十种概率密度函数.docx

1、十种概率密度函数一十种概率密度函数function zhifangtu(x,m)%画数据的直方图,x表示要画的随机数,m表示所要画的条数%a=min(x);b=max(x);l=length(x);h=(b-a)/m;%量化xx=x/h;x=ceil(x);w=zeros(1,m);for i=1:l for j=1:m if (x(i)=j)%x(i)落在j的区间上，则w(j)加1 w(j)=w(j)+1; else continue end endendw=w/(h*l);z=a:h:(b-h);bar(z,w);title(直方图)function y=junyun(n)%0-1的均匀分

2、布，n代表数据量，一般要大于1024%y=ones(1,n);x=ones(1,n);m=;x0=mod(ceil(m*rand(1,1),m);x0=floor(x0/2);x0=2*x0+1;u=11;x(1)=x0;for i=1:n-1 x(i+1)=u*x(i)+0; x(i+1)=mod(x(i+1),m); x(i)=x(i)/m;end%x(n)单位化x(n)=x(n)/m;y=x;function y=zhishu(m,n)%指数分布,m表示指数分布的参数,m不能为0.n表示数据量,n一般要大于1024%x=junyun(n);for i=1;n if (x(i)=0) x(

3、i)=0.0001; else continue; endend u=log(x);y=-(1/m)*u;function y=ruili(m,n)%瑞利分布,m是瑞利分布的参数,n代表数据量,n一般要大于1024%x=junyun(n);for i=1:n if (x(i)=0) x(i)=0.0001; else continue; endend u=(-2)*log(x);y=m*sqrt(u);function y=weibuer(a,b,n)%韦布尔分布,a,b表示参数,b不能为0.n表示数据量,一般要大于1024%a=1时,是指数分布%a=2时,是瑞利分布%x=junyun(n);

4、for i=1:n if (x(i)=0) x(i)=0.0001; else continue; endendu=-log(x);y=b*u.(1/a);function y=swerling(n)%swelingII分布%r=ones(1,n);u=junyun(n);v=junyun(n);for i=1:n if (u(i)=0) u(i)=0.0001; else continue endendfor i=1:n if (u(i)=v(i) u(i)=u(i)+0.0001 else continue endend t=-2*log(u);h=2*pi*v;x=sqrt(t).*co

5、s(h);z=sqrt(t).*sin(h);y=(r/2).*(x.2+z.2);function y=bernoulli(p,n)%产生数据量为n的贝努利分布,其中p属于(0-1)之间。%-%u=junyun(n);y=zeros(1,n);for i=1:n if(u(i)=p) y(i)=1; else y(i)=0; endendfunction y=duishuzhengtai(a,b,n)%产生对数正态分布，a,b为随机分布的参数，n为数据量%x=gaussian(n);u=sqrt(b)*x+a;y=exp(u);function y=kaifeng(m,n)%产生开丰分布，其

6、中m代表开丰分布的自由度，n表示产生的点数量%y=zeros(1,n);if(floor(m/2)=m/2) for i=1:m/2 x1,x2=gaussian(n); for j=1:n y(j)=x1(j)2+x2(j)2+y(j); end endelse for i=1:floor(m/2) x1,x2=gaussian(n); for j=1:n y(j)=x1(j)2+x2(j)2+y(j); end end x=gaussian(n); for j=1:n y(j)=y(j)+x(j)2; endendfunction y=dajiama(a,b,n)%产生伽马随机分布的数据，

7、a、b为随机分布的参数，数据量为n%k=1;if(a1) while(k1) p=-log(exp(1)+a)/exp(1)-y2)/a); if(x1p(a-1) y(k)=p; k=k+1; else continue; end else p=y2(1/a); if(x1=1) while(k=log(z) y(k)=x; k=k+1; else continue; end endendy=b*y;function y=beitafenbu(a1,a2,n)%产生贝他分布的随机数，其中a1、a2是贝他分布的参数，n代表数据量%x1=dajiama(a1,1,n);x2=dajiama(a2

8、,1,n);y=x1./(x1+x2);function y1,y2=gaussian(n)%产生数据量为n的两个相互独立高斯分布y1、y2%-%k=1;y1=zeros(1,n);y2=zeros(1,n);while(k=1) continue; elseif(s=0) k=k+1; else y1(k)=v1*sqrt(-2*log(s)/s); y2(k)=v2*sqrt(-2*log(s)/s); k=k+1; endendfunction y=canshu(x);y=ones(1,2);n=length(x);y(1)=sum(x)/n;z=x-y(1);z=z.2;y(2)=su

9、m(z)/(n-1);function y=correlation(x)%计算x的自相关函数%n=length(x);for i=1:n x1(i)=x(n+1-i);endy=conv(x,x1);二三种相关杂波function y=gaussianpu(x)%由数据量为n的高斯白噪声产生向量为n，功率谱为高斯型的高斯随机向量%N=0:20;f=20;T=1/256;c=2*f*T*sqrt(pi)*exp(-4*f2*pi2*T2*N.2);n=length(x);y=zeros(1,n);for k=1:n for i=20:-1:0 if (k-i)=0) continue; else

