Practice - Derivation of the Convolution Sum
Practice Questions
Test your understanding with targeted questions
What does the convolution sum represent?
💡 Hint: Think about how inputs affect outputs in a linear system.
What is the impulse function denoted as?
💡 Hint: Recall the special function that focuses all energy at a single point.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the output of a DT-LTI system represented by?
💡 Hint: Think about how the output relates to the input and the system's characteristics.
True or False: Linearity in systems allows us to add different responses together.
💡 Hint: Consider how combining signals works in systems.
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Challenge Problems
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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.
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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