Question

The Fourier series coefficient of time domain signal x (t) is X[k] = jδ[k-1] – jδ[k+1] + δ[k+3] + δ[k-3], the fundamental frequency of the signal is ω=2π. The signal is ___________

(a) 2(cos 3πt – sin πt)

(b) -2(cos 3πt – sin πt)

(c) 2(cos 6πt – sin 2πt)

(d) -2(cos 6πt – sin 2πt)

This question was addressed to me during an online exam.

I'd like to ask this question from Fourier Series Coefficients in section Fourier Series of Signals and Systems

Answer 1

The correct option is (c) 2(cos 6πt – sin 2πt)

To elaborate: \(x (t) = ∑_{k=-∞}^∞ X[k]e^{j2πkt}\)

= je^j2πt – je^-j2πt + e^j6πt + e^-j6πt

= 2(cos 6πt – sin 2πt).