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Which of the following statements is/are correct? 1. A continuous-time system is a system in which, continuous-time input signals are applied, resulting in continuous-time output signals. 2. A system is said to be linear if it follows the superposition theorem. 3. A system is said to be non-linear if it follows the superposition theorem.

Which of the following statements is/are correct? 1. A continuous-time system is a system in which, continuous-time input signals are applied, resulting in continuous-time output signals. 2. A system is said to be linear if it follows the superposition theorem. 3. A system is said to be non-linear if it follows the superposition theorem. Correct Answer 1 and 2 only 

Concept:

Linear System:

When a system satisfies the principle of superposition which comprises of additivity and homogeneity, then it is said to be linear, else nonlinear system.

Additivity property:

If  x­1(t) → y1(t)  and  x2(t) → y2(t)

Then x­1(t) + x­2(t) → y1(t) + y2(t) 

Homogeneity property:   

Ax­1(t) + Bx­2(t) → Ay1(t) + By2(t

Continuous-time signal:

1) A signal of continuous amplitude and time is known as a continuous-time signal or an analog signal.

2) Whereas, a system which takes continuous-time signal as input and provides continuous-time output is also termed as a continuous-time system.


Analysis:

Statement 1:  A continuous-time system is a system in which, continuous-time input signals are applied, resulting in continuous-time output signals.

(True statement by the definition of continuous-time signal).

Statement 2: A system is said to be linear if it follows the superposition theorem. ( True statement by the definition of a linear system).

Statement 3: A system is said to be non-linear if it follows the superposition theorem. This is a False statement. The true statement for the non-linear system is “it does not follow superposition theorem.”

So, statement 1,2 are correct & statement 3 is false 

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