(a) Table 8.1 lists a number of symmetry properties of the DFS for periodic sequence...

(a) Table 8.1 lists a number of symmetry properties of the DFS for periodic sequences, several of which we repeat here. Prove that each of these properties is true. In carrying out your proofs, you may use the definition of the DFS and any previous property in the list. (For example, in proving property 3, you may use properties 1 and 2.)

From the properties proved in part (a), show that for a real periodic sequence x˜ [n], the following symmetry properties of the DFS hold: