how do I fit a double exponential equation? there are two double exponential waveforms and I need to fit the equation into each waveform

This is how the waveforms look like. I transferred the datas from Excel. The data was obtained using an oscilloscope when I compared the lightning voltage waveforms for with and without an attenuator. Now my job is to fit the double exponential equation into each of these waveforms to compare the difference for the two situations (with and without attenuator).

The double exponential equation for lightining voltage is:

Answer 1

[Walter Roberson]

You can use cftool with a custom equation.

Be warned that sum of exponential are notoriously difficult to fit. If your initial values are not quite close to the best values then it is quite common for the fitting coefficients to be very different from the best coefficients.

[Siti Fatimah Mohamed Hisham]

Hello. Thank you so much for your response! And you are right, the fit isn't very perfect, but I'll take what I can get. Thank you.

[Walter Roberson]

No no no. Look at the ranges on the coefficients. They cross 0 pretty much mirror. The fitting cannot decide between negative and positive coefficients. The fits are the same on both sides to within tolerance, in the region tested.

In such cases it is often the case that there *is* a distinctly preferred fitting but that the catch basin for it is narrow and not found by the fitting function.

But in your case when you fit you did not put in any bounds so b and d can trade places which adds to the mess.

[Siti Fatimah Mohamed Hisham]

oh. how should/do I put the bounds so to obtain better fitting?

[Walter Roberson]

Click on Fit Options to enter upper and lower bounds. You will not be able to directly code to ensure that d>b. However you can rewrite d as b+doffset and set the lower bound on doffset to 0.