%Generate the x values:
x=0:.25:10;
x2=0:.01:10;

%generate normal errors for the x values.
err=.25*randn(1,length(x));

%Find the mean function for the data
z=sin(2*x).*exp(-.2.*x);

%Simulate the observed data by adding noise
y=z+err;
z=sin(2*x2).*exp(-.2.*x2);

%plot the real function
plot(x2,z,'k-')
hold on
plot(x,y,'bo')
hold off

%There are 41 values for x, so we can fit a 40 order polynomial to the
%data.
polFit=polyfit(x,y,40);
%Then find the values of the fit over the values of: 

y_poly=polyval(polFit,x2);

%Then the fit onto the plot
plot(x2,z,'k-')
hold on
plot(x,y,'r.')

plot(x2,y_poly,'b-')
hold off;

%Open our data set
 U = load('data1');
t = U.trace_x';
disp = U.trace_y(4,:);
N = length(t);
time = t;
[maxd,index] = max(disp);   % do some truncation to eliminate the data before the maximum
time = time(index:N)-time(index);
disp = disp(index:N);
disp = disp';
disp = disp - mean(disp);
d_data = disp;
plot(time, disp,'b.');
xlabel('t');
ylabel('y(t)');

polFit=polyfit(time,disp,150);
%Then find the values of the fit over the values of: 

y_poly=polyval(polFit,time);

%Then the fit onto the plot
plot(time,disp,'k.',time,y_poly,'b-');
xlabel('t');
ylabel('y(t)');