How to find the impulse function?

[billtodd]

Homework Statement

I found the impulse function in the frequency space to be: $H(\omega)=1-\exp(2i\omega )$, and I want to find its $h[n]$.

Relevant Equations

Fourier analysis.

So I have: $H(\omega)=(\exp(-i\omega)-\exp(i\omega))\exp(i\omega)$, I denote by $Z(\omega)=\exp(i\omega)$, to get: $H(\omega)=Z(-\omega)Z(\omega)-Z(\omega)^2$, now, I want to find $h[n]$, I think it should be: $h[n]=z[-n]*z[n]+z[n]*z[n]$.

But I am not sure how to calculate the discrete convolutions, any help?

Thnaks!

 

[anuttarasammyak]

Transform 1 and -e^2i$\omega$ each and sum them up. It does not work?

 

[billtodd]

It's ok, thanks!