Have you gone through any published stuff related to your work ?

Dear Anurag,

I would consider the use of Prony analysis to estimate parameters of a signal represented as a sum of damped complex exponentials or sinusoids.

http://www.engr.uconn.edu/~sas03013/docs/PronyAnalysis.pdf

WEGELIN, Frederico A. ; MAGALHÃES, Robson ; Almeida, L.A.L. ; FONTANA, M. . Condition Monitoring of Power Transformers Using Acoustic Signal Prony's Analysis. In: Instrumentation and Measurement Technology Conference, 2005, Ottawa. Proceedings of the Instrumentation and Measurement Technology Conference, 2005.

Start with the time constant of the exponential envelope and the frequency spectrum of the signal. For finding the envelope, please remember that the magnitude of the analytic signal is the envelope of the original signal (see properties of the Hilbert transform). Please see the following Matlab script:

t = 0:1e-4:1;

x = [1+cos(2*pi*25*t)].*cos(2*pi*100*t);

clf;

y = hilbert(x);       % y is the analytic signal

plot(t,x,'b')         % plot original signal in blue

xlabel('Seconds')

hold on

plot(t,imag(y),'g')   % plot Hilbert transform part in green

legend('Original','Hilbert')

X=[0,1];

Y=[0,0];

plot(X,Y)             % plot the x axis

%plot(t,[-1;1]*abs(y),'r','LineWidth',2)      % Both +ve and -ve envelopes

plot(t,abs(y),'r','LineWidth',2)  % Plot only +ve envelope

xlim([0 0.1])                                   % plot just part of it

xlabel('Seconds')

title('The absolute value of the Analytic Signal is the envelope; the zero crossings of the HT are the peaks', 'FontSize',16);

Best of luck ;-)

I didn't mean to use it directly.

I said "start with..."

Best of luck  

:-)

I have been working with the signals for a few days now and have found the following features to be useful:

1. Max. peak to peak amplitude

2. Peak frequency in signal

3 Total power in signal.

4.Frequency upto which half of the power is contained.

The idea for these features came from the following paper: Bohadana, A. B.; Kraman, S. S., 1992: "Consistency of sternal percussion performed manually and with mechanical thumper".

However, those features did not exploit the exponentially damped nature of the signals. Finding the time constant of the exponential envelope and the frequency spectrum of the signal (as suggested by Fernando Soares Schlindwein) directly did not workout very well probably because the signal is a sum of several exponentially damped sinusoids. Prony Analysis (as suggested by Luiz Ameida) and Matrix Pencil method could be useful in exploiting the exponentially damped nature. I will keep you updated with my findings. :-)

Hi Fernando,

You are right. The method could be implemented after passing the signal through several bandpass filters with cutoff frequencies such that only one prominent frequency lies in the signal in each band. This way the signal should fit better into a EDS model. It is one of the methods I am working on presently and will keep you updated. :-)

Dear Anurag,

See recent paper by S.Ye, E.Aboutanios, An algorithm for the parameter estimation of multiple superimposed exponentials in noise (2015). 

DOI: 10.1109/ICASSP.2015.7178613

For one prevailing frequency you may indeed use Hilbert transform, as suggested Fernando Soares Schlindwein. However, this approach is also not so simple. First, you should strictly adopt Hilbert-twin algorithm to eliminate ripples on the exponential envelope. Then, one may precisely estimate the signal parameters.

To tackle several exponentially damped sinusoids embedded in noise follow the line of thinking suggested by Ye and Aboutanios.

Yours,

Leszek Magalas

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