Extracting multiple envelopes from a signal

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I have a signal which when observed carefully shows a three individual sinusoidal signals (figures attached). I want these three individual signals to be extracted in terms of amplitude, frequency and phase. Please help!

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Accepted Answer

Cedric Wannaz
Cedric Wannaz on 17 Oct 2017
Quick cheap trick gets 2/3. Was going to bed, no time for more but that could be a starting point.
function main
load( 'MultipleSignalEnvelope', 'ITDc0' ) ;
plot( ITDc0, 'b.' ) ;
grid on ;
hold on ;
t = 1 : numel( ITDc0 ) ;
A = 1.2 ;
P = fminsearch( @objective, zeros(3,1) ) ;
plot( A*sin((t+P)/360*2*pi).' ) ;
function mindif = objective( P )
mindif = sum( min( abs( ITDc0-A*sin((t+P)./360*2*pi )))) ;
Cedric Wannaz
Cedric Wannaz on 20 Oct 2017
Edited: Cedric Wannaz on 20 Oct 2017
You will have to try. Define P as a vector with 6 components instead of 3, the first three being amplitudes and the next three being "phases". In the objective function, replace A with P(1:3) and P with P(4:6). Also, update the initial conditions. Instead of zeros(3,1), try to start e.g.. with three unit amplitudes and three null phases: [ones(3,1);zeros(3,1)].
Note that you could use FMINCON and define constraints, e.g. upper and lower bounds for the amplitude and phases.
Also note that you'd better try to see if you could get help from someone with experience in digital signal processing, because this approach is just a quick trick. If you reword your question in a new thread and nobody answers, you may be able to hire someone for not that much on sites that market freelancers.

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More Answers (1)

Image Analyst
Image Analyst on 11 Aug 2017
Edited: Image Analyst on 11 Aug 2017
Look at the fft.
First Last
First Last on 17 Oct 2017
I am sorry, I miss understood your earlier comments. It should be autonomous.

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