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Q1:

If h1[n] = 3δ[n] + δ[n - 1], h2[n] = 2δ[n] + δ[n - 2]
h3[n] = δ[n] - 3δ[n - 1] + 7δ[n - 4] + 6δ[n - 6]
h[n] = h1[n] * h2[n] + h3[n] * h1[n] has value

A {6, 18, 7, 4, 0, - 6, 9}

B {9, 0, - 6, 21, 7, 6, 1}

C {7, - 1, 3, 1, 7, 0, 6}

D {9, - 6, 0, 1, 21, 7, 18, 6}

ANS:D - {9, - 6, 0, 1, 21, 7, 18, 6}

h1[n] * h2[n] + h3[n] * h1[n] = h1[n] * (h2[n] + h3[n]) Distributive property for convolution, (h2[n] + h3[n]) = 3δ(n) - 3δ(n - 1) + δ(n - 2) + 7δ(n -4) + 6δ(n - 6) then h1(n) * (h2(n) + h3(n)) {9, - 6, 0, 1, 21, 7, 18, 6}.



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