10、 y(k)=y(k)+c(21-i)*x(k-i); end end for i=20:40 if (k-i)=0) continue; else y(k)=y(k)+c(i-19)*x(k-i); end endendy=0.5*y;function y=weibuerpu(a,b,n)%由数据量为n的高斯白噪声产生向量为n，功率谱为高斯型的韦布尔分布的随机向量% z1,z2=gaussian(n);z1=5*z1;z2=5*z2;y1=sqrt(ba/2)*z1;y2=sqrt(ba/2)*z2;x1=gaussianpu(y1);x2=gaussianpu(y2);x1=sqrt(ba/

11、2)*x1;x2=sqrt(ba/2)*x2;y=x1.2+x2.2;b=canshu(y);y=y-b(1);function y=duishuzhengtaipu(a,b,n)%由数据量为n的高斯白噪声产生向量为n，功率谱为高斯型的对数正态随机向量%a表示标准方差,b表示均值%z1=gaussian(n);x=gaussianpu(z1);y=a*x;y=exp(y);y=b*y;b=canshu(y);y=y-b(1); %去掉直流分量function y=swerling2pu(n)%由数据量为n的高斯白噪声产生向量为n，功率谱为高斯型的斯维凌II型随机向量%r=6;z1,z2=gau

12、ssian(n);x1=gaussianpu(z1);x2=gaussianpu(z2);y=x1.2+x2.2;y=r*y;b=canshu(y);y=y-b(1); %去掉直流分量function y=kexipu(m,n)%由数据量为n的高斯白噪声产生向量为n，功率谱为柯西谱的高斯随机向量wc=2*pi*256;T0=1/(256*m);x=gaussian(n);y=zeros(1,n);y(1)=wc*T0*x(1);for i=2:n y(i)=wc*T0*x(i)+exp(-wc*T0)*y(i-1);endb=canshu(y);%y=y-b(1); %去掉直流分量y=conv

13、(y,y);y=fft(y);y=abs(y);i=1:2*n-1;plot(i,y)function plotpu(x)%绘出随机数的功率谱密度函数频域的图形。%w=fft(x);w=abs(w);v=2*pi/length(w);i=0:v:(2*pi-v);plot(i,w);三.雷达系统仿真function t,s,g,f0,fs,f1=huibo%产生目标回波信号x,系统噪声y，地物杂波z以及回波p%f0=3*107; %发射信号频率w=0; %发射信号初始相位c=3*108; %光速l=c/f0; %雷达信号波长(载波波长)R=40000; %目标范围Vd=200; %雷达与目标之

14、间的径向速度fd=2*Vd/l; %多普勒频率Tr=600/f0; %脉冲重复周期N=10; %雷达脉冲串长度f1=f0/5; %调频带宽是发射信号频率的1/5k=10*f1/Tr;fs=3*f0; %仿真采样频率Ts=1/fs;%Tt=2*R/c;Btar=4*pi*R/l; %M=floor(Tr*fs); %一个脉冲重复周期内的采样点数M=600mt1=floor(2*Tr*fs/5);%mt1=720mt2=floor(3*Tr*fs/10);%mt2=540mt3=floor(7*Tr*fs/10);%mt3=1260mt4=floor(3*Tr*fs/5);%mt4=1080mt5

15、=mt1-mt2;%mt5=180Vgain=6;s=zeros(M,N); %回波幅度起伏 for m=1:M for n=1:N v(m,n)=(u(mt1-m)-u(mt2-m)*Vgain*cos(2*pi*f0*(m-mt2)*Ts+2*pi*k*Ts*(m-mt2)/2*(m-mt2)*Ts+2*pi*fd*n*Tr); g(m,n)=(u(mt3-m)-u(mt4-m)*Vgain*cos(2*pi*(f0*(m-mt4)*Ts+k*Ts*(m-mt4)/2*(m-mt4)*Ts); %u(t)是发射信号包络 endendfor i=1:M/10 t(i)=Vgain*cos(2

16、*pi*(k*Ts*(M/10-i)/2*(M/10-i)*Ts);endfor n=1:N y(1:M,n)=gaussian(M); %系统噪声服从高斯分布endfor n=1:N z(1:M,n)=swerling2pu(M); %地物杂波服从swerling2型分布ends=v+g+y+z;%s=v+g;m,n=size(s);x=zeros(1,m*n);q=zeros(1,m*n);x=s(:);q=g(:);p=x;i=0:length(p)-1;subplot(2,1,1);plot(i,x),title(目标回波信号); %目标回波信号xsubplot(2,1,2); l=c

17、anshu(x);b=x-l(1);plotpu(b),title(目标回波频谱); function y=gaofang(s,f0,fs,f1)%高频放大器%M,N=size(s);Vgain=3; %高放增益w1=(f0-4*f1/3)*2*pi/fs; %w1=26pi/45w3=(f0-f1/3)*2*pi/fs; %w3=29pi/45w2=(f0+7*f1/3)*2*pi/fs; %w2=37pi/45w4=(f0+4*f1/3)*2*pi/fs; %w4=34pi/45th=min(w3-w1),(w2-w4);%w3-w1=pi/15,w2-w4=pi/15M1=ceil(6.

