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!