On Mar 4, 12:39 pm, Andor <andor.bari...@gmail.com> wrote:
> 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.
>

this is essentially the sampling theorem. the CTFT transforms from
one domain (let's call it the "time domain") to a reciprocal domain
(the "frequency domain"). when you sample uniformly in one domain,
that has the effect of copying, shifting, and overlap-adding in the
other domain.

i've posted a reasonably good proof of it (if you can accept the
Neanderthal engineering understanding of the dirac impulse function)
but it has found it's way to Wikipedia

http://en.wikipedia.org/wiki/Nyquist...or_the_theorem

before they kicked me out.

r b-j