Question

Which one of the following is an example of a bounded signal?

(a) e^t coswt

(b) e^t sinw(-t)

(c) e^-t coswt

(d) e^t cosw(-t)

I have been asked this question in an online interview.

This is a very interesting question from System Classification and Properties in portion Signals and Systems Basics of Signals and Systems

Answer 1

The correct option is (c) e^-t coswt

Explanation: A bounded signal is the one which satisfies the condition |x(t)|< M < ∞ for all t.

Clearly, the signals e^t coswt, e^t sinw(-t) and e^t cosw(-t) are exponentially growing signals as the power of the function is positive i.e., the signals will grow beyond infinity. Whereas the signal e^-t coswt is an exponentially decaying signal, hence it will decay to zero and will always be less than infinity. Therefore, it is bounded.