Curve-fitting part of a data set

Hello. I have an array of data which looks like this. http://s12.postimg.org/7ja47a6b1/temp.jpg

I need to use the polyfit command to determine the best fitting exponential for the time roughly between 1.7 and 2.25. I'm given the equation Temp(t) = Temp0 * exp(-(t-t0)/tau), where t0 is the time corresponding to temperature Temp0 (I can select where to begin my curve-fitting, but it is confined to the area roughly between 1.7 and 2.3). Here is my attempt.

%'time' vector ranges from 1.5 to 2.5
p = polyfit(time, log(Temp), 1);

%Arbitrary starting point
t0 = 1.71;

tau = -1./p(1)
Temp0 = exp(p(2))

tp = 1.7:0.01:2.3;

Temp_t = Temp0*exp(-(tm-t0)/tau);
plot(time, Temp, tp, Temp_t)

My curve ends up looking like this http://s7.postimg.org/igces77pn/temp2.jpg What am I doing incorrectly? How can I align the curve-fit line and the data points. I am told that circshift may help, but I couldn't grasp the function of the command after reading the help file. Any help would be greatly appreciated. Thank you!

Answer 1

[David Sanchez]

If I am not wrong, you are doing this:

% tau = -1./p(1)
% Temp0 = exp(p(2))
% Temp_t = Temp0*exp(-(tm-t0)/tau);          % -> 
% Temp_t = exp(p(2))*exp((tm-t0)*p(1));      % ->
Temp_t = exp( p(2)+(tm-t0)*p(1) );

Instead, I think you should just grab your Temp amd time data in your region of interest (1.7 to 2.3) taking care on grabbing an Temp/time array with the same length than your tp array. Then:

p = polyfit(time, Temp, 1);
Temp_p = p(1)*tp + p(2);
plot(time, Temp, tp, Temp_t)