The system in the image is called a cascaded integrator comb filter (CIC). The K is a positive integer. This filter is often used in practice because it can be implemented without any multipliers. (a) First, consider the “comb filter” denoted above with the impulse response h1(n). Find the system function H1(z) 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?
The system in the image is called a cascaded integrator comb filter (CIC). The K is a positive integer. This filter is often used in practice because it can be implemented without any multipliers. (a) First, consider the “comb filter” denoted above with the impulse response h1(n). Find the system function H1(z) 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?
Introductory Circuit Analysis (13th Edition)
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The system in the image is called a cascaded integrator comb filter (CIC). The K is a positive integer. This filter is often used in practice because it can be implemented without any multipliers.
(a) First, consider the “comb filter” denoted above with the impulse response h1(n). Find
the system function H1(z) 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 function H1(z) 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:+
x(n)
+
h₁(n)
v(n)
+
h2 (n)
y(n)
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