Sum of signal and its probability density

by Chriszz
Tags: pdf, sum of variables
Chriszz is offline
Sep15-13, 08:32 PM
P: 10

I assume that a signal S is expressed as S = a*S1 + b*S2,
where a, b are weight constant, and S1, S2 are the different signals.

In addition, S1, S2 have similar distribution such as Gaussian or Laplacian distribution,
and theirs pdf is p_S1 and p_S2.

In the above assumption, what is the pdf of signal S ?
How can I derive or reference of this pdf p_S ???

Please help me.
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jbunniii is offline
Sep15-13, 10:42 PM
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In general, the answer depends upon the joint distribution of ##S_1## and ##S_2##. If they are statistically independent, then the answer is much simpler: the pdf of ##S## is the convolution of the pdfs of ##aS_1## and ##bS_2##. For a proof, see here for example:
Chriszz is offline
Sep16-13, 02:39 AM
P: 10
Thank you for your reply.
In addition, I have additional question. In the special case, if these two signals are similar (almost same), is there other special relation or equation ?

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