Code covered by the BSD License

# MATLAB for Digital Communication

by

### Won Yang (view profile)

The MATLAB programs in "MATLAB/Simulink for Digital Communication" authored by Won Y. Yang et. al

dc02e05.m
```%dc02e05.m: Statistical Property of White Noises
% the autocorrelation and distribution (histogram) of a white noise
clear, clf
Nb=8; %number of samples per bit time interval
M=5000; N=M*Nb; % Sample size
Tb=1; dt=Tb/Nb; % Bit time interval and sampling interval
xlim=10; xx=-xlim:0.02:xlim;
NB=40; % Number of bins
randn('state',0); %return randn() to its default initial state
w=randn(1,N)/sqrt(dt); % divide by sqrt(dt) so that integral(w^2(t))dt=1
for i=1:2
if i==1
sigma2= w*w'/N % phiw(0)=integral(w^2(t))dt/(N*dt)
sgm2=1/dt; f=exp(-xx.^2/2/sgm2)/sqrt(2*pi*sgm2);
nn=[-N/2:N/2]; tt=nn*dt; nnt=nn+N+1;
else
w=cos(2*pi*[0:Nb-1]/Nb)*reshape(w,Nb,M)*sqrt(2/Tb)*dt; %Eq.(E2.5.1)
sigma2= w*w'/M % phiw[0]=sum(w^2(n))*Tb/(M*Tb)
f=exp(-xx.^2/2)/sqrt(2*pi);
nn=[-M/2:M/2]; tt=nn*Tb; nnt=nn+M+1;
end
phiw=xcorr(w,'u');
subplot(219+2*i), plot(tt,phiw(nnt))
idx=find(abs(w)<=xlim);
w1=w(idx); N1=length(w1);
subplot(220+2*i)
[ns,cs]=hist(w1,NB);
dx=cs(2)-cs(1);
hist(w1,NB), hold on, plot(xx,N1*f*dx,'r')
% plot(xx,f*dx,'r',cs,ns/N1,':')
end
```