# What are the advantages of recursive prony?

Suppose I have following signal:

fs = 20;     % Sampling rate [Hz]
Ts = 1/fs;     % Sampling period [s]
duration = 25; % Duration [sec]
t = 0: Ts : duration-Ts; % Time vector
ss1 = (160.74*exp(-0.15*t)).*cos((2*pi*0.5*t));  %signal 1%
ss4 = zeros(1,length(t));  %signal 2%
tz = 0: Ts : 12-Ts;
for i = 1:length(tz)
ss4(i) = 30.54*exp(-0.25*tz(i)).*cos((2*pi*4*tz(i)));
end

xp = ss1+ss4;


My window length is of 10 second. In first 10 second, it has 200 samples and it calculates two frequency i.e. 4 Hz and 2 Hz. In recursive estimation this continues till 240 samples and from 241st sample onward frequency calculation deviates due to mixed samples. For example if one will choose his current window as 41:241 (200 samples or 10 sec) data point then frequency estimation comes out to be .5001 and 4.001 Hz and second value keep on increasing while it should decrease actually. All is happening because of mixed sampling points. Some of them are double frequency components while some are single one as one proceeds. I want to know what was the real motive behind recursive Prony? If someone needs Prony code please mention. I hope u are aware of this.

• Wikipedia - Prony's method Prony analysis (Prony's method) was developed by Gaspard Riche de Prony in 1795. However, practical use of the method awaited the digital computer.[1] Similar to the Fourier transform, Prony's method extracts valuable information from a uniformly sampled signal and builds a series of damped complex exponentials or sinusoids. This allows for the estimation of frequency, amplitude, phase and damping components of a signal. – Russell McMahon Feb 17 '14 at 14:23