There are two common definitions of inverse Fourier transform depending on how the frequency variable is interpreted. (See https://en.wikipedia.org/wiki/Fourier_transform#Other_conventions) The stackexchange post is using the angular frequency ω that differs by the factor 2π from frequency variable assumed by SymPy. The transforms are also differently normalized. That may explain the differing results.
Kalevi Suominen On Tuesday, April 10, 2018 at 9:16:57 AM UTC+3, Janko Slavič wrote: > > I am trying to replicate this: > > https://math.stackexchange.com/questions/2280196/inverse-fourier-transform-of-a-partial-fraction-decomposition > with sympy. > > With Mathematica I get just the same behavior as the above theory suggest. > > With sympy I it looks wrong. At t<0, I get the result close to the correct > one for t>0. (I was not able to include all the assumptions in sympy). > > Here is the sympy code: > > import sympy as sym > sym.init_printing() > ω = sym.symbols('omega', real=True, positive=True) > R, λ = sym.symbols('R, lambda', complex=True) > t = sym.symbols('t', real=True, positive=True) > α = R/(sym.I*ω-λ)+sym.conjugate(R)/(sym.I*ω-sym.conjugate(λ)) > α > sym.inverse_fourier_transform(α, ω, -t) > > > and the Mathematica: > > a = InverseFourierTransform[ R/(I omega - lambda) + Conjugate[R]/(I omega > - Conjugate[lambda]), omega, t, > FourierParameters -> {1, -1}] > Simplify[a, {Re[lambda] < 0, t > 0}] > > Is the sympy result really wrong? > -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to sympy+unsubscr...@googlegroups.com. To post to this group, send email to sympy@googlegroups.com. Visit this group at https://groups.google.com/group/sympy. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/119a93ac-a193-49e6-92cf-6872ca99b2cc%40googlegroups.com. For more options, visit https://groups.google.com/d/optout.
