# Is my solution to the DTFT of a delta function correct?

I am newer to signal processing math and just figured out something cool (hopefully). I was trying to see how the DTFT of the delta function is 1, because thats what my book says. I could only find youtube tutorials that didnt really explain it mathmatically, so i tried to do it on my own. Is my process correct? See pic.

Thanks!

-Dom

• That's correct. For any sequence $f[n]$ you have $\delta[n-k]f[n]=\delta[n-k]f[k]$, so the sum $\sum_n\delta[n-k]f[n]$ always equals $f[k]$. – Matt L. Jul 10 at 6:18

You are absolutely correct. For more cool, calculate the DTFT of $$\delta \left(n - k \right)$$.