Practice Convolution With The Impulse Function (2.1.4.5) - Time Domain Analysis of Continuous-Time Systems
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Convolution with the Impulse Function

Practice - Convolution with the Impulse Function

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is the result of convolving a function with the Dirac delta function?

💡 Hint: Think about the identity property.

Question 2 Easy

If x(t) is convolved with delta(t - 5), what will be the output?

💡 Hint: Recall how shifting works in convolution.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the outcome of convolving any signal x(t) with delta(t)?

It shifts the signal
It alters the signal
It leaves the signal unchanged

💡 Hint: Think about what happens to the original signal.

Question 2

Convolving a signal x(t) with delta(t - t0) results in:

x(t + t0)
x(t)
x(t - t0)

💡 Hint: Recall how shifting works in convolution.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Derive the output of a continuous signal e^(-2t)u(t) convolved with delta(t - 3).

💡 Hint: Consider how shifting affects the exponential function.

Challenge 2 Hard

Prove that if any continuous signal is convolved with the delta function, the total area under the resultant curve remains constant.

💡 Hint: Think about the definition of the integration of the delta function.

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Reference links

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