Consider the following procedure (a) Form the sequence v[n] = x2[2n] where x2[n] is...

Consider the following procedure

(a) Form the sequence v[n] = x₂[2n] where x₂[n] is given by Eq. (8.166). This yields

(b) Compute V [k], the N-point DFT of v[n].

Demonstrate that the following is true:

Note that this algorithm uses N-point rather than 2N-point DFTs as required in Eq. (8.167). In addition, since v[n] is a real sequence, we can exploit even and odd symmetries to do the computation of V [k] in one N/4-point complex DFT.