The Fast Multiplication

x=11234;
  y=52342;
  X=Reverse[IntegerDigits[x]];
  Y=Reverse[IntegerDigits[y]];
  n=Length[X]+Length[Y]+1;
  X=PadRight[X,n];
  Y=PadRight[Y,n];
  U=InverseFourier[X];
  V=InverseFourier[Y];
  Q=Round[Re[Fourier[U*V]*Sqrt[n]]];
  Sum[Q[[k]] 10^(k-1),{k,n}]
 x*y

The inverse Fourier Transform

f=Sum[X[[k]] t^(k-1),{k,Length[X]}]; 
N[Table[f /. t->Exp[-I 2Pi k/n],{k,0,n-1}]]/Sqrt[n]

Chop[InverseFourier[X]]

The Fourier Transform

MyFourier[s_]:=Module[{n=Length[s]},
   (Table[Exp[I 2Pi k l/n],{k,0,n-1},{l,0,n-1}]/Sqrt[n]).s];
MyFourier[{3,4,5,23,24,2}] //N

Chop[Fourier[{3,4,5,23,24,2}]]