# Sum of signal and its probability density (special case )

## Main Question or Discussion Point

Dear,

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 ???

As I known, the pdf of S is the convolution of pdfs of S_1 and S_2.

However, in the special case, if these two signals are similar (almost same), is there other special relation or equation ?

Please help me.
Thanks.

## Answers and Replies

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Mentor
The convolution of two Gaussians is another Gaussian. I don't know of nice formulas for a Laplace distribution.