Sum of signal and its probability density (special case )

In summary, the conversation discusses the expression of a signal S as a weighted combination of two signals S1 and S2, with similar distributions. The question is raised about the pdf of S and its relationship to the pdfs of S1 and S2. It is mentioned that in the case of similar signals, the convolution of their pdfs results in another Gaussian. However, there is no known formula for the case of a Laplace distribution.
  • #1
Chriszz
11
0
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.
 
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  • #2
The convolution of two Gaussians is another Gaussian. I don't know of nice formulas for a Laplace distribution.
 

1. What is the sum of signal and its probability density in the context of science?

The sum of signal and its probability density refers to a mathematical calculation that combines the values of a signal with the likelihood of those values occurring. In other words, it is a way to quantify the likelihood of a particular signal or event occurring.

2. How is the sum of signal and its probability density calculated?

The sum of signal and its probability density is calculated by multiplying the value of the signal by its probability density function (PDF) and then adding up all of these products. This is represented by the formula: ∑(signal * PDF).

3. What is the special case of the sum of signal and its probability density?

The special case of the sum of signal and its probability density refers to situations where the signal is a continuous function and the probability density function is a continuous probability distribution. This allows for the use of integration to calculate the sum, rather than discrete summation.

4. What does the sum of signal and its probability density tell us about a system?

The sum of signal and its probability density provides insight into the behavior and characteristics of a system. It can help us understand the likelihood of specific events occurring and can be used to make predictions about future outcomes.

5. How is the concept of sum of signal and its probability density applied in scientific research?

The sum of signal and its probability density is a fundamental concept in statistics and is widely used in scientific research. It is particularly useful in fields such as physics, engineering, and biology, where researchers need to analyze and interpret data from experiments and observations.

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