哈爾濱工程大學(xué) 研究生 隨機過程課程實驗報告~

1、第一題： 用PC機產(chǎn)生0,1均勻分布的白色序列 (1) 打印出前50個數(shù) (2) 分布檢驗 (3) 均值檢驗 (4) 方差檢驗 (5) 計算出相關(guān)函數(shù)源程序:clear;clc;x=rand(1,2000);fprintf('1.輸出前50個數(shù):');for i=1:5 j=1:10; X(i,j)=x(i-1)*10+j);endX % 打印出前50個數(shù)y1=x(find(x>=0&x<0.1);t(1)=length(y1);y2=x(find(x>=0.1&x<0.2);t(2)=length(y2);y3=x(find(x>

2、=0.2&x<0.3);t(3)=length(y3);y4=x(find(x>=0.3&x<0.4);t(4)=length(y4);y5=x(find(x>=0.4&x<0.5);t(5)=length(y5);y6=x(find(x>=0.5&x<0.6);t(6)=length(y6);y7=x(find(x>=0.6&x<0.7);t(7)=length(y7);y8=x(find(x>=0.7&x<0.8);t(8)=length(y8);y9=x(find(x>

3、=0.8&x<0.9);t(9)=length(y9);y10=x(find(x>=0.9&x<1);t(10)=length(y10) ; fprintf('2.分布檢驗:');tsubplot(2,1,1);hist(x,10); % 分布檢驗fprintf('3.均值檢驗:');EX=mean(x) % 均值檢驗fprintf('4.方差檢驗:');DX=var(x) % 方差檢驗fprintf('5.計算相關(guān)函數(shù):');for m=-10:1:10 j=2000-abs(m); for i

4、=1:j C(i)=(x(abs(m)+i)-EX).*(x(i)-EX); end B(m+11)=sum(C)/j;endfor i=1:3 j=1:7; Bx(i,j)=B(i-1)*7+j);endBx % 計算相關(guān)函數(shù)subplot(2,1,2)m=-10:10;plot(m,B)1.輸出前50個數(shù):X = Columns 1 through 8 0.1315 0.6175 0.4759 0.0236 0.8753 0.0960 0.5479 0.0746 0.8483 0.4888 0.4260 0.5609 0.6730 0.1103 0.7614 0.4912 0.5077 0

5、.5892 0.0702 0.0386 0.4879 0.3002 0.0358 0.7934 0.4440 0.4423 0.5000 0.0325 0.0196 0.2932 0.0558 0.7208 0.8507 0.1279 0.4534 0.6225 0.4175 0.6702 0.0820 0.8725 Columns 9 through 10 0.9542 0.2516 0.5314 0.5983 0.5083 0.0165 0.8429 0.5442 0.4153 0.55662.分布檢驗:t = 210 192 197 202 197 214 198 191 188 211

6、圖（1）分布檢驗3.均值檢驗:理論值：EX =0.5實際值：EX =0.49914.方差檢驗:理論值：DX =1/12實際值：DX =0.0839均值和方差表：理論值實際值EX1/20.4991EX21/30.3330DX1/120.08395.計算相關(guān)函數(shù):Bx = 0.0022 0.0011 -0.0010 -0.0014 -0.0013 0.0034 -0.0051 -0.0026 0.0018 -0.0019 0.0838 -0.0018 0.0019 -0.0025 -0.0051 0.0033 -0.0014 -0.0015 -0.0013 0.0009 0.0020圖（2）相關(guān)函

7、數(shù)第二題：用PC機產(chǎn)生分布的正態(tài)序列(1)打印出前50個數(shù)(2)分布檢驗(3)均值檢驗(4)方差檢驗(5)計算出相關(guān)函數(shù)源程序：clear;clc;x=randn(1,2000);fprintf('1.輸出前50個數(shù):');for i=1:5 j=1:10; X(i,j)=x(i-1)*10+j);endX % 打印出前50個數(shù)y1=x(find(x>=0&x<0.1);t(1)=length(y1);y2=x(find(x>=0.1&x<0.2);t(2)=length(y2);y3=x(find(x>=0.2&x<

8、0.3);t(3)=length(y3);y4=x(find(x>=0.3&x<0.4);t(4)=length(y4);y5=x(find(x>=0.4&x<0.5);t(5)=length(y5);y6=x(find(x>=0.5&x<0.6);t(6)=length(y6);y7=x(find(x>=0.6&x<0.7);t(7)=length(y7);y8=x(find(x>=0.7&x<0.8);t(8)=length(y8);y9=x(find(x>=0.8&x<

