Practice - Recursive Systems (Infinite Impulse Response - IIR Systems)
Practice Questions
Test your understanding with targeted questions
What is the main difference between IIR and FIR systems?
💡 Hint: Consider the role of past outputs in system calculations.
Define BIBO stability.
💡 Hint: Think about ensuring predictable behavior in a system.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does the term IIR stand for?
💡 Hint: Remember what 'infinite' implies about the duration of the response.
True or False: IIR systems guarantee stability regardless of the coefficients chosen.
💡 Hint: Reflect on what stability requires in mathematical terms.
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Challenge Problems
Push your limits with advanced challenges
You are given an IIR system characterized by the coefficients a = [0.5, -0.2] and b = [1, 0.3]. Analyze if the system is stable by finding its characteristic roots.
💡 Hint: Use the quadratic formula to find the roots, and check their absolute values against 1.
Given the impulse response h[n] of an IIR system is proposed as h[n] = (0.5)^n u[n] - (0.3)^n u[n], analyze its stability by assessing the absolute summability.
💡 Hint: Compare the growth rates of the exponential terms for n tending to infinity.
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Reference links
Supplementary resources to enhance your learning experience.