The Complex Exponential MCQ’s

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

1. What is the magnitude of exp(2+3j)?
a) exp(2.3)
b) exp(3)
c) exp(2)
d) exp(3/2)

2. What is the fundamental frequency of exp(2pi*w*j)?
a) 1pi*w
b) 2pi*w
c) w
d) 2w

3. 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

4. Total energy possessed by a signal exp(jwt) is?
a) 2pi/w
b) pi/w
c) pi/2w
d) 2pi/3w

5. What is the power possessed by a signal exp(jwt)?
a) 1
b) 0.5
c) 1w
d) w

6. exp(jwt) is periodic
a) for any w
b) for any t
c) for no w
d) for no t

7. Sinusoidal signals multiplied by decaying exponentials are referred to as
a) Amplified sinusoids
b) Neutralized sinusoids
c) Buffered sinusoids
d) Damped sinusoids

8. What is the period of exp(2+pi*j/4)t?
a) 4
b) 8
c) 16
d) 20

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

10. The most general form of complex exponential function is:
a) eσt
b) eΩt
c) est
d) eat

11. When is a complex exponential signal sinusoidal?
a) σ =0 and Ω = 0
b) σ < 0 and Ω = 0
c) σ = 0 and Ω ≠ 0
d) σ ≠ 0 and Ω ≠ 0

12. exp[jwn] is periodic
a) for any w
b) for any t
c) for w=2pi*M/n
d) for t = 1/w

13. A complex exponential signal is a decaying exponential signal when
a) Ω = 0 and σ > 0
b) Ω = 0 and σ = 0
c) Ω ≠ 0 and σ < 0
d) Ω = 0 and σ < 0

14. An exponentially growing sinusoidal signal is:
a) σ = 0 and Ω = 0
b) σ > 0 and Ω ≠ 0
c) σ < 0 and Ω ≠ 0
d) σ = 0 and Ω ≠ 0

15. Determine the nature of the signal: x(t) = e-0.2t [cosΩt + jsinΩt].
a) Exponentially decaying sinusoidal signal
b) Exponentially growing sinusoidal signal
c) Sinusoidal signal
d) Exponential signal

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