Practice Derivation Of The Convolution Sum (6.1.2.1) - Time Domain Analysis of Discrete-Time Systems
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Derivation of the Convolution Sum

Practice - Derivation of the Convolution Sum

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Practice Questions

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Question 1 Easy

What does the convolution sum represent?

💡 Hint: Think about how inputs affect outputs in a linear system.

Question 2 Easy

What is the impulse function denoted as?

💡 Hint: Recall the special function that focuses all energy at a single point.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the output of a DT-LTI system represented by?

A single impulse response
The convolution of the input signal and the impulse response
The summation of all past outputs

💡 Hint: Think about how the output relates to the input and the system's characteristics.

Question 2

True or False: Linearity in systems allows us to add different responses together.

True
False

💡 Hint: Consider how combining signals works in systems.

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Challenge Problems

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Challenge 1 Hard

Consider a discrete-time system with impulse response h[n] = 0.5δ[n] + 0.5δ[n-1]. If the input signal x[n] = u[n] (unit step), find the output y[n] using convolution.

💡 Hint: Remember to evaluate non-zero overlapping pairs of the signals.

Challenge 2 Hard

If you composite two input signals, x[n] = δ[n] and h[n] = u[n], what will be the resulting output signal using convolution?

💡 Hint: Consider what happens when you convolve with an impulse.

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