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When the sequences x1 [n] = u [n] and x2 [n] = u [n-3], the output of LTI system is given as _____

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When the sequences x1 [n] = u [n] and x2 [n] = u [n-3], the output of LTI system is given as _____

(a) y[n] = n-2, n>3

(b) y[n] = n-2, n≥3

(c) y[n] = n+2, n>3

(d) y[n] = n-2, n≤3

This question was addressed to me in homework.

My doubt is from Convolution : Impulse Response Representation for LTI Systems in portion Time Domain Representation for LTI Systems of Signals and Systems

1 Answer

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by (42.1k points)
Right choice is (b) y[n] = n-2, n≥3

The best I can explain: The output y[n] =∑^∞k=-∞u(k)u(n-k-3), by solving the above summation either by graphically or by direct summation we get .

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