Determine the Fourier series coefficients X i [k], i = 1,..., 4, for each of the following
Question:
Determine the Fourier series coefficients Xi[k], i = 1,..., 4, for each of the following periodic discrete-time signals. Explain the connec-tion between these coefficients and the symmetry of the corresponding signals.
(a) x1[n] has a fundamental period N = 5 and in a period x1[n] = 1 in − 1 ≤ n ≤ 1 and x1 [ − 2] = x1[2] = 0.
(b) x2 [n] has a fundamental period N = 5 and in a period x2[n] = 0.5 n in – 1 ≤ n ≤ 1 and x2[ − 2] = x2[2] = 0.
(c) x3[n] has a fundamental period N = 5 and in a period x3[n] = 2n in – 1 ≤ n ≤ 1 and x3 [ − 2 ] = x3[2] = 0.
(d) x4[n] has a fundamental period N = 5 and in a period x4[n] = n in − 1 ≤ n ≤ 1 and x4[ − 2] = x4[2] = 0.
(e) Consider a period of x1[n]starting at n = 0 and find the Fourier series coefficients. How do they compare with the ones found above?
Step by Step Answer:
a Summation Ztransform The fX1kg are real since the signal is even ...View the full answer
