I have been trying to obtain the Fourier transform for time domain root-raised-cosine pulse using Mathematica. The answer I'm getting from Mathematica is not the correct answer. When I input the frequency domain response of the RRC pulse and take the inverse Fourier transform, I don't get the correct answer. Can someone please explain this? I'm trying to get the correct answer as a sanity check before getting modified pulse shapes. The code I have used is given below.
FourierTransform[ (4*a*t*Cos[((1 + a)*Pi*t)/Ts] + Ts*Sin[((1 - a)*Pi*t)/Ts])/ (Pi*t*(Ts^(-1))^(3/2)*(-16*a^2*t^2 + Ts^2)), t, ω ]