The discrete-time Fourier series representation of a signal x[n] with period N is written as x[n] = \sum ↙\stackrel{N−1}{k = 0}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 a 4 = 1. The signal is

Correct Answer is : 1+2e(j2π6n)cos⁡(2π6n)

2 + 2e^{− (j\frac{2\pi }{6}n) }\cos ⁡ (\frac{2\pi }{6}n)

1 + 2e^{ (j\frac{2\pi }{6}n) }\cos ⁡ (\frac{2\pi }{6}n)

1 + 2e^{ (j\frac{2\pi }{3}n) }\cos ⁡ (\frac{2\pi }{6}n)

2 + 2e^{ (j\frac{2\pi }{6}n) }\cos ⁡ (\frac{2\pi }{6}n)

GATE Electrical Engineering (EE) 2022 Solved Paper

Question : 33 of 65

Marks: +1, -0

The discrete-time Fourier series representation of a signal x[n] with period N is written as

x[n] = ∑ ↙{k = 0}↖{N−1}a_{k}e^{j(2knπ \/ 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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