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Decomposition of a biexponential signal

Posted 11 years ago
Is there a way to decompose a biexponential decay curve into two seperate monoexponentials?
4 Replies
Are you looking to fit some data to a statistical model that is a biexponential decay curve? When you say you have a curve, what exactly do you have? Do you have a function, or a set of data points?
POSTED BY: Sean Clarke
Hi,

As Sean correctly pointed out, if you know the model and want to find model parameters for it, then FindFit[] is for you.
Here is an example:
 (* test function *)
 
 f[x_] := 5. Exp[-0.98 x] + 3. Exp[-1.34 x];
 (* plot it *)
 Plot[f[x], {x, 0, 3}, PlotRange -> All]
 (* data *)
 data = Table[{x, f[x]}, {x, 0, 3, 0.01}];
 (* find fit *)
 FindFit[data, a Exp[b x] + d Exp[c x], {a, b, c, d}, x]

I.M.
POSTED BY: Ivan Morozov
Hi, Thank you for replying,
I have a set of data points (y) that I want to fit using an already known biexponential decay curve of the form: y = x1*exp(-a*z1) + x2*exp(-a*z2), where a is a vector of known values. What I would like to get is values x1, x2, z1, z2 for every y value.
Katerina
Hi, Katerina,

I'm afraid getting system parameters for each data point from a set is not possible, and such problem is not well defined.
In fact, all statistical features are best described by mean and deviation (if you assume that parameters are normally distributed).
For example, least square method or SVD can be used to find distribution params.

I.M.
POSTED BY: Ivan Morozov
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