Check whether x [n] = 7 sin (6Ï€n) is periodic and if it is period calculate its fundamental period? - Signals and Systems

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

Check whether x [n] = 7 sin (6Ï€n) is periodic and if it is period calculate its fundamental period?

A)

Non periodic

B)

Periodic with fundamental period 1

C)

Periodic with fundamental period 3

D)

Periodic with fundamental period 6Ï€

Correct Answer : Option (B) : Periodic with fundamental period 1

Explanation : X [n] = 7 sin (6πn) is a periodic discrete time signal with period 1. By substituting w = 6π and m=3 in w=^2πm⁄_N we get N =1.

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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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