This set of Signals & Systems Multiple Choice Questions & Answers (MCQs) focuses on “The Complex Exponential”.

1. What is exp(ja) equal to, where j is the square root of unity?

a) cos ja + jsin a

b) sin a + jcos a

c) cos j + a sin j

d) cos a + jsin a

View Answer

Explanation: This is the corollary of DeMoivre/Euler’s Theorem.

2. What is the magnitude of exp(2+3j)?

a) exp(2.3)

b) exp(3)

c) exp(2)

d) exp(3/2)

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Explanation: exp(a+b) =exp(a) * exp(b), and |exp(3i)| = 1.

3. What is the fundamental frequency of exp(2pi*w*j)?

a) 1pi*w

b) 2pi*w

c) w

d) 2w

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Explanation: Fundamental period = 2pi/w, hence fundamental frequency will be w.

4. Total energy possessed by a signal exp(jwt) is?

a) 2pi/w

b) pi/w

c) pi/2w

d) 2pi/3w

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Explanation: Energy possessed by a periodic signal is the integral of the square of the magnitude of the signal over a time period.

5. Sinusoidal signals multiplied by decaying exponentials are referred to as

a) Amplified sinusoids

b) Neutralized sinusoids

c) Buffered sinusoids

d) Damped sinusoids

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Explanation: The decaying exponentials dampen the amplitudes of sinusoids. Hence, the term damped sinusoids.

6. What is the power possessed by a signal exp(jwt)?

a) 1

b) 0.5

c) ^{1}⁄_{w}

d) w

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Explanation: The power = Energy/Time period for a periodic signal. Hence, Power = 1.

7. What is the period of exp(2+pi*j/4)t?

a) 4

b) 8

c) 16

d) 20

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Explanation: The fundamental period = 2pi/(pi/4) = 8.

8. exp(jwt) is periodic

a) for any w

b) for any t

c) for no w

d) for no t

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Explanation: Any two instants, t and t + 2pi will be equal, hence the signal will be periodic with period 2pi.

9. Define the fundamental period of the following signal x[n] = exp(2pi*j*n/3) + exp(3*pi*j*n/4)?

a) 8

b) 12

c) 18

d) 24

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Explanation: The first signal, will repeat itself after 3 cycles. The second will repeat itself after 8 cycles. Thus, both of them together will repeat themselves only after LCM(8,3) = 24 cycles.

10. exp[jwn] is periodic

a) for any w

b) for any t

c) for w=2pi*M/n

d) for t = 1/w

View Answer

Explanation: Discrete exponentials are periodic only for a particular choice of the fundamental frequency.

**Sanfoundry Global Education & Learning Series – Signals & Systems.**

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