# Sum of signal and its probability density

• Chriszz
In summary, the pdf of signal S depends on the joint distribution of S1 and S2. If they are statistically independent, then the pdf of S is the convolution of the pdfs of aS1 and bS2. In the special case where S1 and S2 are similar, there may be other special relations or equations.
Chriszz
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 ?

Thanks.

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 ?

## What is the sum of signal and its probability density?

The sum of signal and its probability density refers to the mathematical concept of adding the values of a signal (such as a sound wave or an electrical current) and its probability density function. This sum can give insight into the behavior and characteristics of the signal.

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

The sum of signal and its probability density is typically calculated using integration, which involves finding the area under the probability density curve. This area represents the total probability of the signal occurring within a specific range of values.

## Why is the sum of signal and its probability density important in science?

The sum of signal and its probability density is important because it allows scientists to analyze and understand the behavior of signals in a quantitative way. This can help in fields such as physics, engineering, and statistics, where the characteristics of signals are crucial.

## What does a high sum of signal and probability density indicate?

A high sum of signal and probability density indicates that the signal is more likely to occur within a certain range of values, as the area under the probability density curve will be larger. This can give insight into the strength or intensity of the signal.

## How does the sum of signal and its probability density relate to uncertainty?

The sum of signal and its probability density can give information about the uncertainty of the signal, as a wider or more spread out probability density curve indicates a higher level of uncertainty. This can be useful in determining the accuracy and reliability of the signal's measurements.

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