For all the following problems, h*x denotes h convolved with x. $ indicates integral.

1. Find the value of [d(t) – d(t-1)] * -x[t+1].

a) x(t+1) – x(t)

b) x(t) – x(t+1)

c) x(t) – x(t-1)

d) x(t-1) – x(t+1)

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2. If h1, h2 and h3 are cascaded, find the overall impulse response

a) h1 * h2 * h3

b) h1 + h2 + h3

c) h3

d) all of the mentioned

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3. Find the value of [d(t-3) – d(t-1)] * x[t+3].

a) x(t+3) – x(t+2)

b) x(t) – x(t+1)

c) x(t) – x(t+2)

d) x(t-1) – x(t+2)

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4. If h1, h2 and h3 are cascaded, and h1 = u(t), h2 = d(t) and h3 = d(t), find the overall impulse response

a) s(t)

b) d(t)

c) u(t)

d) all of the mentioned

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5. Find the value of [d(t) – u(t-1)] * x[t+1].

a) x(t+1) – $x(t)

b) $x(t) – x(t+1)

c) x(t) – $x(t-1)

d) $x(t-1) – x(t+1)

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6. If h1, h2 and h3 are cascaded, and h1 = u(t+4), h2 = d(t-3) and h3 = d(t-5), find the overall impulse response

a) u(t-4)

b) u(t-6)

c) u(t-8)

d) all of the mentioned

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7. Find the value of [u(t) – d(t-1)] * -x[t+1].

a) $x(t+1) – x(t)

b) x(t) – $x(t+1)

c) $x(t) – x(t-1)

d) $x(t-1) – x(t+1)

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8. If h1, h2 and h3 are parallelly summed, find the overall impulse response

a) h1 + h2 + h3

b) h1 – h2 + h3

c) h1*h2*h3

d) all of the mentioned

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9. Find the value of [u(t) – u(t+1)] * x[t+1].

a) $x(t+1) – $x(t+3)

b) $x(t) – $x(t+2)

c) $x(t) – $x(t-1)

d) $x(t+1) – $x(t+2)

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10. If h1, h2 and h3 are cascaded, and h1 = u(t), h2 = exp(t) and h3 = sin(t), find the overall impulse response

a) sin(t)*exp(t)*u(t)

b) sin(t) + exp(t) + u(t)

c) u(t)*sin(t)

d) all of the mentioned

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