Fourier Series Transform Proof Help

[evotunedscc]

Can someone fill in the blank between these two steps? I can't find Fourier series proof anywhere and my professor just left it out.

(1) y(t+nT)=y(t)

(2) y(t)=$$A_{0}$$ + $$\Sigma^{\infty}_{n=1}$$[$$A_{n}$$cos(n$$\omega$$t) + $$B_{n}$$sin(n$$\omega$$t)]

(The omega is going crazy on me... it's not supposed to be superscripted, just multiplied by n and t)

 

[HallsofIvy]

Can someone fill in the blank between these two steps? I can't find Fourier series proof anywhere and my professor just left it out.

(1) y(t+nT)=y(t)

(2) y(t)=$$A_{0}$$ + $$\Sigma^{\infty}_{n=1}$$[$$A_{n}$$cos(n$$\omega$$t) + $$B_{n}$$sin(n$$\omega$$t)]

(The omega is going crazy on me... it's not supposed to be superscripted, just multiplied by n and t)

What do you mean by "steps between them"? The first just says y is periodic with period T and the second is the general expression of a Fourier series of a function periodic with period $2\pi/\omega$- there is no mention of "T".

As for the LaTex, I would recommend putting the entire thing in [ t e x] not just individual parts:

$$y(t)=A_{0}+ \Sigma^{\infty}_{n=1}[A_{n}cos(n\omega t) + B_{n}sin(n\omega t)]$$

It looks better and is easier to type!

 

[dhris]

I would say that a general "Fourier expansion" is actually an integral. What (1) implies is that the modes are discrete and thus the integral becomes a sum, and therefore $\omega=2 \pi/T$, as Halls mentioned. Maybe this is the missing step you mean?

 

[Nima-k2]

have u find the gap between those two statements[evotunedscc]?