18、6*pi/th)+1; %M1=99%n=0:M1-1;w5=(w1+w3)/2;w6=(w4+w2)/2;%w5=11pi/18,w6=71pi/90h=wide(w6,M1)-wide(w5,M1);w=(hamming(M1);h=h.*w;L=length(h);s=Vgain*s;z=zeros(M+L-1,N);y=zeros(M,N);K=ceil(L/2);for i=1:N for j=1:10 z(1+(j-1)*M/10:j*M/10+L-1,i)=conv(h,s(1+(j-1)*M/10:j*M/10,i); y(1+(j-1)*M/10:j*M/10,i)=z(1+

19、(j-1)*M/10+K:j*M/10+K,i); endendw=y(:);subplot(3,1,1);i=0:length(w)-1;plot(i,w),title(高放);subplot(3,1,2);plotpu(w),title(频谱);subplot(3,1,3);plotpu(h),title(幅频特性);function y=hunpin(s,f0,fs,f1)%进行混频，输出为中频信号%M,N=size(s);i=0:M-1;z1=cos(2*pi*2*f0*i/3/fs);y1=zeros(M,N);for i=1:N y1(1:M,i)=(z1.*s(1:M,i);en

20、dw1=(f0-5*f1)*2*pi/(3*fs);%w1=pi/9w3=(f0-2*f1)*2*pi/(3*fs);%w3=1.6pi/9w2=(f0+8*f1)*2*pi/(3*fs);%w2=0.4piw4=(f0+5*f1)*2*pi/(3*fs);%w4=pi/3th=min(w3-w1),(w2-w4); %w3-w1=0.2pi/3,w2-w4=0.2pi/3M1=ceil(6.6*pi/th)+1; %M1=99%n=0:M1-1;w5=(w1+w3)/2;w6=(w4+w2)/2;%w5=1.3pi/9,w6=1.1pi/3h=wide(w6,M1)-wide(w5,M1);

21、wth=(hamming(M1);h=h.*wth;L=length(h);z=zeros(M+L-1,N);y=zeros(M,N);K=ceil(L/2);for i=1:N for j=1:10 z(1+(j-1)*M/10:j*M/10+L-1,i)=conv(h,s(1+(j-1)*M/10:j*M/10,i); y(1+(j-1)*M/10:j*M/10,i)=z(1+(j-1)*M/10+K:j*M/10+K,i); endendw=y(:);v=y1(:);subplot(4,1,1);i=0:length(w)-1;plot(i,w),title(混频);subplot(4,

22、1,2);plotpu(v),title(频谱);subplot(4,1,3);plotpu(w);subplot(4,1,4);plotpu(h),title(幅频特性); function y=zhongfang(s,f0,fs,f1)%中频放大器%M,N=size(s);Vgain=5; %中放增益w1=(f0-5*f1)*2*pi/(3*fs);%w1=pi/9w3=(f0-2*f1)*2*pi/(3*fs);%w3=1.6pi/9w2=(f0+8*f1)*2*pi/(3*fs);%w2=0.4piw4=(f0+5*f1)*2*pi/(3*fs);%w4=pi/3th=min(w3-w

23、1),(w2-w4); %w3-w1=0.2pi/3,w2-w4=0.2pi/3M1=ceil(6.6*pi/th)+1; %M1=99%n=0:M1-1;w5=(w1+w3)/2;w6=(w4+w2)/2;%w5=1.3pi/9,w6=1.1pi/3h=wide(w6,M1)-wide(w5,M1);w=(hamming(M1);h=h.*w;L=length(h);s=Vgain*s;z=zeros(M+L-1,N);y=zeros(M,N);K=ceil(L/2);for i=1:N for j=1:10 z(1+(j-1)*M/10:j*M/10+L-1,i)=conv(h,s(1+(

24、j-1)*M/10:j*M/10,i); y(1+(j-1)*M/10:j*M/10,i)=z(1+(j-1)*M/10+K:j*M/10+K,i); endendw=y(:);subplot(3,1,1);i=0:length(w)-1;plot(i,w),title(中放);subplot(3,1,2);plotpu(w),title(频谱);subplot(3,1,3);plotpu(h),title(幅频特性);function I,Q=xiangganjianbo(s,fs,f0,f1)%相位相干检波%M,N=size(s);i=0:M-1;z1=cos(2*pi*f0*i/(3*f