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When two LTI systems with impulse responses ha (t) and hb (t) are cascaded then equivalent response is given by ______

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When two LTI systems with impulse responses ha (t) and hb (t) are cascaded then equivalent response is given by ______

(a) h(t) = ha(t) + hb(t)

(b) h(t) = ha(t) – hb(t)

(c) h(t) = ha(t) hb(t)

(d) h(t) = ha(t) * hb(t)

This question was posed to me during an interview.

Question is taken from Properties of the Impulse Response Representation for LTI Systems topic in portion Time Domain Representation for LTI Systems of Signals and Systems

1 Answer

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The correct answer is (d) h(t) = ha(t) * hb(t)

Explanation: The equivalent impulse response of two systems connected in series (cascaded) is given by convolution of individual impulse responses.

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