Question

A LTI system is characterized by ___________

(a) Unit impulse response

(b) Time shifted impulses

(c) Unit step response

(d) Response to any signal(bounded)

This question was posed to me during an online interview.

The query is from Fourier Series and LTI Systems in division Fourier Series of Signals and Systems

Answer 1

Right answer is (a) Unit impulse response

The best I can explain: The response of an LTI system to an arbitrary input is given by,

\(Y[n] = ∑_{k=-∞}^∞ x[k]h[n]\), where \(x[n] = ∑_{k=-∞}^∞ x[k]δ[n-k]\) represents sequences as a linear combination of shifted unit impulses δ[n-k]. Thus, any LTI system is completely characterized by its unit impulse response.