1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Fourier transform of rectangular pulse (Waves)

  1. May 9, 2009 #1
    1. The problem statement, all variables and given/known data

    F(w) is the Fourier transform of f(t). Write down the equation for F(w) in terms of f(t).
    A rectangular pulse has height H and total length t0 in time. Show that as a function of w, the amplitude density is propertional to sinc(wt0/2).

    2. Relevant equations

    F(w) = integral from -infinity to +infinity of: f(t)exp(-iwt)dw

    3. The attempt at a solution

    integral from -t0/2 to +t0/2 of: h*exp(-iwt)dw

    I have access to the solution to this problem, which says that it should be:
    integral from -t0/2 to +t0/2 of: h*exp(-iwt)dt,
    but I don't understand why I'm integrating wrt t now, when the definition says w.

    Could somebody please explain this?

    Thanks in advance.
  2. jcsd
  3. May 9, 2009 #2


    User Avatar
    Homework Helper

    Where do you get that definition from? Think about it, you want to find a function [itex]F(\omega)[/itex], but if you calculate the integral you've written down as the "definition" then the integration boundaries will be inserted into [itex]\omega[/itex] after the integration. As as a result you won't have a function with variable [itex]\omega[/itex].

    The correct definition is (normalization conventions can be different):
    F(\omega)}=\int_{-\infty}^\infty e^{-i \omega t} dt
  4. May 9, 2009 #3
    Actually I got that definition from the solution to the question. It makes a whole lot more sense now, thanks for your reply!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook