# Intuitions on Kumaresan-Tufts algorithm for exponential fit

I am analyzing a transient signal presumably consisting of superposed exponentials. Such a case is indicated for the Prony analysis, but my data aren't noiseless enough, so I have turned to the Kumaresan-Tufts (KT) algorithm.

After reading the original article (Estimating the Parameters of Exponentially Damped Sinusoids and Pole-Zero Modeling in Noise, 1982) and a bit of googling I made use of the Matlab package Complex Exponential Analysis and more or less things work

My concern is now an intuition on the process - or, better, on its input parameters (cause FFT-like thinking is of course out of question):

• What should I expect of increasing or decreasing of model order?
• How can I assess the number of modes decinig for signal reconstruction and how can I pick them from the output parameters (dampings, frequencies, complex amplitudes)?
• Is there any recommended signal treatment before the KT method is applied? Such as detrending the data for FFT.
• Does time-inverting of the signal providing any help? It would mean damped exponentials instead of growing.
• Several years ago I did research on a different (or at least more current) approach to exponential curve/function fitting/modeling. Although I didn't actually implement it I did see my way clear to using it. I can give some references and after some thought (to make sure my memory is refreshed) some ideas about how it can be used; but it's basically using a specialized form of orthogonal polynomials and decreasing the residual PSD with exponentials as the basis functions. The search term would be Muntz polynomials. – rrogers Aug 23 '17 at 12:39
• Sorry if my last posting seemed off topic but I do think my analysis approach clarifies the questions asked. Even though they were about a different algorithm. The Muntz approach is a lot more signal oriented than others I have seen. Personally, I managed to get Prony to work most of the time. – rrogers Aug 23 '17 at 12:46
• @rrogers, is there an outline of your approach on the web ? Any comments on the methods in 12439-complex-exponential-analysis ? Thanks – denis Oct 6 '17 at 13:23
• I will look at the link. My proposed method is simple: There is an orthogonal set of basis functions for any choice of exponential $a*exp(b*x)$ parameters. We successively choose new basis functions with parameters a_x,b_x so that the new orthogonal vector minimizes the squared values of the previous residuals. The idea is that the optimization is done against the power/square of the new residuals. So the successive residuals are always diminished. The reason for this criterion is that I have run system identification optimization where extra terms did not converge. Which is silly. – rrogers Oct 6 '17 at 15:06