When is a complex exponential signal pure DC? - Signals and Systems

Electronics and Communication Engineering (ECE) : Signals and Systems - Quiz(MCQ)

When is a complex exponential signal pure DC?

A)

Ïƒ = 0 and Î© < 0

B)

Ïƒ = 0 and Î© = 0

C)

Ïƒ < 0 and Î© = 0

D)

Ïƒ < 0 and Î© < 0

Correct Answer : Option (B) : Ïƒ = 0 and Î© = 0

Explanation : A complex exponential signal is represented as x(t)= e^st
Where, s = σ + jΩ
⇒ x(t) = e^σt [cosΩt + jsinΩt] When, σ = 0 and Ω = 0 ⇒ x(t) = e⁰ [cos0 + jsin0] = 1 × 1 = 1 which is pure DC.

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For a Gaussian process, auto-correlation sequence also implies that

A)

ergodic process

B)

statistical dependence

C)

statistical independence

D)

All of the above

Correct Answer : statistical dependence

Consider the following statements

1. If ensemble and time averages of a random process are identical, the process is ergodic.
2. If ensemble and time average of a random process are not identical, the process is ergodic.
3. An ergodic process is stationary.
4. A stationary process is necessarily ergodic.

Which of the above statements are correct?

A)

1 only

B)

1 and 3 only

C)

1 and 4 only

D)

1, 3 and 4 only

Correct Answer : 1 and 3 only

In RLC circuits the state variables generally selected are

A)

voltages across capacitors

B)

currents through resistances and capacitances

C)

currents through inductances and voltages across capacitances

D)

currents through resistances and voltages across capacitors

Correct Answer : currents through inductances and voltages across capacitances

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