Question

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

(a) System is Linear, time-invariant, causal and stable

(b) System is Linear, time-invariant and causal

(c) System is Linear, time-invariant and stable

(d) System is Linear, causal and stable

This question was posed to me in an interview.

This key question is from Properties of Systems topic in division Signals and Systems Basics of Signals and Systems

Answer 1

Right option is (c) System is Linear, time-invariant and stable

The explanation is: y1 (t) = |v (t)|, y2 (t) = |k v (t)|= |k|y1 (t)

If k is negative, |k| y1 (t) ≠k y1 (t)

Since it is not homogeneous, so non-linear system.

Again, y1 (t) = |v (t)|, y2 (t) = |y (t-t0)| = y1 (t-t0)

∴ System is time invariant.

The response at any time t=t0, depends only on the excitation at that time and not on the excitation at any later time, so causal system.

If x (t) is bounded then y (t) is also bounded, so stable system.