Reference no: EM13861638
Problem 1: Determine the Fourier series coefficients of the following signals:
1. x1[n] = 2 + cos(πn/3 + π/6) + sin(π/2)
2. x2[n] = ∑∞k=-∞ [ (-1)kδ(n - 2k)]
Problem 2: What time-domain signals have the following Fourier series/transform representations:
1. X1[k] = cos(πk/3) + cos(πk/2 + π/3)
2. X2(ω) = ∑2k=-2 δ(ω - kπ/4) (|ω| ≤ π)
Problem 3: The FS representation of x[n] is given by X[k] = sin(kπ/3). Use Fourier series properties, without determining x[n], to determine the following DT signals:
1. v[n] = x[n + 1] ∗ x[n - 1] (*: convolution)
2. w[n] = sin(πn/2) x[n].
Problem 4: Determine the Fourier transform methods to determine the response of the following systems for the given input:
1. h1[n] = sin(2πn/5)/πn and x1[n] = sin(πn/3 + π/4) + cos(3πn/4)
2. h2[n] = sin(πn/3) cos(πn/2)/πn and x2[n] = sin(πn/3 + π/4) + cos(3πn/4)
3. h3[n] = (1/2)|n| and x3[n] = (-1)n
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