This program uses the Prony method to fit data to F(t) = \sum_{i=1}^{m} a_i e^{b_i t}.

prony.py

def prony(t, F, m):
  """Input  : real arrays t, F of the same size (ti, Fi)
            : integer m - the number of modes in the exponential fit
     Output : arrays a and b such that F(t) ~ sum ai exp(bi*t)"""

	import numpy as np
	import numpy.polynomial.polynomial as poly

	# Solve LLS problem in step 1
	# Amat is (N-m)*m and bmat is N-m*1
	N    = len(t)
	Amat = np.zeros((N-m, m))
	bmat = F[m:N]

	for jcol in range(m):
		Amat[:, jcol] = F[m-jcol-1:N-1-jcol]
		
	sol = np.linalg.lstsq(Amat, bmat)
	d = sol[0]

	# Solve the roots of the polynomial in step 2
	# first, form the polynomial coefficients
	c = np.zeros(m+1)
	c[m] = 1.
	for i in range(1,m+1):
		c[m-i] = -d[i-1]

	u = poly.polyroots(c)
	b_est = np.log(u)/(t[1] - t[0])

	# Set up LLS problem to find the "a"s in step 3
	Amat = np.zeros((N, m))
	bmat = F

	for irow in range(N):
		Amat[irow, :] = u**irow
		
	sol = np.linalg.lstsq(Amat, bmat)
	a_est = sol[0]

	return a_est, b_est

Dear Sachin Shanbhag,
Thank you for providing such prony method code... I am very interested in applying such code with different applications... Could you help me with a simple example to explain how to use this function for non linear data regression?...
Thanks & Best Regards

Hi @shane5ul ,
Thank you for providing simple prony method code. I am using it for analysis for power system small signal analysis.
Thanks

@sentry