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I have a frequency modulated signal which must contain only $ g(t)=B.\cos(\omega(t).t+\phi)$, but it gets the form as below

$$ f(t)=B.\cos(\omega(t).t+\phi)+A_1.\cos(\omega(t-t_1).t+\phi_1)+A_2.\cos(\omega(t-t_2).t+\phi_2)+...$$ where $$A_k<<B$$ $\omega(t)$ values are limited (for instance, it would get values $950<\omega(t)<1050$)

I am going to extract $g(t)$ from $f(t)$. Any suggestion? Note that all sines are in the same frequency bandwidth, therefore filtering does not work.

thank you for your kind replies, in advance.

Hosein Rahnama
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Kami A
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  • Welcome to MSE. :) There is also a specialized community for signal processing. Take a look at http://dsp.stackexchange.com. Maybe you get better answers there. :) – Hosein Rahnama Nov 26 '15 at 08:08
  • I supposed there is dedicated to dsp (digital signal processing). I would find more helpful answers from mathematicians. thank you :) – Kami A Nov 26 '15 at 08:15
  • I don't know about signal processing but it seems to me that you have a numerical data of $f(t)$ which has some noises and these noises are written as $A_k$ terms. Am I right? :) I am a little confused about what information we have and what we want! Can you add some more details to the question? :) – Hosein Rahnama Nov 26 '15 at 08:30
  • Yes, $A_k$s are time-domain shifted version of $g(t)$ which are disturbing. – Kami A Nov 26 '15 at 08:35
  • So what is known and what is unknown? :) I can't understand that what inputs do you have and what outputs you are looking for! Maybe it is due to my lack of knowledge from SP. :) – Hosein Rahnama Nov 26 '15 at 08:42
  • Indeed, I am going to eliminate or reduce effect of $A_k$ in f(t). supposing $A_1$ has maximum value of $A_k$, then one solution would be $$ f(t)-\frac{A_1}{B}.f(t-t_1)$$ since $B>>A1$, so effect of disturbing $A_1$ will be eliminated, but some other minor terms are added to the final result. I wonder if there is other solution to eliminate or reduce effects of disturbing elements with amplitude of $A_k$ – Kami A Nov 26 '15 at 08:47
  • sorry, $$f(t)-\frac{A_1}{B}.f(t-d)$$ where $$d=\frac{\phi_1}{\omega(t+t_1)t_1+\phi}$$ – Kami A Nov 26 '15 at 09:01
  • f(t) is known, g(t) is unknown – Kami A Nov 26 '15 at 09:08
  • It's not clear if $\phi$ is known, for example. And $w(t)$ – leonbloy Nov 28 '15 at 12:23
  • For a simplified form, suppose $\phi=\phi_k=0$.$ \omega(t) $ is unknown. – Kami A Nov 28 '15 at 14:17

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