Question

A square-law system is/has

• A. Invertible
• B. Not invertible
• C. Distinct inputs must produce distinct outputs
• D. \(x(t)\) and \(x(-t)\) produce distinct outputs

Hint:

If two different inputs produce the same output, the system is not invertible. For \[ y=x^2, \] both \(+a\) and \(-a\) generate the same output.

Answer 1

The Correct Option is B

Concept: A system is invertible if distinct inputs always produce distinct outputs. For a square-law system, \[ y(t)=x^2(t). \]

Step 1: Check whether different inputs can produce the same output.
Consider \[ x_1(t)=a \] and \[ x_2(t)=-a. \] Then \[ y_1(t)=a^2, \] and \[ y_2(t)=(-a)^2=a^2. \] Thus, \[ y_1(t)=y_2(t). \]

Step 2: Interpret the result.
Two different inputs produce exactly the same output. Therefore the original input cannot be uniquely recovered. Hence the system is not invertible. \[ \boxed{\text{Not invertible}} \]