restart; u:=t->piecewise(t<0,0,1):f:=unapply(exp(-t/5)*u(t),t);cv:=1/sqrt(2*Pi): FT[f]:=inttrans[fourier](cv*f(t),t,w); assume(w,real):R:=unapply(Re(FT[f]),w);C:=unapply(Im(FT[f]),w); Mag:=unapply(simplify(sqrt(R(w)^2+C(w)^2)),w); Phase:=unapply(arctan(C(w)/R(w)),w); plot(f(x),x=-10..10);plot(Phase(w),w=-10..10);plot(Mag(w),w=-10..10); inttrans[invfourier](Mag(w)/cv,w,x); MagInv:=unapply(%,x); plot(MagInv(x),x=-10..10); # Not a replica of f(x)! # Answer check. inttrans[invfourier](Mag(w)*exp(I*Phase(w))/cv,w,x);