On 3 Mrz., 22:31, "dr3amr2" <dnguy...@du.edu> wrote:
> Hi everyone, this is my first time posting and I hope that its in the right
> place and not violating any rules. *I have already tried searching about
> this topic on this website but I was unsuccessful in finding what I was
> seeking for. *
>
> This is for my independent study and my goals are to prove two
> relationships.
> 1. *Prove that the Fourier Series (FS) gives the same results as the
> Continuous-Time Fourier Transform (CTFT). *

You won't find such a proof.

> Using the FS's coefficients
> along with the X(jw) of the CTFT.
>
> From my research, I know that we have to use the Dirc Comb and convolve it
> with the FS, but from there I'm just lost
>
> 2. *Prove that the Discrete-Time Fourier Transform is the same as CTFT. *

Another proof you wont find.

>
> The relation between DTFT and CTFT in sampling is X(e^jwTs) =
> X(e^jw)|w=wTs = (1/Ts)(sumation)Xc(j(w-((2*pi*k)/Ts))). *I just don't know
> what theorem to use to prove this relationship. *
>
> So can someone help me out or guide me to the right direction? *

What exactly do you want to do?

Regards,
Andor