Engineering How to find the impulse function?

AI Thread Summary
To find the impulse function from the given frequency response H(ω), the user has transformed H(ω) into a form involving Z(ω), which simplifies the analysis. The proposed impulse response h[n] is expressed as a combination of Z[-n] and Z[n]. However, the user is uncertain about calculating the discrete convolutions necessary to derive h[n]. Suggestions include transforming specific terms and summing them, although the user finds this approach ineffective. Further clarification on discrete convolution techniques is needed for accurate computation.
billtodd
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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!
 
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Transform 1 and -e^2i##\omega## each and sum them up. It does not work?
 
It's ok, thanks!
 
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