## 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)