(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Computer the Fourier transform of U(t), where U(t) = 1 for |t| < 1, and U(t) = 0 for |t| > 1.

2. Relevant equations

Fourier Transform: F(w) = ∫U(t)e^{-iwt}dt (bounds: ∞, -∞)

3. The attempt at a solution

If |t| < 1, obviously F(w) = 0.

If |t| > 1,

F(w) = (-1/wt)*[cos(-wt) + i sin(-wt)] |^{∞}- (-1/wt)*[cos(-wt) + i sin(-wt)] |^{-∞}.

How do I evaluate that? Obviously lim_{t-->∞}cos(-wt) and lim_{t-->∞}sin(-wt) don't exist. Or am I missing something important?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Easy Fourier Transform

**Physics Forums | Science Articles, Homework Help, Discussion**