Two DT signals, sk(n) and sl(n), are said to be orthogonal over an interval [N1, N2] if...

Two DT signals, s_k(n) and s_l(n), are said to be orthogonal over an interval [N₁, N₂] if

If A_k — 1, the signals are called orthonormal.

(a) Prove the relation

(b) Illustrate the validity of the relation in part (a) by plotting for every value of k = 1, 2, ... , 6, the signals [Note: For a given k, n the signal s_k(n) can be represented as a vector in the complex plane.]

(c) Show that the harmonically related signals

are orthogonal over any interval of length N.