A real-valued N-point sequence x(n) is called DFT bandlimited if its DFT X(k) = 0 for W...

A real-valued N-point sequence x(n) is called DFT bandlimited if its DFT X(k) = 0 for We insert (L — 1)N zeros in the middle of X(k) to obtain the following LN-point DFT:

Show that

where

Explain the meaning of this type of processing by working out an example with N =4, L= 1,and X (k) = {1,0,0,1}.