9、0.9);t(9)=length(y9);y10=x(find(x>=0.9&x<1);t(10)=length(y10) ; fprintf('2.分布檢驗:');tsubplot(2,1,1);hist(x,10); % 分布檢驗fprintf('3.均值檢驗:');EX=mean(x) % 均值檢驗fprintf('4.方差檢驗:');DX=var(x) % 方差檢驗fprintf('5.計算相關(guān)函數(shù):');for m=-10:1:10 j=2000-abs(m); for i=1:j C(i)=(x(a

10、bs(m)+i)-EX).*(x(i)-EX); end B(m+11)=sum(C)/j;endfor i=1:3 j=1:7; Bx(i,j)=B(i-1)*7+j);endBx % 計算相關(guān)函數(shù)subplot(2,1,2)m=-10:10;plot(m,B)1.輸出前50個數(shù):X = Columns 1 through 8 -1.0457 -1.0045 -0.7384 -0.9445 -0.1354 -0.4226 1.5979 -0.3811 0.3409 0.5486 -1.0160 -1.6335 -1.8104 -0.0349 0.6758 -0.8909 -0.9381 -1

11、.5436 0.1596 -0.3688 -1.0122 0.1134 0.8850 -0.5823 -0.3197 1.6065 1.0613 0.3005 0.3511 0.9522 -0.6329 -0.8587 -0.0243 0.9170 -0.5015 -0.2513 1.6728 -1.3644 -0.3351 1.2946 Columns 9 through 10 0.2348 -0.3093 -1.8913 2.2175 -0.7176 -0.6733 1.7461 -0.55610.4811 -0.25202.分布檢驗:t =71 81 70 78 66 62 71 71

12、58 49圖（3）分布檢驗3.均值檢驗:理論值：EX =0實際值：EX = -0.00544.方差檢驗:理論值：DX =1實際值：DX = 0.9916均值和方差表：理論值實際值EX0-0.0054DX170.99165.計算相關(guān)函數(shù):Bx = -0.0097 -0.0258 -0.0077 0.0131 0.0244 -0.0224 0.0590 0.0228 0.0272 0.0208 0.9911 0.0212 0.0271 0.0224 0.0588 -0.0223 0.0238 0.0125 -0.0083 -0.0255 -0.0082圖（4）相關(guān)函數(shù)第三題：設(shè)為正態(tài)白色序列，服從

13、分布，求(1) (2) (3) (4) ，并畫出(m)圖源程序：clfclearp=randn(1,1001);k=2:1001;x=p(k)+4.*p(k-1);m=mean(x)m1=mean(x.2)s=m1-m.2for i=-10:10l=0;p=1000-abs(i);for k=1:pl=l+x(k+abs(i)-m*x(k)-m;endb(i+11)=l/p;endi=-10:10;plot(i,b) 1. 均值EX：理論值：EX =0實際值：EX =-0.02092.均方值： EX2：理論值：EX2= 17實際值：EX2= 16.39993. 方差DX：理論值：DX = 17

14、實際值：DX = 16.3995均值和方差表：理論值實際值EX0-0.0290EX21716.3999DX1716.39954. 相關(guān)函數(shù)：(m) = 0.1462 0.6689-0.03190.14730.1085-0.37090.22990.67210.12144.441816.8904 4.44180.12140.67210.2299-0.37090.10850.1473-0.03190.66890.1462圖（5） 相關(guān)函數(shù)第四題：設(shè),k=0,1,2,為N（0，1）正態(tài)白序列，N(0,1) 令，=1,2,1000; 。求：；源程序：clfclear;x0=0;for i=1:1000;

15、x(1,i)=-0.707*x0+randn;x0=x(1,i);endm=mean(x(:,100:end)m1=mean(x(:,100:end).2)s=m1-m.2for i=-10:10l=0;p=1000-abs(i);for k=1:pl=l+x(k+abs(i)-m*x(k)-m;endb(i+11)=l/p;endi=-10:10;plot(i,b)1.均值 EX：理論值：EX =0實際值：EX = 0.00272. 均方值：EX2：理論值：EX2= 2實際值：EX2= 1.96163.方差 DX：理論值：DX = 2實際值：DX = 1.9616均值和方差表：理論值實際值E

