4. [20 points] Let us consider a periodic signal g(t) with complex (exponential) F.S. coefficients denoted by

{Dm}, where n = 0, +1, +2,....

(a) Find F.S. coefficients for g(t+to), for some constant to.

(b) Find F.S. coefficients for g(at), for some real valued constant a.

(c) Prove that if g(t) is a real valued signal, then F.S. coefficients satisfy conjugate symmetry, i.e.,

Dn = Dn

(d) Prove that if g(t) is an even signal, then F.S. coefficients are also even, i.e., D₁ = D-n-

(e) Prove that if g(t) is an odd signal, then F.S. coefficients are also odd, i.e., Dn=-D-n.