Practice Fundamental Relationship To Impulse (6.1.1.3.3) - Time Domain Analysis of Discrete-Time Systems
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Fundamental Relationship to Impulse

Practice - Fundamental Relationship to Impulse

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is the value of δ[0]?

💡 Hint: It is defined as 1 at n=0.

Question 2 Easy

What does the unit step function u[n] equal for n=-1?

💡 Hint: Recall the defining condition of u[n].

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the definition of the unit impulse function δ[n]?

1 at n=0; 0 elsewhere
0 for all n
1 for all n

💡 Hint: Think about where the function has non-zero values.

Question 2

True or False: The unit step function u[n] is 1 for negative values of n.

True
False

💡 Hint: Recall the definition of u[n].

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Given a system with an impulse response h[n] = 0.5^n u[n], compute the output for an input x[n] = δ[n]. Discuss the implications.

💡 Hint: Consider what happens when you apply δ[n] to the impulse response.

Challenge 2 Hard

Create an example where a discrete signal is constructed using the sifting property of deltas. Show the calculations for x[n] = δ[n] + 2δ[n-1] + 3δ[n-2].

💡 Hint: Pay attention to scaling and shifting within constructed signals.

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Reference links

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