16、X00.0027EX221.9616DX21.96164. 相關(guān)函數(shù) (m)：圖（6）相關(guān)函數(shù)第五題,=2,=1/2,取采樣周期=/2,=2/=4滿足采樣定理：,N=5,10,20。 比較與。源程序：X='sin(t)' subplot(2,1,1); ezplot(X);Buchang=0.05;N=10; m=1;for t=-2*pi:Buchang:2*pisum=0;for n=(0-N):Nsum=sum+(sin(n*pi/2)*sin(t-pi*n/2)/(t-n*pi/2); endY(m)=sum; m=m+1;endt=-2*pi:Buchang:2*pi

17、;hold onplot(t,Y,':');title('N取10時的比較圖形');subplot(2,1,2); ezplot(X);N=20; m=1;for t=-2*pi:Buchang:2*pisum=0;for n=(0-N):Nsum=sum+(sin(n*pi/2)*sin(t-pi*n/2)/(t-n*pi/2); endY(m)=sum; m=m+1;endt=-2*pi:Buchang:2*pi;hold onplot(t,Y,':');title('N取20時的比較圖形');X(t)圖形用實線表示；Y(t)

18、 圖形用虛線表示；結(jié)果如下圖：圖（7）第六題：,求：(1) 列出Astrom表(2) 判別穩(wěn)定性(3) 若穩(wěn)定：？源程序：A=zeros(40,21);k=zeros(1,20);for i=1:21A(1,i)=2*i-1;endfor j=1:20if mod(j,2)=1;A(2,j)=A(1,j+1);elseA(2,j)=0;end;end;k(1)=A(1,1)/A(2,1);for i=3:40if mod (i,2)=1;for j=(i+1)/2:2:20;A(i,j)=A(i-2,j);if j=20;A(i,j+1)=A(i-2,j+1)-A(i-1,j+1)*k(i-1

19、)/2);elseA(i,j+1)=41;end;endelsefor j=i/2:2:20A(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) 列出Astrom表Columns 1 through 8 1.0000 3.0000 5.0000 7.0000 9.0000 11.0000 13.0000 15.0000 3.0000 0 7.0000 0 11.0000 0 15.0000 0 0 3.0000 2.6667 7.0000 5.3333 11.0000 8.0000 15.0000

20、0 2.6667 0 5.3333 0 8.0000 0 10.6667 0 0 2.6667 1.0000 5.3333 2.0000 8.0000 3.0000 0 0 1.0000 0 2.0000 0 3.0000 0 0 0 0 1.0000 0 2.0000 0.0000 3.0000 0 0 0 0 0 0.0000 0 0.0000 0 0 0 0 0 -Inf 0.0000 -Inf 0 0 0 0 -Inf 0 -Inf 0 0 0 0 0 0 -Inf NaN -Inf 0 0 0 0 0 NaN 0 NaN 0 0 0 0 0 0 NaN NaN 0 0 0 0 0 0

21、 NaN 0 0 0 0 0 0 0 0 NaN 0 0 0 0 0 0 0 NaN 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

22、 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Columns 9 through 16 17.0000 19.0000 21.0000 23.0000 25.0000 27.0000 29.0000 31.0000 19.0000 0 23.0000 0 27.0000 0 31.0000 0 10.6667 19.0000 13.3333 23.0000 16.0000 27.0000

23、18.6667 31.0000 0 13.3333 0 16.0000 0 18.6667 0 21.3333 10.6667 4.0000 13.3333 5.0000 16.0000 6.0000 18.6667 7.0000 4.0000 0 5.0000 0 6.0000 0 7.0000 0 0.0000 4.0000 0 5.0000 0.0000 6.0000 0.0000 7.0000 0 0 0 0.0000 0 0.0000 0 0 0.0000 NaN 0 -Inf 0.0000 -Inf 0.0000 NaN NaN 0 -Inf 0 -Inf 0 NaN 0 NaN

24、NaN NaN -Inf NaN -Inf NaN NaN 0 NaN 0 NaN 0 NaN 0 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN 0 NaN 0 NaN 0 NaN 0 NaN NaN NaN NaN NaN NaN NaN NaN 0 NaN 0 NaN 0 NaN 0 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN 0 NaN 0 NaN 0 NaN 0 0 NaN NaN NaN NaN NaN NaN NaN 0 NaN 0 NaN 0 NaN 0 NaN 0 0 NaN NaN NaN NaN NaN

