## Trigonometric Fourier Series MCQ’s

This set of Signals & Systems Multiple Choice Questions & Answers (MCQs) focuses on “Trigonometric Fourier Series”.

1. 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)

2. The unit impulse response of the system c (t) = -4e-t + 6e-2t for t>0. The step response of the same system for t ≥ 0 is _______________
a) -3e-2t – 4e-t + 1
b) -3e-2t + 4e-t – 1
c) -3e-2t – 4e-t – 1
d) 3e-2t + 4e-t – 1

3. The Fourier transform of sin(2πt) e-t u (t) is ____________
a) 12j(11+j(ω−2π)+11+j(ω+2π))
b) 12j(11+j(ω−2π)–11+j(ω+2π))
c) 12j(11+j(ω+2π)–11+j(ω−2π))
d) 1j(11+j(ω+2π)–11+j(ω−2π))

4. Given a real valued function x (t) with period T. Its trigonometric Fourier series expansion contains no term of frequency ω = 2π (2k)T; where, k = 1, 2….. Also no terms are present. Then, x(t) satisfies the equation ____________
a) x (t) = x (t+T) = -x (t + T2)
b) x (t) = x (t+T) = x (t + T2)
c) x (t) = x (t-T) = -x (t – T2)
d) x (t) = x (t-T) = x (t – T2)

5. The lengths of two discrete time sequence x1[n] and x2[n] are 5 and 7 respectively. The maximum length of a sequence x1[n] * x2[n] is ____________
a) 5
b) 6
c) 7
d) 11

6. If the FT of x(t) is 2ω sin⁡(πω), then the FT of ej5t x(t) is ____________
a) 2ω−5 sin⁡(πω)
b) 2ω+5 sin⁡{π(ω-5)}
c) 2ω+5 sin⁡(πω)
d) 2ω−5 sin⁡{π(ω-5)}

7. Given a periodic rectangular waveform of frequency 1 kHz, symmetrical about t=0 and having a pulse width of 500 µs and amplitude 5 V. The Fourier series is ___________
a) 2.5 + 3.18 cos (2π × 103 t) – 1.06 cos (6π × 103 t)
b) 2.5 – 3.18 cos (2π × 103 t) – 1.06 cos (6π × 103 t)
c) 2.5 + 3.18 cos (2π × 103 t) + 1.06 cos (6π × 103 t)
d) 2.5 – 3.18 cos (2π × 103 t) + 1.06 cos (6π × 103 t)

8. A waveform is given by v(t) = 10 sin2π 100 t. The magnitude of the second harmonic in its Fourier series representation is ____________
a) 0 V
b) 20 V
c) 100 V
d) 200 V

9. A signal x (t) has its FT as X (f). The inverse FT of X(3f +2) is _____________
a) 12x(t2)ej3πt
b) 13x(t3)e−j4πt/3
c) 3x(3t)e-j4πt
d) x(3t + 2)

10. The first two components of trigonometric Fourier series of the given signal is ____________

a) 0, 4/π
b) 4/π, 0
c) 0, -4/π
d) -4/π, 1

11. A linear phase channel with phase delay Tp and group delay Tg must have ____________
a) Tp = Tg = constant
b) Tp ∝ f and Tg ∝ f
c) Tp = constant and Tg ∝ f
d) Tp ∝ f and Tg = constant

12. The impulse response of a continuous time system is given by h(t) = δ(t-1) + δ(t-3). The value of the step response at t=2 is _______________
a) 0
b) 1
c) 2
d) 3

13. The convolution of two continuous time signals x(t) = e-t u(t) and h(t) = e-2t u(t) is ________________
a) (et – e2t) u (t)
b) (e-2t – e-t) u (t)
c) (e-t – e-2t) u (t)
d) (e-t + e-2t) u (t)

14. The z-transform of cos(π3 n) u[n] is __________
a) z2(2z−1)(z2−z+1), 0<|z|<1
b) z2(2z−1)(z2−z+1), |z|>1
c) z2(1−2z)(z2−z+1), 0<|z|<1
d) z2(1−2z)(z2−z+1), |z|>1

15. The Laplace transform of the function cosh2(t) is ____________
a) s2+2s(s2+4)
b) s2−2s(s2−4)
c) s2−2s(s2+4)
d) s2+2s(s2−4)

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