Question

Which of the following systems is stable?

(a) y(t) = log(x(t))

(b) y(t) = sin(x(t))

(c) y(t) = exp(x(t))

(d) y(t) = tx(t) + 1

The question was posed to me at a job interview.

This question is from BIBO Stability topic in portion Signals and Systems Basics of Signals and Systems

Answer 1

Right choice is (b) y(t) = sin(x(t))

The best I can explain: Stability implies that a bounded input should give a bounded output. In a,b,d there are regions of x, for which y reaches infinity/negative infinity. Thus the sin function always stays between -1 and 1, and is hence stable.