Fourier series expansion using the Curve Fitting Tool

I have some very perplexing results I obtained using the Curve Fitting Tool which I am having difficulty interpreting and reconciling the results. This is the 1st time I used this tool so I hope someone with some experience can assist me with the results I obtained. I am using MATLAB 2012b.

I used the code below to generate a pressure profile vs time. The time vector & the P results I have attached in the Pdata.mat file.

A=1; p=A*(1-time/0.01).*exp(-time/0.01);

I used the code generation wizard within the Curve Fitting Tool to generate the m-file that is attached. Within that m-file the following initial guess at the Fourier series coefficients:

opts.StartPoint = [7.1054e-15 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 12.5664];

I then executed the FIT operation & the results for Fourier series coefficients are in the .txt file. I then copied those results & pasted them into MATLABcurvefit.m to check the results. I got nothing that resembled what is in Pdata.mat. Despite this discrepancy the Curve Fitting Tool generated fitted curve depicted in curve fit results.jpg. The fit depicted here is EXCELLENT!

So I am completely BAFFLED. How does the Curve Fitting Tool show excellent results, yet when I used the results from the .txt file in MATLABcurvefit.m the results are dreadful?

Really would appreciate an explanation.

[Jeff]

OK, so I need more significant figures? How do I get the Curve Fit Tool to output the results with more sig figs?

Answer 1

[John D'Errico]

Almost always when someone complains of exactly this problem, it is because they did not in fact use the correct coefficients. Instead, they copied 4 significant digits, pasted them in. But MATLAB did not estimate 5 digits. So what did you do?

Here are the coefficients from the text file, exactly as you said.

       a0 =   2.589e+07  (1.61e+07, 3.567e+07)
       a1 =  -2.918e+07  (-4.097e+07, -1.739e+07)
       b1 =  -3.622e+07  (-4.928e+07, -2.317e+07)
       a2 =  -7.159e+06  (-8.454e+06, -5.865e+06)
       b2 =   3.284e+07  (2.019e+07, 4.55e+07)
       a3 =    1.73e+07  (1.139e+07, 2.321e+07)
       b3 =  -8.643e+06  (-1.298e+07, -4.311e+06)
       a4 =  -7.895e+06  (-1.112e+07, -4.667e+06)
       b4 =  -3.616e+06  (-4.282e+06, -2.951e+06)
       a5 =   7.232e+05  (1.553e+05, 1.291e+06)
       b5 =   2.853e+06  (1.888e+06, 3.819e+06)
       a6 =   4.273e+05  (3.462e+05, 5.083e+05)
       b6 =  -5.679e+05  (-8.266e+05, -3.092e+05)
       a7 =  -1.092e+05  (-1.471e+05, -7.122e+04)
       b7 =        3528  (-1.4e+04, 2.105e+04)
       a8 =        5249  (2399, 8099)
       b8 =        6116  (4905, 7326)
       w =       3.406  (3.325, 3.488)

Then look at what you did...

a0=2.589e+07;
a1=-2.918e+07;
b1=-3.622e+07;
a2=-7.159e+06;
b2=3.284e+07;
...

And, exactly as I said, you used 4 digit approximations to a list of numbers. That is a BAD idea. It is assured to result in crapola. What did you get? Yep. Crapola.

The point is, you did not in fact use the results. You used a poor approximation to the results, and you got a poor result. SURPRISE!

[Jeff]

OK, so I need more significant figures? How do I get the Curve Fit Tool to output the results with more sig figs?

[John D'Errico]

NEVER just copy numbers out of the command window and then try to use them. NEVER. This is not a question of getting the curve fitting toolbox to report more digits.

Instead, learn how to extract the coefficients. Use them as numbers. Don't use copy and paste.

F = fit(rand(10,1),rand(10,1),'poly1')
F = 
     Linear model Poly1:
     F(x) = p1*x + p2
     Coefficients (with 95% confidence bounds):
       p1 =     0.02812  (-1.131, 1.187)
       p2 =       0.516  (-0.1666, 1.199)

C = coeffvalues(F)
C =
     0.028123      0.51602

As you see here, those coefficients have many more significant digits.

format long g
C
C =
        0.0281228534598042         0.516020244723809

[Jeff]

OK, you are doing this in the command window. I was using the Curve Fitting Tool GUI. I cannot seem to find where or how to adjust the format of the output results for the coefficients. Have you worked with that GUI & know how to adjust the format?

[Jeff]

Thank you for your assistance. It works. The one thing that bothers me is that P vs t curve is less than unity. I am a bit miffed that the coefficients for the Fourier components are so HUGE, on the order of 10^7. This concerns me on a sensitivity issue. Nonetheless, this does work.

THANKS