Figure P8.3 shows three periodic sequences through These sequences can be expressed in...

Figure P8.3 shows three periodic sequences through These sequences can be expressed in a Fourier series as

(a) For which sequences can the time origin be chosen such that all the are real?

(b) For which sequences can the time origin be chosen such that all the (except for k an integer multiple of N) are imaginary?

(c) For which sequences does = 0 for k = ±2,±4,±6?