Below is a script using matlab m-file to decompose the small signal oscillation mode parameter by using prony analysis. The goal is to achieve the frequency and damping ratio of simulated damped sinusoidal signal. Using this simple script (which prony toolbox is available in matlab) one can utilize for another damped sinusoidal data to get the same parameter.
% Using prony analysis to identify small signal oscillation mode parameter
clear all
close all
fs=56;
ts=1/fs;
t=(0:113)*ts;
y=exp(-0.1.*t).*cos(2*pi*7.*t)+(1/4)*exp(-0.25.*t).*cos(2*pi*70.*t+pi/8);
plot(t,y)
xlabel(‘Time (s)’)
ylabel(‘y(t)’)
% prony
NB=4; NA=4;
[b,a6] = prony(y,NB,NA); % Prony Analysis
p = roots(a6);
p = log(p);
reig= real(p)/ts; % imaginer
ieig= imag(p)/ts; % real
freq=abs(ieig/(2*pi)); % Frequency Oscillation
dr=-reig./(sqrt(reig.^2+ieig.^2)); % Damping Ratio
Figure 1. Simulated Damped Sinusoidal Signal, y(t)