- #1

thomas49th

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## Homework Statement

From the definition of the Fourier transform, find the Fourier transform of rect(t-5).

## Homework Equations

[tex]G(w) = \int^{\infty}_{-\infty}g(t)e^{jwt}dt[/tex]

## The Attempt at a Solution

So, I sketched the function which has area 1 and centre at 5, with its lower bound @ 4.5 and upper at 5.5. SOOOO cannot I not just write

[tex]G(w) = \int^{5.5}_{4.5}1e^{jwt}dt[/tex]

for it's Fourier transform? Is that allowed. I know the rect function some how turns into sinc, but in this case how?

I can prove with limits -a and +a but when you have 2 positive or 2 negative limits you don't get the sin(-ax) = -sin(ax) which keeps the sine and gets rid of the cosine!

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