Fit exponential decay functions
Marquardt-Levenberg fitting to exponential functions
"Fit exponential decay functions" performs a nonlinear fitting of the given signal to a sum of two exponential functions of the form
by using nonlinear Marquardt-Levenberg optimization. It is necessary to give starting values that can either be fitted or held fixed.
If at least one parameter is to be fitted, the progress of the fitting can be observed in the Dataplore ® message window, where the current estimations of the parameters are displayed.
The signal returned from this function corresponds to the fitting function with parameters that give the best fit for the input singal.
This function takes either one or two signals as input; if two signals are given, the second one is used as a weighting function consisting of the individual standard deviations of the input signal samples. Note that both signals must be equal in size, scale and shift.
Otherwise, if a single signal is given, all signal samples are weighted equally.
Parameters of "Fit exponential decay functions" are
- the offset, corresponding to
- a flag denoting if the offset is to be fitted (1) or to be held fixed (0)
- the first coefficient a
- a flag denoting if a is to be fitted (1) or to be held fixed (0)
- the second coefficient b
- a flag denoting if b is to be fitted (1) or to be held fixed(0)
- the first time constant tau1
- a flag denoting if tau1 is to be fitted (1) or to be held fixed (0)
- the second time constant tau2
- a flag denoting if tau2 is to be fitted (1) or to be held fixed (0).
If fitting flags are omitted, Dataplore ® defaults to fit(1) the corresponding values.
In order to achieve satisfying fitting results, try to give start parameters that are not too far away from the expected resulting values. To that end, you can try to successively fit single parameters while holding fixed other parameters whose estimations already seem to be good enough.
y = ExpDecFit(x,offset,a,aflag,b,bflag,tau1,tau1flag,tau2,tau2flag);
y = ExpDecFit([x,weight],offset,a,aflag,b,bflag,tau1,tau1flag,tau2,tau2flag);
Note that x can be a standard or an XY plot signal.
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