gngauss.m

高斯白噪声的算法源代码

function[gsrv1,gsrv2]=gngauss(m,sgma)
%  高斯随机变量1,高斯随机变量2,发生器generate
%   I was asked to realize the gaussian distribution,which may be generated by the matlab function randn,normrnd...... 
%   but it is still necessary to know how to realize it just by uniform random numbers in (0,1). 
%   here is a way.for simplicity I suppose sigma=1 and u=0,the standard normal distribution. 

%   we should know that we can not give the analystic equation of the probabilty distrbution function of  gaussian distribution. 
%   but we know that R(x)=1-exp(-x^2/(2*sigma^2)) when x>=0 and R(x)=0 when x<0.R(x) is the probability distribution function of relay distribution. 

%   and the gaussian distribution has the following relationship: 
%  c=x*cos(theta) 
%  d=x*sin(theta) 
%  where c,d are two gaussian variables,x is the variable in the former function. 
%  theta is the random variable in the uniform distribution of(0,2*pi). 
%  if we have R(x)=A,A is uniformly distributed in (0,1) 
%  then x= sqrt(2*sigma^2*ln(1/1-A)). 
%  and another variable B uniformly distributed in (0,1),suppose 
%  theta=2*pi*B 
%  then we have two statically independent gaussian random variables c ,d . 
%  if you want to have more variables,just to make A ,B vectors. 
%  the realization: 

%  m=0; sgma=1; 
%  N=1000; 
%  u=rand(1,N); 
%  %  z=sgma*(sqrt(2*log(1./(1-u)))); 
%  u=rand(1,N); 
%  gsrv2=m+z.*sin(2*pi*u); 
%  gsrv1=m+z.*cos(2*pi*u); 
%  g=[gsrv1,gsrv2]; 
%  hist(g); 

%  if the gaussian distribution is not standard, just to change m and sigma.



if nargin==0,
	m=0;sgma=1;
elseif nargin==1,
	sgma=m;m=0;
end;

u=rand;
z=sgma*(sqrt(2*log(1/(1-u))));
u=rand;
gsrv1=m+z*cos(2*pi*u);
gsrv2=m+z*sin(2*pi*u);