- #1

CoolDude420

- 201

- 9

## Homework Statement

Hi,

So we started sampling/sampling theorem, dirac delta, DTFT in a digital signal processing module and I'm kinda confused. I understand how to derive the following formulae but these two formulae are so different to each other that I don't understand why?

We are first told that the spectrum of the sampled signal is,

I completely understand where this comes from (the whole dirac delta part/sifting property and FT property). Okay all makes sense now. Then we are introduced to the DTFT and again I understand the derivation but the result is really different,

Now, how can these two things be equal to each other? I mean in both cases, we were deriving the frequency spectrum of the sampled signal. Why are the answers so different?