- #1
aimforclarity
- 33
- 0
Hi,
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 statement
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!
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 statement
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!