十种概率密度函数Word下载.docx
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十种概率密度函数Word下载.docx
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x
(1)=x0;
n-1
x(i+1)=u*x(i)+0;
x(i+1)=mod(x(i+1),m);
x(i)=x(i)/m;
%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;
continue;
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
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
else
u=-log(x);
y=b*u.^(1/a);
functiony=swerling(n)
%swelingII分布
%%%%%%%%%%%%%%%%%%%%%%
r=ones(1,n);
u=junyun(n);
v=junyun(n);
if(u(i)==0)
u(i)=0.0001;
if(u(i)==v(i))
u(i)=u(i)+0.0001
elsecontinue
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。
%-----------------------
%
y=zeros(1,n);
if(u(i)<
=p)
y(i)=1;
y(i)=0;
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
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if(floor(m/2)==m/2)
fori=1:
m/2
[x1,x2]=gaussian(n);
y(j)=x1(j)^2+x2(j)^2+y(j);
else
floor(m/2)
x=gaussian(n);
y(j)=y(j)+x(j)^2;
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>
p=-log(((exp
(1)+a)/exp
(1)-y2)/a);
if(x1<
p^(a-1))
y(k)=p;
k=k+1;
p=y2^(1/a);
exp(-p))
elseif(a>
=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;
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
%---------------------------------------
y1=zeros(1,n);
y2=zeros(1,n);
while(k<
u1=junyun
(1);
u2=junyun
(1);
v1=2*u1-1;
v2=2*u2-1;
s=v1^2+v2^2;
if(s>
elseif(s==0)
y1(k)=v1*sqrt(-2*log(s)/s);
y2(k)=v2*sqrt(-2*log(s)/s);
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
%%%%%%%%%%%%%%%%%%%%%%%%%
x1(i)=x(n+1-i);
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);
fork=1:
fori=20:
-1:
if((k-i)<
=0)
y(k)=y(k)+c(21-i)*x(k-i);
40
y(k)=y(k)+c(i-19)*x(k-i);
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);
%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=r*y;
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);
y
(1)=wc*T0*x
(1);
fori=2:
y(i)=wc*T0*x(i)+exp(-wc*T0)*y(i-1);
%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
M/10
t(i)=Vgain*cos(2*pi*(k*Ts*(M/10-i)/2*(M/10-i)*Ts));
forn=1:
y(1:
M,n)=gaussian(M)'
;
%系统噪声服从高斯分布
z(1:
M,n)=swerling2pu(M)'
%地物杂波服从swerling2型分布
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;
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);
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);
w=y(:
subplot(3,1,1);
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-1;
z1=cos(2*pi*2*f0*i/3/fs);
y1=zeros(M,N);
y1(1:
M,i)=(z1.*s(1:
M,i)'
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
%w3-w1=0.2pi/3,w2-w4=0.2pi/3
%w5=1.3pi/9,w6=1.1pi/3
wth=(hamming(M1))'
h=h.*wth;
v=y1(:
subplot(4,1,1);
混频'
subplot(4,1,2);
plotpu(v),title('
subplot(4,1,3);
plotpu(w);
subplot(4,1,4);
functiony=zhongfang(s,f0,fs,f1)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%中频放大器
Vgain=5;
%中放增益
中放'
function[I,Q]=xiangganjianbo(s,fs,f0,f1)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%相位相干检波
z1=cos(2*pi*f0*i/
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