ch7 隨機信號的產(chǎn)生與處理

1、234 56 7,cos 2(7 1)iix tAft8,1cos 2(72)iix tAuft9% File: c7_sinewave.mf = 1;% frequency of sinusoidfs = 100;% sampling frequencyt = (0:200)/fs;% time vectorfor i=1:20 x(:,i) = cos(2*pi*f*t+rand(1)*2*pi); y(:,i) = cos(2*pi*f*t+rand(1)*pi/2); z(:,i) = (1+rand(1)*cos(2*pi*f*t);endsubplot(3,1,1); plot(t

2、,x,k); ylabel(x(t)subplot(3,1,2); plot(t,y,k); ylabel(y(t)subplot(3,1,3); plot(t,z,k); ylabel(z(t)% End of script file.10 11 00.511.52-101x(t)00.511.52-101y(t)00.511.52-202z(t)1200.20.40.60.811.21.41.61.82-101x(t)00.20.40.60.811.21.41.61.82-101y(t)00.20.40.60.811.21.41.61.82-202z(t)13 14x=random bin

3、ary(nbits,nsamples)+i*random binary (nbits,nsamples) 101Sample Indexxd020406080-101Sample Indexxq160100200300400500600700800-1.5-1-0.500.511.5Sample Indexxd0100200300400500600700800-1.5-1-0.500.511.5Sample Indexxq171mod( )(73)iixaxcm18191mod( )(74)iixaxcm20 212211(714)makm 1,1,2,3,2(715

4、)iakimm 23242526% File: c7_LCDemo1.mm = 2048; c = 1; seed = 1;% default values of m and ca1 = 65; a2 = 1229;% multiplier valuesix1 = seed; ix2 = seed;% initialize algorithmx1 = zeros(1,m); x2 = zeros(1,m); % initialize arraysfor i=1:m ix1 = rem(ix1*a1+c),m); x1(i) = ix1/m; ix2 = rem(ix2*a2+c),m); x2

5、(i) = ix2/m;endsubplot(1,2,1)y1 = x1(1,2:m),x1(1,1);plot(x1,y1,.)% plot results for a1subplot(1,2,2)y2 = x2(1,2:m),x2(1,1);plot(x2,y2,.)% plot results for a2% End of script file.2700.5100.20.40.60.8100.5100.20.40.60.812822211 1(7 19)1 NnNnNX nX nDNXn2222(720)xDEXYE XEXYa2921(721)YXZ222222112 111(722

6、)DEXXZZ30% File: c7_Durbinfunction D = durbin(x)N = length(x);% length of input vectory = x-mean(x);% remove dcydiff = y(2:N)-y(1:(N-1);% numerator summandNum = sum(ydiff.*ydiff);% numerator factor of D Den = sum(y.*y);% denominator factor of DD = Num/Den;% Durbin factor% End of function file.222221

7、1(723)D 31% File: c7_LCDemo2m = 2048; c = 1; seed = 1;a1 = 65; a2 = 1229;ix1 = 1; ix2 = 1;x1 = zeros(1,m); x2 = zeros(1,m);for i=1:m ix1 = rem(ix1*a1+c),m); x1(i) = ix1; ix2 = rem(ix2*a2+c),m); x2(i) = ix2;endD1 = c7_Durbin(x1); D2 = c7_Durbin(x2); % calculate Durbin parametersrho1 = 1-D1/2; rho2 =

8、1- D2/2;% calculate correlationtext1 = The value of D1 is ,num2str(D1), and rho1 is ,num2str(rho1),.;text2 = The value of D2 is ,num2str(D2), and rho2 is ,num2str(rho2),.; disp(text1)disp(text2)% End of script file.32c71.CDemo2The value of D1 is 1.9925 and rhol is 0.0037273.The value of D2 is 1.6037

9、 and rho2 is 0.19814.3334 xi+1(16807xi)mod(2147483647) （7-24） ( )cos210000 10000cos210001 10000(725)x ttt35111171mod 30269(726)170mod 30307(727)172mod 30323(728)iiiiiixxyyzz36 mod 1(729)302693030730323iiiixyzu16555425264690(730)a 1330269 30307 303232.7817 10(731)m 37 3839404142(732)XUFX 1(733)XXFU43

10、 Pr(734)XFxXx44 1PrPr(735)XXXFxFUxUFxFx45 exp -( ), 0(736)Xfxx u x1,0( )=(737)0,0 xu xx 0exp -exp(738)xXFxy dyxexp(739)XU 46exp(740)XU 1ln(741)XU 47% File: c7_uni2expclear all% be safen = input(Enter number of points );b = 3;% set pdf parameteru = rand(1,n);% generate Uy_exp = -log(u)/b;% transforma

11、tionN_samp,x = hist(y_exp,20);% get histogram parameterssubplot(2,1,1)bar(x,N_samp,1)% plot histogramylabel(Number of Samples)xlabel(Independent Variable - x)subplot(2,1,2)y = b*exp(-3*x);% calculate pdfdel_x = x(3)-x(2);% determine bin widthp_hist = N_samp/n/del_x;% probability from histogramplot(x

12、,y,k,x,p_hist,ok)% compareylabel(Probability Density)xlabel(Independent Variable - x)legend(true pdf,samples from histogram,1) % End of script file.4800.511.520102030Number of SamplesIndependent Variable - x00.511.520123Probability DensityIndependent Variable - xtrue pdfsamples from histogram4900.51

