Convolution of exp(-mod(x))

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  • #1
Unredeemed
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Homework Statement


Prove that the convolution of [itex]e^{-\left|x\right|}[/itex] is [itex](1-x)e^{x}[/itex] for x<0 and [itex](1+x)e^{-x}[/itex] for x>0

Homework Equations





The Attempt at a Solution



I plug through the integral in the standard way and take the limits as x tends to positive and negative infinity etc. But, I keep getting that the convolution is zero?

Any help would be greatly appreciated.
 

Answers and Replies

  • #2
Dick
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Homework Statement


Prove that the convolution of [itex]e^{-\left|x\right|}[/itex] is [itex](1-x)e^{x}[/itex] for x<0 and [itex](1+x)e^{-x}[/itex] for x>0

Homework Equations





The Attempt at a Solution



I plug through the integral in the standard way and take the limits as x tends to positive and negative infinity etc. But, I keep getting that the convolution is zero?

Any help would be greatly appreciated.

You're doing f*f, right? You don't need to take limits in x. You just need to write down the integral and carefully work out what the absolute values are on each interval. Show your work. How did you get 0?
 
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