f[i] = Table[(sin[i*0.01])^2, {i, 100}]

g[w] = Fourier[f[i]]

g[ω] = {FourierSinTransform[Exp[-t]*Sin[5*t], t, ω], 
        FourierCosTransform[Exp[-t]*Sin[5*t], t, ω]}

G[ω] = Abs[g[ω]]