Determine the equivalent response when two LTI systems with impulse responses ha (t) and hb (t) are cascaded.Group of answer choicesh(t) = ha(t) * hb(t)h(t) = ha(t) โ hb(t)h(t) = ha(t) hb(t)h(t) = ha(t) + hb(t)
Question
Determine the equivalent response when two LTI systems with impulse responses ha (t) and hb (t) are cascaded.Group of answer choicesh(t) = ha(t) * hb(t)h(t) = ha(t) โ hb(t)h(t) = ha(t) hb(t)h(t) = ha(t) + hb(t)
Solution
The equivalent response when two Linear Time-Invariant (LTI) systems with impulse responses ha(t) and hb(t) are cascaded is given by the convolution of the two impulse responses. Therefore, the correct answer is:
h(t) = ha(t) * hb(t)
This is because in LTI systems, the output for the cascaded systems is the convolution of the individual systems' impulse responses.
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