Fourier Transform of a shifted & scaled rectangular pulse I'm trying to find the Fourier Transform of the following rectangular pulse:

$$ x(t) = rect(t - 1/2) $$

This is simply a rectangular pulse stretching from 0 to 1 with an amplitude of 1. It is 0 elsewhere. I tried using the definition of the Fourier Tranform:

$$ X(\omega) = \int_0^1 (1)*e^{-j\omega*t}dt $$

However carrying out the relatively simple integration and subbing in the bounds results for me in this:

$$ X(\omega) = \frac{1}{j\omega}[e^{-j\omega} - 1] $$

&amp; unfortunately wolfram alpha has a different answer when I use it to compute this fourier transform. It's got the sinc function;
I'd appreciate any help on this, if I've got some giant conceptual error. I have an exam on this stuff in a bit less than a week :/

Edit: also realized I used j; it's the same with i (the imaginary #)
They are equal to each other. Rewrite it using the following:

$$
( e^{-j\omega} - 1 ) = e^{-j\omega/2}( e^{-j\omega/2} - e^{j\omega/2} ).
$$
You are doing a little mistake buddy, the Fourier transform of shifted rectangular function (given as ques) will be,
$X(w)=\frac1{-jw}\left(e^{-jw} - 1\right)$. Then solve.