DFT of real sequences with special symmetries (a) Using the symmetry properties of Sec...

DFT of real sequences with special symmetries

(a) Using the symmetry properties of Section 7.2 (especially the decomposition properties), explain how we can compute the DFT of two real symmetric (even) and two real antisymmetric (odd) sequences simultaneously using an N -point DFT only.

(b) Suppose now that we are given four real sequences i =1, 2, 3, 4, that are all symmetric Show that the sequences

are antisymmetric

(c) Form a sequence x(n) using and show how to compute the DFT i = I, 2, 3, 4 from the N-point DFT X(k) of x(n).

(d) Are there any frequency samples of that cannot be recovered from X(k)? Explain.