Which among the following is an invertible system? - Signals and Systems

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

Which among the following is an invertible system?

A)

y[n] = 0

B)

y[n] = 2x[n]

C)

y(t) = x2(t)

D)

y(t) = dx(t)/dt

Correct Answer : Option (B) : y[n] = 2x[n]

Explanation : A system is said to be invertible if it’s input can be found out from its output. Implying, if a system has same outputs for several inputs then it is impossible to find the correct input as output is same for many. Therefore, a system is invertible if it gives distinct outputs to distinct inputs. It is non-invertible if it gives same outputs for many inputs.

Option a produces 0 output for any input → Non-invertible
Option b produces different outputs for different inputs and also it’s inverse system is (1/2)y[n] → Invertible
Option c, we get same output for both positive and negative values → Non-invertible
Option d, we get 0 for all constant input values → Non-invertible.

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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

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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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