# Fourier transform of sinusoidal functions

1. Feb 23, 2014

### asdf12312

1. The problem statement, all variables and given/known data

2. Relevant equations
sinc(x) = $\frac{sin(x)}{x}$

3. The attempt at a solution
bit unsure how to get started?? i know transform of rectangular pulse pτ(t)=τ*sinc(τω/2∏)

also that sin(ωt)= ejωt-e-jωt / (2)

I could also probably sketch sinc(t/2∏), if that helps.

Last edited: Feb 23, 2014
2. Feb 24, 2014

### asdf12312

OK, so I guess I wasn't really thinking. There is duality property listed in my book, can I use that?

since x(t) ⇔ X(ω) then pτ(t)=τ*sinc($\frac{τω}{2\pi}$)

by duality X(t) ⇔ 2$\pi$*x(-ω) then τ*sinc($\frac{τt}{2\pi}$)=2$\pi$pτ(ω)

so for a) it would be 2$\pi$p1(ω). got this right at least? and how would i sketch this. would i be able to swap ω with t and just sketch the rectangular function p1(t) with amplitude 2$\pi$??

Last edited: Feb 24, 2014