1. Which of them are real signals? (Please use the property of Fourier series) 100 k x₂ (1) = [ ( 1 ) ² Σ()*** 50t k=0 2π 100 x₂ (t) = Σ cos(k)ejkt k=-100 100 jk x3 (t) = Σ / sin (1) e/k² k=-100

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1. Which of them are real signals? (Please use the property of Fourier series)
-Σ(;)
x₁ (t) =
k
ejk
2π
50
x₂ (t) =
100
Σ cos(kn)e
k=-100
2πT
jk 50
X3 (t) =
∞
x[n] = A₁ + > Ak sin(wên + Þk)
k=1
100
Σ / sin (47) ²0
kπ 2π
jk
j
50
2
k=-100
2. A real discrete time periodic signal x[n], whose period N = 5. Its nonzero Fourier series
coefficients: a = 1, a₂ = α±₂ = e¹², α² = α±4 = 2e. Please express x[n] in the form of
.π
*
*
Transcribed Image Text:1. Which of them are real signals? (Please use the property of Fourier series) -Σ(;) x₁ (t) = k ejk 2π 50 x₂ (t) = 100 Σ cos(kn)e k=-100 2πT jk 50 X3 (t) = ∞ x[n] = A₁ + > Ak sin(wên + Þk) k=1 100 Σ / sin (47) ²0 kπ 2π jk j 50 2 k=-100 2. A real discrete time periodic signal x[n], whose period N = 5. Its nonzero Fourier series coefficients: a = 1, a₂ = α±₂ = e¹², α² = α±4 = 2e. Please express x[n] in the form of .π * *
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