This can easily be verified by substituting the definition of the DFT into the IDFT definition, changing the summation index of the DFT from *n* to *m* to avoid name capture problems (*n* is a dummy variable, so can be changed freely without altering the value of the expression):

The inner summation above is zero for all *m*<>*n*, and equal to *N* for *m*=*n*, (*m*,*n *= 0..*N*-1). (The proof of this is presented in Annex B.) In other words, using 'Kroneker Delta' notation:

So, the expression for *f(n)* becomes:

©1999 - Engineering Productivity Tools Ltd.