十种概率密度函数.docx
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十种概率密度函数.docx
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十种概率密度函数
一十种概率密度函数
functionzhifangtu(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x
x=x/h;
x=ceil(x);
w=zeros(1,m);
fori=1:
l
forj=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
end
end
w=w/(h*l);
z=a:
h:
(b-h);
bar(z,w);
title('直方图')
functiony=junyun(n)
%0-1的均匀分布,n代表数据量,一般要大于1024
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
y=ones(1,n);
x=ones(1,n);
m=100000;
x0=mod(ceil(m*rand(1,1)),m);
x0=floor(x0/2);
x0=2*x0+1;
u=11;
x
(1)=x0;
fori=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;
functiony=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);
fori=1;n
if(x(i)==0)
x(i)=0.0001;
else
continue;
end
end
u=log(x);
y=-(1/m)*u;
functiony=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);
fori=1:
n
if(x(i)==0)
x(i)=0.0001;
else
continue;
end
end
u=(-2)*log(x);
y=m*sqrt(u);
functiony=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);
fori=1:
n
if(x(i)==0)
x(i)=0.0001;
else
continue;
end
end
u=-log(x);
y=b*u.^(1/a);
functiony=swerling(n)
%swelingII分布
%%%%%%%%%%%%%%%%%%%%%%
r=ones(1,n);
u=junyun(n);
v=junyun(n);
fori=1:
n
if(u(i)==0)
u(i)=0.0001;
else
continue
end
end
fori=1:
n
if(u(i)==v(i))
u(i)=u(i)+0.0001
elsecontinue
end
end
t=-2*log(u);
h=2*pi*v;
x=sqrt(t).*cos(h);
z=sqrt(t).*sin(h);
y=(r/2).*(x.^2+z.^2);
functiony=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);
fori=1:
n
if(u(i)<=p)
y(i)=1;
else
y(i)=0;
end
end
functiony=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);
functiony=kaifeng(m,n)
%产生开丰分布,其中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)
fori=1:
m/2
[x1,x2]=gaussian(n);
forj=1:
n
y(j)=x1(j)^2+x2(j)^2+y(j);
end
end
else
fori=1:
floor(m/2)
[x1,x2]=gaussian(n);
forj=1:
n
y(j)=x1(j)^2+x2(j)^2+y(j);
end
end
x=gaussian(n);
forj=1:
n
y(j)=y(j)+x(j)^2;
end
end
functiony=dajiama(a,b,n)
%产生伽马随机分布的数据,a、b为随机分布的参数,数据量为n
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
k=1;
if(a<1)
while(k<=n)
x1=junyun
(1);
x2=junyun
(1);
y2=(exp
(1)+a)/exp
(1)*x2;
if(y2>1)
p=-log(((exp
(1)+a)/exp
(1)-y2)/a);
if(x1
y(k)=p;
k=k+1;
else
continue;
end
else
p=y2^(1/a);
if(x1 y(k)=p; k=k+1; else continue; end end end elseif(a>=1) while(k<=n) x1=junyun (1); x2=junyun (1); v=(2*a-1)^(-0.5)*log(x1/(1-x2)); x=a*exp(v); z=x1^2*x2; w=a-log(4)+(a+sqrt(2*a-1))*v-x; if(w>=log(z)) y(k)=x; k=k+1; else continue; end end end y=b*y; functiony=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(a2,1,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<=n) u1=junyun (1); u2=junyun (1); v1=2*u1-1; v2=2*u2-1; s=v1^2+v2^2; if(s>=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; end end functiony=canshu(x); y=ones(1,2); n=length(x); y (1)=sum(x)/n; z=x-y (1); z=z.^2; y (2)=sum(z)/(n-1); functiony=correlation(x) %计算x的自相关函数 %%%%%%%%%%%%%%%%%%%%%%%%% n=length(x); fori=1: n x1(i)=x(n+1-i); end y=conv(x,x1); 二.三种相关杂波 functiony=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*f^2*pi^2*T^2*N.