% program ex_15_3.m to generate data for  model selection
% programmed by B.Joseph Dec 27, 2000
%
% first generate data
%
% we will use a prbs signal on a known system to generate data
% a first order system with g(s)=1/(s+1) is considered
%
clear

close;echo on;clc;

sys=tf([1],[1   1])
% convert to discrete time 
sysd=c2d(sys,.1)
% get prbs input signal covering freq from .1 to 10
% prbs is a matalb mfile that generates sequences of 
% random pulses
% see chapter 16 for a description
clc;
echo on;

u=prbs(.5,10,.1,1);u=[u;u];
t=0:.1:length(u)*.1-.1; % this computes the time sequence
% obtain response of system
%
[y,t]=lsim(sysd,u);

% add some noise to the data
% divide the data into two parts one for testing 
len=fix(length(y)/2);
 u1=u(1:len);y1=y(1:len);ut=u(len+1:2*len);yt=y(len+1:2*len);
y1=y1+randn(length(y1),1)*0.1;
;
save ch15ex3.mat