Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Mathematica: Fourier Transform by hand of sin

  1. Jan 20, 2012 #1

    i do not understand why i can find the FT of sin in mathematica using the built in function but not by integrating, even thoiugh they should be the same:

    Integrate[Exp[i(ω-ω0) t,{t, -∞, ∞}, Assumptions ->ω0 el Reals && ω el Reals]

    but the statment
    FourierTransform[Sin[ω0 x], x, ω]
    gives me the answer in dirac deltas
    I Sqrt[\[Pi]/2] DiracDelta[ω - ω0] - I Sqrt[\[Pi]/2] DiracDelta[ω + ω0]

    also i would be interested if you could explain to me from what condition the root 2pi appears before the FT, and how we can normalize plane waves to dirac Deltas.

    Thanks a lot!!!
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted

Similar Threads for Mathematica Fourier Transform
Mathematica Storing Mathematica output
Mathematica Mathematica to MATLAB
Mathematica Cannot do the integral of the Hyper-geometric function?
Mathematica Cannot Plot This Function in Mathematica
Mathematica While Loop in Mathematica