Question

Which among the following is an invertible system?

(a) y[n] = 0

(b) y[n] = 2x[n]

(c) y(t) = x^2(t)

(d) y(t) = dx(t)/dt

This question was addressed to me in exam.

Query is from Properties of Systems in section Signals and Systems Basics of Signals and Systems

Answer 1

Right option is (b) y[n] = 2x[n]

Easiest 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.