Register to reply

Sum of signal and its probability density

by Chriszz
Tags: pdf, sum of variables
Share this thread:
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.
Phys.Org News Partner Mathematics news on
Professor quantifies how 'one thing leads to another'
Team announces construction of a formal computer-verified proof of the Kepler conjecture
Iranian is first woman to win 'Nobel Prize of maths' (Update)
Sep15-13, 10:42 PM
Sci Advisor
HW Helper
PF Gold
jbunniii's Avatar
P: 3,288
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:
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 ?

Register to reply

Related Discussions
Power Spectral Density - how can I get a link back to the original signal Classical Physics 3
Probability density/Radial Probability density Quantum Physics 0
Probability of Signal getting through. General Math 26
Probability of (not) distinguish signal Precalculus Mathematics Homework 1
What's the difference between probability and probability density Quantum Physics 5