- #1

- 27

- 3

## Homework Statement

Find [tex] R(\tau) [/tex] if a) [tex]S(\omega) = \frac{1}{(4+\omega^2)^2} [/tex]

## Homework Equations

I have given [tex] \frac{4}{4+\omega^2} [/tex] <==> [tex] e^{-2|\tau|} [/tex]

## The Attempt at a Solution

So [tex] S(\omega) = \frac{1}{(4+\omega^2)^2}=

\frac{1}{16}\frac{4}{(4+\omega^2)}\frac{4}{(4+\omega^2)} [/tex]

[tex] R(\tau)= \frac{1}{16} e^{-2|\tau|} * e^{-2|\tau|} [/tex]

Where * is convolution

So

[tex] R(\Tau) = \frac {1}{8}\int_{0}^{\infty} e^{-2(\tau-\alpha)} e^{-2\alpha} d\alpha [/tex]

But that turns out to be infinite. Does anyone have any idea where I went wrong?

Last edited: