990.9999000
1.00000.550000000
0.58900.50220.99980000
1.00000.550000000
0.20630.652800000
0.8262000000
2.由奥斯特姆表可看出系统稳定。
3.
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