25、NaN 0 0 NaN 0 NaN 0 NaN 0 0 0 0 NaN NaN NaN NaN NaN 0 0 0 NaN 0 NaN 0 NaN 0 0 0 0 NaN NaN NaN NaN 0 0 0 0 NaN 0 NaN 0 0 0 0 0 0 NaN NaN NaN 0 0 0 0 0 NaN 0 NaN 0 0 0 0 0 0 NaN NaN 0 0 0 0 0 0 NaN 0 0 0 0 0 0 0 0 NaN 0 0 0 0 0 0 0 NaN 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

26、0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Columns 17 through 21 33.0000 35.0000 37.0000 39.0000 41.0000 35.0000 0 39.0000 0 0 21.3333 35.0000 24.0000 39.0000 41.0000 0 24.0000 0 41.0000 0 21.3333 8.0000 24.0000 -7.1250 0 8.0000 0 -7.1250 0 0 0 8.0000 43.0000 -7.1250 41.0000 0 43.

27、0000 0 41.0000 0 0 -Inf 43.0000 -Inf 0 -Inf 0 -Inf 0 0 NaN -Inf NaN -Inf 41.0000 0 NaN 0 41.0000 0 NaN NaN NaN NaN 0 NaN 0 NaN 0 0 NaN NaN NaN NaN 41.0000 0 NaN 0 41.0000 0 NaN NaN NaN NaN 0 NaN 0 NaN 0 0 NaN NaN NaN NaN 41.0000 0 NaN 0 41.0000 0 NaN NaN NaN NaN 0 NaN 0 NaN 0 0 NaN NaN NaN NaN 41.00

28、00 0 NaN 0 41.0000 0 NaN NaN NaN NaN 0 NaN 0 NaN 0 0 NaN NaN NaN NaN 41.0000 0 NaN 0 41.0000 0 NaN NaN NaN NaN 0 NaN 0 NaN 0 0 NaN NaN NaN NaN 41.0000 0 NaN 0 41.0000 0 NaN NaN NaN NaN 0 NaN 0 NaN 0 0 0 NaN NaN NaN 41.0000 0 NaN 0 41.0000 0 0 0 NaN NaN 0 0 0 NaN 0 0 0 0 0 NaN 41.0000 0 0 0 41.0000 0

29、 Columns 1 through 8 0.3333 1.1250 2.6667 Inf 0 NaN NaN NaN Columns 9 through 16 NaN NaN NaN NaN NaN NaN NaN NaN Columns 17 through 20 NaN NaN NaN NaN(2) 判別穩(wěn)定性：由奧斯特姆表可以看出系統(tǒng)不穩(wěn)定。(3) 第七題：已知如下圖所示的離散系統(tǒng)，其中，求(1) 列出Astrom表(2) 判別穩(wěn)定性(3) =？源程序：A1=1 0 -0.01;B1=1 0.5 0.6;F=conv(conv(A1,A1),B1); %卷積求多項式系數(shù)As=zeros

30、(13,7);As(1,1:7)=F;Bs=zeros(13,7);Bs(1,6)=1;Bs(1,7)=-0.5500;aK=zeros(1,6);bK=zeros(1,6);for j=1:7As(2,j)=As(1,7-j+1);Bs(2,j)=As(2,j);end;aK(1,1)=As(1,7)/As(2,7);bK(1,1)=Bs(1,7)/Bs(2,7);for i=3:13if mod(i,2)=1 %奇數(shù)行元素for j1=1:7-(i-1)/2;As(i,j1)=As(i-2,j1)-As(i-1,j1)*aK(i-1)/2);Bs(i,j1)=Bs(i-2,j1)-Bs(i

31、-1,j1)*bK(i-1)/2);end else %偶數(shù)行元素for j2=1:(7-(i-2)/2);As(i,j2)=As(i-1,7-(i-2)/2-j2+1);Bs(i,j2)=As(i,j2);end;aK(i/2)=As(i-1,7-(i-2)/2)/As(i,7-(i-2)/2); bK(i/2)=Bs(i-1,7-(i-2)/2)/Bs(i,7-(i-2)/2);endend%求取系統(tǒng)輸出方差s=0;for i=1:2:11s=s+Bs(i,7-(i-1)/2)2/Bs(i+1,7-(i-1)/2);ends=s+Bs(13,1)2/As(13,1);s=s/As(1,1)disp(As)disp(aK)disp(Bs)disp(bK)(1) 列出Astrom表A表： 1.0000 0.50