# Miscellaneous Examples on Fourier Series MCQ’s

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

1. A voltage having the waveform of a sine curve is applied across a capacitor. When the frequency of the voltage is increased, what happens to the current through the capacitor?

a) Increases

b) Decreases

c) Remains same

d) Is zero

2. What is the steady state value of F (t), if it is known that F(s)=2s(S+1)(s+2)(s+3)?

a) 12

b) 13

c) 14

d) Cannot be determined

3. A signal g (t) = 10 sin (12πt) is ___________

a) A periodic signal with period 6 s

b) A periodic signal with period 106 s

c) A periodic signal with period 16 s

d) An aperiodic signal

4. What is the steady state value of F (t), if it is known that F(s) = 10(s+1)(s2+1)?

a) -5

b) 5

c) 10

d) Cannot be determined

5. A CRO probe has an impedance of 500 kΩ in parallel with a capacitance of 10 pF. The probe is used to measure the voltage between P and Q as shown in the figure. The measured voltage will be?

a) 3.53 V

b) 3.47 V

c) 5.54 V

d) 7.00 V

6. The Fourier series expansion of a real periodic signal with fundamental frequency f_{0} is given by g_{p} (t) = ∑∞n=−∞Cnej2πnf0t. Given that C_{3} = 3 + j5. The value of C_{-3} is ______________

a) 5 + 3j

b) -5 + 3j

c) -3 – j5

d) 3 – j5

7. A periodic rectangular signal X (t) has the waveform as shown below. The frequency of the fifth harmonic of its spectrum is ______________

a) 40 Hz

b) 200 Hz

c) 250 Hz

d) 1250 Hz

8. The Fourier series coefficient of the signal z(t) = Re{x(t)} is ____________

a) X[k]+X[−k]2

b) X[k]−X[−k]2

c) X[k]+X∗[−k]2

d) X[k]−X∗[−k]2

9. A signal e^{-at} sin (ωt) is the input to a real linear time invariant system. Given K and ∅ are constants, the output of the system will be of the form Ke^{-bt} sin (vt + ∅). The correct statement among the following is __________

a) b need not be equal to a but v must be equal to ω

b) v need not be equal to ω but b must be equal to a

c) b must be equal to a and v must be equal to ω

d) b need not be equal to a and v need not be equal to ω

10. The Fourier series representation of an impulse train denoted by s(t) = ∑∞n=−∞δ(t−nT0) is given by _____________

a) 1T0∑∞n=−∞exp(−j2πntT0)

b) 1T0∑∞n=−∞exp(−jπntT0)

c) 1T0∑∞n=−∞exp(jπntT0)

d) 1T0∑∞n=−∞exp(j2πntT0)

11. The RMS value of a rectangular wave of period T, having a value of +V for a duration T_{1} (< T) and −V for the duration T − T_{1} = T_{2}, equals _____________

a) V

b) V2√

c) T1−T2T V

d) T1T2 V

12. Let us suppose that the impulse response of a causal LTI system is given as h (t). Now, consider the following two statements:

Statement 1- Principle of superposition holds

Statement 2- h (t) = 0(for t<0)

Which of the following is correct?

a) Statement 1 is correct and Statement 2 is wrong

b) Statement 2 is correct and Statement 1 is wrong

c) Both Statement 1 and Statement 2 are wrong

d) Both statement 1 and Statement 2 are correct

13. For which of the following a Fourier series cannot be defined?

a) 3 sin (25t)

b) 4 cos (20t + 3) + 2 sin (710t)

c) exp(-|t|) sin (25t)

d) 1

14. A periodic square wave is formed by rectangular pulses ranging from -1 to +1 and period = 2 units. The ratio of the power in the 7th harmonic to the power in the 5th harmonic for this waveform is equal to ____________

a) 1

b) 0.5

c) 2

d) 2.5

15. A useful property of the unit impulse 6 (t) is ________________

a) 6 (at) = a 6 (t)

b) 6 (at) = 6 (t)

c) 6 (at) = 1a 6(t)

d) 6(at) = [6(t)]^{a}

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