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The system below is known as a cascaded integrator comb (CIC) filter: + x(n) + + v(n) + + 2-1 y(n) h₁(n) h2(n) where K is a positive integer. This filter is often used in practice because it can be imple- mented without any multipliers and has very good performance. (a) First, consider the "comb filter" denoted above with the impulse response h₁(n). Find the system function H₁(2) and sketch a pole/zero diagram. Is this filter stable? (b) Second, consider the “integrator" denoted above with the impulse response h₂(n). Find the system function H2(z) and sketch a pole/zero diagram. Is this filter stable? (c) Sketch the frequency response of the overall system. Is the overall system stable? (d) Explain how this system can be used as part of a discrete-time interpolator. What would be the meaning of K? Would there be any potential benefit if x(n) is oversampled?

The system below is known as a cascaded integrator comb (CIC) filter: + x(n) + + v(n) + + 2-1 y(n) h₁(n) h2(n) where K is a positive integer. This filter is often used in practice because it can be imple- mented without any multipliers and has very good performance. (a) First, consider the "comb filter" denoted above with the impulse response h₁(n). Find the system function H₁(2) and sketch a pole/zero diagram. Is this filter stable? (b) Second, consider the “integrator" denoted above with the impulse response h₂(n). Find the system function H2(z) and sketch a pole/zero diagram. Is this filter stable? (c) Sketch the frequency response of the overall system. Is the overall system stable? (d) Explain how this system can be used as part of a discrete-time interpolator. What would be the meaning of K? Would there be any potential benefit if x(n) is oversampled?

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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The system below is known as a cascaded integrator comb (CIC) filter: + x(n) + + v(n) + + 2-1 y(n) h₁(n) h2(n) where K is a positive integer. This filter is often used in practice because it can be imple- mented without any multipliers and has very good performance. (a) First, consider the "comb filter" denoted above with the impulse response h₁(n). Find the system function H₁(2) and sketch a pole/zero diagram. Is this filter stable? (b) Second, consider the “integrator" denoted above with the impulse response h₂(n). Find the system function H2(z) and sketch a pole/zero diagram. Is this filter stable? (c) Sketch the frequency response of the overall system. Is the overall system stable? (d) Explain how this system can be used as part of a discrete-time interpolator. What would be the meaning of K? Would there be any potential benefit if x(n) is oversampled?
Transcribed Image Text:The system below is known as a cascaded integrator comb (CIC) filter: + x(n) + + v(n) + + 2-1 y(n) h₁(n) h2(n) where K is a positive integer. This filter is often used in practice because it can be imple- mented without any multipliers and has very good performance. (a) First, consider the "comb filter" denoted above with the impulse response h₁(n). Find the system function H₁(2) and sketch a pole/zero diagram. Is this filter stable? (b) Second, consider the “integrator" denoted above with the impulse response h₂(n). Find the system function H2(z) and sketch a pole/zero diagram. Is this filter stable? (c) Sketch the frequency response of the overall system. Is the overall system stable? (d) Explain how this system can be used as part of a discrete-time interpolator. What would be the meaning of K? Would there be any potential benefit if x(n) is oversampled?
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