Monday, September 25, 2017

Prony Method

Given N equispaced data-points \(F_i = F(t = i \Delta t)\), where \(i = 0, 1, ..., N-1\), the Prony method can be used to fit a sum of m decaying exponenitals: \[F(t) = \sum_{i=1}^{m} a_i e^{b_i t}. \] The 2m unknowns are \(a_i\) and \(b_i\).

In the Prony method, the number of modes in the exponential (m) is pre-specified. There are other methods, which are more general.

Here is a python subprogram which implements the Prony method.
If you have arrays t and F, it can be called as:

a_est, b_est = prony(t, F, m)