Hi everyone, this is my first time posting and I hope that its in the righ
place and not violating any rules. I have already tried searching abou
this topic on this website but I was unsuccessful in finding what I wa
seeking for.

This is for my independent study and my goals are to prove tw
relationships.
1. Prove that the Fourier Series (FS) gives the same results as th
Continuous-Time Fourier Transform (CTFT). Using the FS's coefficient
along with the X(jw) of the CTFT.

From my research, I know that we have to use the Dirc Comb and convolve i
with the FS, but from there I'm just lost


2. Prove that the Discrete-Time Fourier Transform is the same as CTFT.

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 kno
what theorem to use to prove this relationship.

So can someone help me out or guide me to the right direction?

Thanks!