^2); n=length(x); y=zeros(1,n); fork=1: n fori=20: -1: 0 if((k-i)<=0) continue; else y(k)=y(k)+c(21-i)*x(k-i); end end fori=20: 40 if((k-i)<=0) continue; else y(k)=y(k)+c(i-19)*x(k-i); end end end y=0.5*y; functiony=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(b^a/2)*z1; y2=sqrt(b^a/2)*z2; x1=gaussianpu(y1); x2=gaussianpu(y2); x1=sqrt(b^a/2)*x1; x2=sqrt(b^a/2)*x2; y=x1.^2+x2.^2; b=canshu(y); y=y-b (1); functiony=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 functiony=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]=gaussian(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 functiony=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); fori=2: n y(i)=wc*T0*x(i)+exp(-wc*T0)*y(i-1); end b=canshu(y); %y=y-b (1); %去掉直流分量 y=conv(y,y); y=fft(y); y=abs(y); i=1: 2*n-1; plot(i,y) functionplotpu(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*10^7;%发射信号频率 w=0;%发射信号初始相位 c=3*10^8;%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1/5 k=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=600 mt1=floor(2*Tr*fs/5);%mt1=720 mt2=floor(3*Tr*fs/10);%mt2=540 mt3=floor(7*Tr*fs/10);%mt3=1260 mt4=floor(3*Tr*fs/5);%mt4=1080 mt5=mt1-mt2;%mt5=180 Vgain=6; s=zeros(M,N);%回波幅度起伏 form=1: M forn=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 end end fori=1: M/10 t(i)=Vgain*cos(2*pi*(k*Ts*(M/10-i)/2*(M/10-i)*Ts)); end forn=1: N y(1: M,n)=gaussian(M)';%系统噪声服从高斯分布 end forn=1: N z(1: M,n)=swerling2pu(M)';%地物杂波服从swerling2型分布 end s=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x subplot(2,1,2); l=canshu(x); b=x-l (1); plotpu(b),title('目标回波频谱'); functiony=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/45 w3=(f0-f1/3)*2*pi/fs;%w3=29pi/45 w2=(f0+7*f1/3)*2*pi/fs;%w2=37pi/45 w4=(f0+4*f1/3)*2*pi/fs;%w4=34pi/45 th=min((w3-w1),(w2-w4));%w3-w1=pi/15,w2-w4=pi/15 M1=ceil(6.6*pi/th)+1;%M1=99 %n=[0: M1-1]; w5=(w1+w3)/2;w6=(w4+w2)/2;%w5=11pi/18,w6=71pi/90 h=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); fori=1: N forj=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); end end w=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'); functiony=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); fori=1: N y1(1: M,i)=(z1.*s(1: M,i)')'; end w1=(f0-5*f1)*2*pi/(3*fs);%w1=pi/9 w3=(f0-2*f1)*2*pi/(3*fs);%w3=1.6pi/9 w2=(f0+8*f1)*2*pi/(3*fs);%w2=0.4pi w4=(f0+5*f1)*2*pi/(3*fs);%w4=pi/3 th=min((w3-w1),(w2-w4));%w3-w1=0.2pi/3,w2-w4=0.2pi/3 M1=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/3 h=wide(w6,M1)-wide(w5,M1); wth=(hamming(M1))'; h=h.*wth; L=length(h); z=zeros(M+L-1,N); y=zeros(M,N); K=ceil(L/2); fori=1: N forj=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); end end w=y(: )'; v=y1(: )'; subplot(4,1,1); i=0: length(w)-1; plot(i,w),title('混频'); subplot(4,1,2); plotpu(v),title('频谱'); subplot(4,1,3); plotpu(w); subplot(4,1,4); plotpu(h),title('幅频特性'); functiony=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/9 w3=(f0-2*f1)*2*pi/(3*fs);%w3=1.6pi/9 w2=(f0+8*f1)*2*pi/(3*fs);%w2=0.4pi w4=(f0+5*f1)*2*pi/(3*fs);%w4=pi/3 th=min((w3-w1),(w2-w4));%w3-w1=0.2pi/3,w2-w4=0.2pi/3 M1=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/3 h=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); fori=1: N forj=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); end end w=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/
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