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Determil 2.19. Consider the cascade of the following two systems S1 and S2, as depicted in Figure P2.19: win] x[n] S2 yin] Figure P2.19 S1 : causal LTI, w[n] = w[n - 1] + x[n]; S2 : causal LTI, y[n] = ay[n – 1] + Bw[n].- The difference equation relating x[n] and y[n] is: 3 21 +y[n – 1] + x[n]. y[n] = (a) Determine a and B. (b) Show the impulse response of the cascade connection of S and S-

Determil 2.19. Consider the cascade of the following two systems S1 and S2, as depicted in Figure P2.19: win] x[n] S2 yin] Figure P2.19 S1 : causal LTI, w[n] = w[n - 1] + x[n]; S2 : causal LTI, y[n] = ay[n – 1] + Bw[n].- The difference equation relating x[n] and y[n] is: 3 21 +y[n – 1] + x[n]. y[n] = (a) Determine a and B. (b) Show the impulse response of the cascade connection of S and S-

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
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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Please answer 2.19
2.14. Which of the following impulse responses correspond(s) to stable LTI systems? (a) h(1) - e-(1-2)Wu(t) (b) h>(t) = e cos(2r)u(1) 2.18. Consider a causal LTI system whose input x[n] and output y[n] are related by the difference equation y[n] = yln – 1] + x[n]. Determine y[n] if x[n] = 8[n – 1]. 2.19. Consider the cascade of the following two systems S1 and S2, as depicted in Figure P2.19: w[n] x[n] yln] Figure P2.19 S : causal LTI, w[n] = swin - 1] + x[n]; S2 : causal LTI, y[n] = ay[n – 1] + Bw[n]. The difference equation relating x[n] and y[n] is: y[n] = - gy[n – 2] + y[n – 1] + x[n]. (a) Determine a and B. (b) Show the impulse response of the cascade connection of Sj and S2. 2.23. Let h(t) be the triangular pulse shown in Figure P2.23(a), and let x(f) be the impulse train depicted in Figure P2.23(b). That is, x(1) = 6(1- KT). Determine and sketch y(1) = x(1) * h(t) for the following values of T: (a) T = 4 (b) T = 2 (c) T = 3/2 (d) T = 1 Figure P2.23
Transcribed Image Text:2.14. Which of the following impulse responses correspond(s) to stable LTI systems? (a) h(1) - e-(1-2)Wu(t) (b) h>(t) = e cos(2r)u(1) 2.18. Consider a causal LTI system whose input x[n] and output y[n] are related by the difference equation y[n] = yln – 1] + x[n]. Determine y[n] if x[n] = 8[n – 1]. 2.19. Consider the cascade of the following two systems S1 and S2, as depicted in Figure P2.19: w[n] x[n] yln] Figure P2.19 S : causal LTI, w[n] = swin - 1] + x[n]; S2 : causal LTI, y[n] = ay[n – 1] + Bw[n]. The difference equation relating x[n] and y[n] is: y[n] = - gy[n – 2] + y[n – 1] + x[n]. (a) Determine a and B. (b) Show the impulse response of the cascade connection of Sj and S2. 2.23. Let h(t) be the triangular pulse shown in Figure P2.23(a), and let x(f) be the impulse train depicted in Figure P2.23(b). That is, x(1) = 6(1- KT). Determine and sketch y(1) = x(1) * h(t) for the following values of T: (a) T = 4 (b) T = 2 (c) T = 3/2 (d) T = 1 Figure P2.23
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