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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.