Question: Figure shows three periodic sequences x 1 [n] through x 3 [n]. These sequences can be expressed in a Fourier series as (a) For which

Figure shows three periodic sequences x1[n] through x3[n]. These sequences can be expressed in a Fourier series as

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

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

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

N-1 X[k]e{2m/N}kn_ [n] = k=) Part C |1...11|....IL.. IlL.. 1.... II.. x[n}

N-1 X[k]e{2m/N}kn_ [n] = k=) Part C |1...11|....IL.. IlL.. 1.... II.. x[n} TI!I

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