13、1.522.5305001000Number of SamplesIndependent Variable - x00.511.522.530123Probability DensityIndependent Variable - xtrue pdfsamples from histogram50 222=exp(742)2Rrrfru r 222220=expexp(743)22rRyyrFrdy5122exp(744)2RU22exp(745)2RU22ln(746)RU525302468050010001500Number of SamplesIndependent Variable -

14、 x0246800.20.4Probability DensityIndependent Variable - xtrue pdfsamples from histogram54% File: c7_uni2rayclear all% be safen = input(Enter number of points );varR = 3;% set pdf parameteru = rand(1,n);% generate Uy_exp = sqrt(-2*varR*log(u);% transformationN_samp,r = hist(y_exp,20);% get histogram

15、parameterssubplot(2,1,1)bar(r,N_samp,1)% plot histogramylabel(Number of Samples)xlabel(Independent Variable - x)subplot(2,1,2)term1 = r.*r/2/varR;% exponentray = (r/varR).*exp(-term1);% Rayleigh pdfdel_r = r(3)-r(2);% determine bin widthp_hist = N_samp/n/del_r;% probability from histogramplot(r,ray,

16、k,r,p_hist,ok)% compare resultsylabel(Probability Density)xlabel(Independent Variable - x)legend(true pdf,samples from histogram,1)% End of script file.555611Pr(747)iiiiiiPxxxcxx11( )(748)XiiiFxFcxx1111Pr(749)iiijjFXxP11()(750)XiiiFXUFcXx111(751)iiiXxUFc571(752)iiFUF58 for all(753)XXMgxfx x / ,0(754

17、)0,XbM axaMgxothers59 /max(755)XbM afx 6061 0Pr accepted (756)aXifx dxVab11Pr accepted (757)iVabM62 11111Pr +,accepted Pr );% set Nfx = zeros(1,N);% array of output samplesu1 = rand(1,N); u2 = rand(1,N);% generate u1 and u2v1 = R*u1;% generate v1v2 = (M/R)*rand(1,N);% generate v2 (g(x)kpts = 0;% ini

18、tialize counterfor k=1:N if v2(k)(M/(R*R)*sqrt(R*R-v1(k)*v1(k); kpts=kpts+1;% increment counter fx(kpts)=v1(k); % save output sample endendfx = fx(1:kpts);N_samp,x = hist(fx,20);% get histogram parameterssubplot(2,1,1)bar(x,N_samp,1)% plot histogramylabel(Number of Samples)xlabel(Independent Variabl

19、e - x)subplot(2,1,2)yt = (M/R/R)*sqrt(R*R-x.*x);% calculate pdfdel_x = x(3)-x(2); % determine bin widthp_hist = N_samp/kpts/del_x;% probability from histogramplot(x,yt,k,x,p_hist,ok)% compareylabel(Probability Density)xlabel(Independent Variable - x)legend(true pdf,samples from histogram,3)text = Th

20、e number of points accepted is ,. num2str(kpts,15), and N is ,num2str(N,15),.;disp(text) % End of script file.65024680100200Number of SamplesIndependent Variable - x0246800.10.2Probability DensityIndependent Variable - xtrue pdfsamples from histogram6602468010002000Number of SamplesIndependent Varia

21、ble - x0246800.10.2Probability DensityIndependent Variable - xtrue pdfsamples from histogram6768221( )exp1(761)22xXyxFxdyQ 2exp/2(762)xQ xydy691/2(763)Nii=0YBU -70 1/2(764)Nii=0E YBE U- 2var1/2(765)iUx dx2var(766)NyiiBU 2(767)yNB7172(768)yBN(769)2yNN737475762222222211( , )expexp22221exp(770)22XYxyfx

22、 yxy77222(771)xyr1tan(772)yx,(773)RRXYXYfrdAfx y dA cossin,(774)XYRXYx rRy rdAfrfx y dA78/,/,cossin(775)sincosXYRdx drdx dx ydAdy drdy ddArrr r222,exp,220,02(777)Rrrfrr 79 22222220expexp,2220(778)Rrrrrfrdr 22201exp,22202(779)rrfdr 80cos(780)XR sin(781)YR 2122lncos2(782)XUU 2122lnsin2(783)YUU 81% Fil

23、e: c7_boxmul.mfunction out1,out2=c7_boxmul(N)u1 = rand(1,N);% generate first uniform RVu2 = rand(1,N);% generate second uniform RVray = sqrt(-2*log(u1);% generate Rayleigh RVout1 = ray.*cos(2*pi*u2);% first Gaussian outputout2 = ray.*sin(2*pi*u2);% second Gaussian output% End of function file.828384

24、Pr10.2146(784)circleboxAreject A 858687888921(785)ZXY 222222221211(786)ZEXYE XE XYE Y 2222221(787)Z 902(788)E XZ 22(789)XZXZE XZ 9120/2(790)nsN f 202(791)snfN 2( )( )(792)YXSfH fSf 9293 2( )(793)YSfH fK ( )/(794)YH fSfK 94 10111(795)1nnnnbb zb zH z a za z95 000|(796)/|ffHf Kfff9600.20.40.60.810246Normalized FrequencyMagnitude Response00.20.40.60.810246Normalized FrequencyMagnitude Response97 21/ 1/,|(797)0,ddffffS f others 1/421/,|(798)0,ddffffHf others989900.020.040.060.08-0.500.5TimeImpulse Response-1000-5000500100000.511.5x 10-3FrequencyPSD100-5000500-40-200FrequencyPSD0