Convolution integral

Can someone explain convolution to me. I have read three different books and gone to office hours and am not getting the fundamentals.
 

quasar987

Science Advisor
Homework Helper
Gold Member
4,774
4
In what context? Do you mean you don't understand some of the "applications"?
 
I'm trying to understand in the context of probability distributions. What the convolution of the sum of two random variables represents.
 

quasar987

Science Advisor
Homework Helper
Gold Member
4,774
4
Oh.

I never really took time to ponder about this. The way it was presented to me was that the convolution appeared kind of coincidentally:

We set out to find the density f of Z=X+Y by finding it's repartition function F and then differentiating it. So we proceed from definition

[tex]F_{Z}(z)=P(X+Y<z)=\int_{-\infty}^{+\infty}\int_{-\infty}^{z-y}f_X(x)f)Y(y)dxdy=\int_{-\infty}^{+\infty}F_X(z-y)f_Y(y)dy[/tex]

This is the convolution [itex]F_X[/itex] and [itex]f_Y[/itex]. The density of Z is found simply by differentiating [itex]F_Z[/itex] wrt z and it gives the convolution of [itex]f_X[/itex] and [itex]f_Y[/itex].


There is probably a way to understand something from this and gain some insights about the relation btw the sum of two random variables.

Let me know if you find something interesting.
 

The Physics Forums Way

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top