Question

For the system y (t) = x^2(t), which of the following holds true?

(a) Invertible

(b) Non-Invertible

(c) Invertible as well as Non-Invertible in its respective domains

(d) Cannot be determined

This question was addressed to me in homework.

This interesting question is from Properties of Systems in chapter Signals and Systems Basics of Signals and Systems

Answer 1

Correct choice is (b) Non-Invertible

The best explanation: When we pass the signal x (t) through the system y (t), the system squares the input. Hence, inverse system should take square root, i.e.

W (t) = \(\sqrt{y (t)} = \sqrt{x^2 (t)}\) = ± x (t)

Thus, two outputs are possible, + x (t) or – x (t)

This means there is no unique output for unique input. Hence, this system is Non-Invertible.