% Example 2:
% Create a renewal process and plot its calculated isi distribution
% Also calculate its autocorrelation function.


% First define some parameters
T=500000;
dt=.1;
winrad=20;

% First define a probability mass function (w)
% over a domain (x)
% We normalize w to make it a density
x=0:.1:11;
w=max(0,-(x-6).^2+25);
w=w/sum(w);
w=w/dt;

% Plot this function so that we can compare it to 
% the isi density
subplot(2,2,1);
plot(x,w);
axis([0 max(x)*1.1 0 max(w)*1.1])
xlabel('x');
ylabel('w');

% Now define the renewal process
p=renewal(@()randnum(w,x),T,dt);

% Calculate the isi density
% Note that instead of specifying the
% number of bins for the histogranm we
% specify the actual bin cneters (x)
[h,t]=isi_density(p,x,dt);

% Plot to compare to the (theoretical) density above
subplot(2,2,2);
plot(t,h);
axis([0 max(x)*1.1 0 max(w)*1.1])
xlabel('t')
ylabel('isi density')

% Calculate the auto-correlation function and plot it
% We first delete the delta function spike at the origin
subplot(2,1,2)
[cc11,x]=cross_corr(p,p,winrad,dt);
cc11(winrad/dt+1)=0;
bar(x,cc11)
xlabel('t')
ylabel('autocorrelation')
axis([-winrad winrad min(cc11)*1.1 max(cc11)*1.5])

% Calculate the CV
ccvv=CV(p,dt)