fourier analysis - NFourierTransform of an interpolating function

I have an interpolating function called rs22 - a solution from NDSolve - which is defined from 0 to about 1 ms. rs22 is a function that reaches a non-zero equilibrium value. (only shown here up to 10ns)

I would like to perform a Fourier transform on this function. I have written down a line of code to do this but it doesn't work at the moment.

Needs["FourierSeries`"](*Yup I have this in my code, thanks for reminding ;)*)

Plot[NFourierTransform[rs22, t, dw, 
  Method -> {"GlobalAdaptive", Method -> "LevinRule", 
    "SymbolicProcessing" -> 0}], {dw, -1*^9, 1*^9}, PlotRange -> All,
  GridLines -> Automatic]

By definition a Fourier transform integrates from -inf to +inf. Is my interpolating function the problem since it is only defined up to 1ms?

I have also tried using NIntegrate instead but the solution changes with the total integration time which is something I don't want. But then again it seems sensible given the form of the product of the interpolating function and the exponential term: Exp(..)*rs22

xmin = -5*^9; xmax = 5*^9;
dwvec = DeleteCases[Table[dw, {dw, xmin, xmax, (xmax - xmin)/80}]];

output = ParallelTable[
   {Δω = dwvec[[j]]
    , popint = 
     NIntegrate[
      Exp[I Δω t] rs[2, 2], {t, 0, 1*^-3}
      , Method -> {"GlobalAdaptive", Method -> "LevinRule", 
        "SymbolicProcessing" -> 0}]}

   , {j, 1, Length[dwvec]}];

I am at loss as to how to perform this calculation.

Answer

From one of my comments:

You could use Piecewise, something like the Fourier transform of Piecewise[{{r2ss, 0 < t < 10^-9}}, 0], or whatever domain instead of 0 < t < 10^-9 is appropriate.

That is, something like:

NFourierTransform[Piecewise[{{r2ss, 0 < t < 10^-9}}, 0], t, dw, 

  Method -> {"GlobalAdaptive", Method -> "LevinRule", 
    "SymbolicProcessing" -> 0}]