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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)

View Answer

Answer: b [Reason:] The delta function convolved with another function results in the shifted function.

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

View Answer

Answer: a [Reason:] The resultant impulse response will be the convolution of all the subsequent impulse responses.

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)

View Answer

Answer: c [Reason:] The delta function convolved with another function results in the shifted function.

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

View Answer

Answer: c [Reason:] The resultant impulse response will be the convolution of all the subsequent impulse responses.

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)

View Answer

Answer: a [Reason:] The delta function convolved with another function results in the shifted function.

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

View Answer

Answer: a [Reason:] The resultant impulse response will be the convolution of all the subsequent impulse responses.

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)

View Answer

Answer: b [Reason:] The delta function convolved with another function results in the shifted function.

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

View Answer

Answer: a [Reason:] The resultant impulse response will be the convolution of all the subsequent impulse responses.

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)

View Answer

Answer: d [Reason:] The delta function convolved with another function results in the shifted function.

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

View Answer

Answer: a [Reason:] The resultant impulse response will be the convolution of all the subsequent impulse responses.

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