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(a) Determine the overall frequency response H(ej@). (b) Determine the length of the impulse response of the overall system. (c) Determine the group delay of the overall system.

(a) Determine the overall frequency response H(ej@). (b) Determine the length of the impulse response of the overall system. (c) Determine the group delay of the overall system.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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**Problem 5.46** Assume that the two linear systems in the cascade shown in Figure P5.46 are linear-phase FIR filters. Suppose that \( H_1(z) \) has order \( M_1 \) (impulse response length \( M_1 + 1 \)) and \( H_2(z) \) has order \( M_2 \). Suppose that the frequency responses are of the form \( H_1(e^{j\omega}) = A_1(e^{j\omega})e^{-j\omega M_1/2} \) and \( H_2(e^{j\omega}) = jA_2(e^{j\omega})e^{-j\omega M_2/2} \), where \( M_1 \) is an even integer and \( M_2 \) is an odd integer. Tasks: (a) Determine the overall frequency response \( H(e^{j\omega}) \). (b) Determine the length of the impulse response of the overall system. (c) Determine the group delay of the overall system. **Figure P5.46:** The diagram displays a cascade of two linear systems. The first box in the system is labeled with the impulse response \( h_1[n] \) and frequency response \( H_1(e^{j\omega}) \). The second box is labeled with the impulse response \( h_2[n] \) and frequency response \( H_2(e^{j\omega}) \). - Input: \( x[n] \) enters the first system. - Output: \( y[n] \) exits the second system, after passing through both linear systems.
Transcribed Image Text:**Problem 5.46** Assume that the two linear systems in the cascade shown in Figure P5.46 are linear-phase FIR filters. Suppose that \( H_1(z) \) has order \( M_1 \) (impulse response length \( M_1 + 1 \)) and \( H_2(z) \) has order \( M_2 \). Suppose that the frequency responses are of the form \( H_1(e^{j\omega}) = A_1(e^{j\omega})e^{-j\omega M_1/2} \) and \( H_2(e^{j\omega}) = jA_2(e^{j\omega})e^{-j\omega M_2/2} \), where \( M_1 \) is an even integer and \( M_2 \) is an odd integer. Tasks: (a) Determine the overall frequency response \( H(e^{j\omega}) \). (b) Determine the length of the impulse response of the overall system. (c) Determine the group delay of the overall system. **Figure P5.46:** The diagram displays a cascade of two linear systems. The first box in the system is labeled with the impulse response \( h_1[n] \) and frequency response \( H_1(e^{j\omega}) \). The second box is labeled with the impulse response \( h_2[n] \) and frequency response \( H_2(e^{j\omega}) \). - Input: \( x[n] \) enters the first system. - Output: \( y[n] \) exits the second system, after passing through both linear systems.
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