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Q6. The diagram in Fig. 1 depicts a cascade connection of two linear time-invariant systems; i.e., the output of the first system is the input to the second system, and the overall output is the output of the second system. LTI System #1 hi[n] LTI System #2 h2[n] y/n] Figure 1: Cascade connection of two LTI systems. Suppose that System #1 is a "predistortion" filter described by the difference equation yn (n] = x[n – 2] + Bæ[n – 3] and System #2 is a distortion filter described by the impulse response: 6 ha[n] = E(-8)*8[n – k). k=1 (a) Determine the impulse response sequence, ha[n], of the second system. Plot ha[n] versus n. (b) Determine the impulse response sequence, h[n] = h1[n] * h2[n], of the overall cascade system. (c) Obtain a single difference equation that relates y[n] to x[n] in Fig. 1. Give numerical values of the filter coefficients for the specific case where ß = 0.75.

Q6. The diagram in Fig. 1 depicts a cascade connection of two linear time-invariant systems; i.e., the output of the first system is the input to the second system, and the overall output is the output of the second system. LTI System #1 hi[n] LTI System #2 h2[n] y/n] Figure 1: Cascade connection of two LTI systems. Suppose that System #1 is a "predistortion" filter described by the difference equation yn (n] = x[n – 2] + Bæ[n – 3] and System #2 is a distortion filter described by the impulse response: 6 ha[n] = E(-8)*8[n – k). k=1 (a) Determine the impulse response sequence, ha[n], of the second system. Plot ha[n] versus n. (b) Determine the impulse response sequence, h[n] = h1[n] * h2[n], of the overall cascade system. (c) Obtain a single difference equation that relates y[n] to x[n] in Fig. 1. Give numerical values of the filter coefficients for the specific case where ß = 0.75.

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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Q6. The diagram in Fig. 1 depicts a cascade connection of two linear time-invariant systems; i.e., the output of the first system is the input to the second system, and the overall output is the output of the second system. LTI System #2 h2[n] LTI yı n] y[n] System #1 Figure 1: Cascade connection of two LTI systems. Suppose that System #1 is a "predistortion" filter described by the difference equation yn [n] = =[n – 2] + Br[n – 3] and System #2 is a distortion filter described by the impulse response: 6 ha{n] = [(-8)*S[n – k]. k=1 (a) Determine the impulse response sequence, ho[n], of the second system. Plot ho[n] versus n. (b) Determine the impulse response sequence, h[n] = h1[n] * h2[n], of the overall cascade system. (c) Obtain a single difference equation that relates y[n] to x[n] in Fig. 1. Give numerical values of the filter coefficients for the specific case where ß = 0.75.
Transcribed Image Text:Q6. The diagram in Fig. 1 depicts a cascade connection of two linear time-invariant systems; i.e., the output of the first system is the input to the second system, and the overall output is the output of the second system. LTI System #2 h2[n] LTI yı n] y[n] System #1 Figure 1: Cascade connection of two LTI systems. Suppose that System #1 is a "predistortion" filter described by the difference equation yn [n] = =[n – 2] + Br[n – 3] and System #2 is a distortion filter described by the impulse response: 6 ha{n] = [(-8)*S[n – k]. k=1 (a) Determine the impulse response sequence, ho[n], of the second system. Plot ho[n] versus n. (b) Determine the impulse response sequence, h[n] = h1[n] * h2[n], of the overall cascade system. (c) Obtain a single difference equation that relates y[n] to x[n] in Fig. 1. Give numerical values of the filter coefficients for the specific case where ß = 0.75.
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