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GATE Electrical Engineering (EE) 2023 Solved Paper

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Question : 50

Total: 65

The discrete-time Fourier transform of a signal 𝑥[𝑛] is 𝑋(Ω) = (1 + 𝑐𝑜𝑠Ω)𝑒^−𝑗Ω. Consider that 𝑥_𝑝[𝑛] is a periodic signal of period N = 5 such that
𝑥_𝑝 [𝑛] = 𝑥[𝑛], for 𝑛 = 0, 1 ,2
= 0, for 𝑛 = 3, 4
Note that xp[n]=Σk=0N−1akej‌

kn. The magnitude of the Fourier series coefficient 𝑎₃ is _______________ (Round off to 3 decimal places).

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