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The Fourier series coefficient of signal x(t) is CK, then what will be Fourier series coefficient of the signal, x(0.5t) + x(t – 0.5) + x(-2t)?

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CIL MT Electrical: 2017 Official Paper
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  1. CK (1 + e-jω0.5k) + C-K
  2. CK (2 + e-jω0.5k) + 0.5 C-K
  3. CK (1 + e-jω0.5k) + CK
  4. CK (2 + e-jω0.5k) + 0.5 CK

Answer (Detailed Solution Below)

Option 1 : CK (1 + e-jω0.5k) + C-K
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Detailed Solution

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Time scaling will not affect the Fourier series coefficient.

x (0.5t) → CK

x (t – 0.5) → e-jω0.5k CK

x(-2t) → C-K

Fourier series coefficient of the given signal is

CK (1 + e-jω0.5k) + C-K
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Q9.The discrete-time Fourier series representation of a signal x[n] with period N is written as \(\rm x[n] = \sum_{k = 0}^{N - 1} a_k e^{j(2kn\pi/N)}\). A discrete-time periodic signal with period N = 3, has the non-zero Fourier series coefficients: a-3 = 2 and a4 = 1. The signal is 
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