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Test: Continuous Time Convolution - Electrical Engineering (EE) MCQ


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20 Questions MCQ Test Signals and Systems - Test: Continuous Time Convolution

Test: Continuous Time Convolution for Electrical Engineering (EE) 2024 is part of Signals and Systems preparation. The Test: Continuous Time Convolution questions and answers have been prepared according to the Electrical Engineering (EE) exam syllabus.The Test: Continuous Time Convolution MCQs are made for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Continuous Time Convolution below.
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Test: Continuous Time Convolution - Question 1

Find the value of h[n]*d[n-1], d[n] being the delta function.

Detailed Solution for Test: Continuous Time Convolution - Question 1

Convolution of a function with a delta function shifts accordingly.

Test: Continuous Time Convolution - Question 2

Find the value of h[n]*d[n-5], d[n] being the delta function.

Detailed Solution for Test: Continuous Time Convolution - Question 2

Convolution of a function with a delta function shifts accordingly.

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Test: Continuous Time Convolution - Question 3

Evaluate (exp(-4t)u(t))*u(t), u(t) being the heaviside function.

Detailed Solution for Test: Continuous Time Convolution - Question 3

Use the convolution formula.

Test: Continuous Time Convolution - Question 4

Find the convolution of x(t) = exp(2t)u(-t), and h(t) = u(t-3)

Detailed Solution for Test: Continuous Time Convolution - Question 4

Divide it into 2 sectors and apply the convolution formula.

Test: Continuous Time Convolution - Question 5

 Find the value of h[n]*d[n+1], d[n] being the delta function.

Detailed Solution for Test: Continuous Time Convolution - Question 5

Convolution of a function with a delta function shifts accordingly.

Test: Continuous Time Convolution - Question 6

Find the convolution of x(t) = exp(3t)u(-t), and h(t) = u(t-3)

Detailed Solution for Test: Continuous Time Convolution - Question 6

Divide it into 2 sectors and apply the convolution formula.

Test: Continuous Time Convolution - Question 7

 Find the value of d(t-34)*x(t+56), d(t) being the delta function.

Detailed Solution for Test: Continuous Time Convolution - Question 7

Convolution of a function with a delta function shifts accordingly.

Test: Continuous Time Convolution - Question 8

Find x(t)*u(t)

Detailed Solution for Test: Continuous Time Convolution - Question 8

Apply the convolution formula. The above corollary exists for any x(t) [not impulsive].

Test: Continuous Time Convolution - Question 9

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

Detailed Solution for Test: Continuous Time Convolution - Question 9

The resultant impulse response will be the convolution of all the subsequent impulse responses.

Test: Continuous Time Convolution - Question 10

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

Detailed Solution for Test: Continuous Time Convolution - Question 10

The resultant impulse response will be the convolution of all the subsequent impulse responses.

Test: Continuous Time Convolution - Question 11

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

Detailed Solution for Test: Continuous Time Convolution - Question 11

The resultant impulse response will be the convolution of all the subsequent impulse responses.

Test: Continuous Time Convolution - Question 12

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

Detailed Solution for Test: Continuous Time Convolution - Question 12

The delta function convolved with another function results in the shifted function.

Test: Continuous Time Convolution - Question 13

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

Detailed Solution for Test: Continuous Time Convolution - Question 13

The resultant impulse response will be the convolution of all the subsequent impulse responses.

Test: Continuous Time Convolution - Question 14

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

Detailed Solution for Test: Continuous Time Convolution - Question 14

The resultant impulse response will be the convolution of all the subsequent impulse responses.

Test: Continuous Time Convolution - Question 15

What is the convolution integral c(t) for a system with input x(t) and impulse response h(t), where x(t) = u(t - 1) - u(t - 3) and h(t) = u(t) - u(t - 2) ?

Detailed Solution for Test: Continuous Time Convolution - Question 15

By using the impulse response of a system, convolution can be used to calculate a system's zero state response (i.e., its response when it has zero initial conditions) to an arbitrary input. Linearity and superposition are used. 
The convolution can be defined as:

u(t)*u(t) = r(t)

Calculation:

Given signals are x(t) = u(t - 1) - u(t - 3) and h(t) = u(t) - u(t - 2) 

x(t) and h(t) is graphically represented by:

c(t) = x(t) * h(t)

c(t) = [u(t -1) - u(t - 3)]*[u(t) - u(t -2)]

c(t) = u(t - 1)*u(t) - u(t -1)*u(t - 2) - u(t - 3)*u(t) + u(t - 3)*u(t - 2)

c(t) = r(t - 1) - r(t - 3) - r(t - 3) + r(t + 5)

c(t) = r(t - 1) -2r(t - 3) + r(t + 5)
The output signal is represented as:

Test: Continuous Time Convolution - Question 16

The convolution sum of x[n] and h[n] is given as:

Detailed Solution for Test: Continuous Time Convolution - Question 16

Discrete Time System:

The convolution of two a signal with a system with impulse response h(n) is represented as:
y[n] = x[n] ∗ h[n]
Continuous Time System:

The convolution of two a signal with a system with impulse response h(t) is represented as:
y(t) = x(t) ∗ h(t)

Test: Continuous Time Convolution - Question 17

We have x(n) = {2, 3, -1, -4} & h(n) = {2,4,1}. If y (n) is convolution of x(n) & h(n), then what is the sum of the initial and final sample of y(n)?

Detailed Solution for Test: Continuous Time Convolution - Question 17

x(n) = {2, 3, -1, -4}
h(n) = {2, 4, 1}


Final Sample = -4
Sum = 4 + (-4) = 0

Test: Continuous Time Convolution - Question 18

What is the convolution integral c(t) for a system with input x(t) and impulse response h(t), where x(t) = u(t - 1) - u(t - 3) and h(t) = u(t) - u(t - 2) ?

Detailed Solution for Test: Continuous Time Convolution - Question 18

Concept:

By using the impulse response of a system, convolution can be used to calculate a system's zero state response (i.e., its response when it has zero initial conditions) to an arbitrary input.  Linearity and superposition are used. 
The convolution can be defined as:

u(t)*u(t) = r(t)

Calculation:

Given signals are x(t) = u(t - 1) - u(t - 3) and h(t) = u(t) - u(t - 2) 

x(t) and h(t) is graphically represented by:

c(t) = x(t) * h(t)

c(t) = [u(t -1) - u(t - 3)]*[u(t) - u(t -2)]

c(t) = u(t - 1)*u(t) - u(t -1)*u(t - 2) - u(t - 3)*u(t) + u(t - 3)*u(t - 2)

c(t) = r(t - 1) - r(t - 3) - r(t - 3) + r(t + 5)

c(t) = r(t - 1) -2r(t - 3) + r(t + 5)

The output signal is represented as:

Test: Continuous Time Convolution - Question 19

The convolution sum of x[n] and h[n] is given as:

Detailed Solution for Test: Continuous Time Convolution - Question 19

Discrete Time System:

The convolution of two a signal with a system with impulse response h(n) is represented as:

y[n] = x[n] ∗ h[n]

Continuous Time System:

The convolution of two a signal with a system with impulse response h(t) is represented as:

y(t) = x(t) ∗ h(t)

Test: Continuous Time Convolution - Question 20

The signal x(t) and h(t) shown in the figures are convolved to yield y(t)


Which one of the following figures represent the output y(t)?

Detailed Solution for Test: Continuous Time Convolution - Question 20

x(t) = δ(t + 1) – δ(t – 1)

x(t) * h(t) = y(t)

= h(t + 1) – h(t – 1)



y(t) = h(t + 1) – h(t – 1)

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