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2- In the figure below, show that if F1 and F2 are LTI, and if x1 = x2, then y1 = Y2- -Show that by convolving the impulse responses of F1, and F2, we can obtain the impulse response of an equivalent LTI system, representing the series connection of the two systems. -Assume that F1, has the impulse response fi = {1, – 2, 0.5}, and that F2, has the impulse response f2 = {5, 2}. Find the impulse response of the equivalent LTI system, representing the series connection of F1 and F2. What is the input-output relationship of this system? X2 V2 F1 F2 Y2 X1 V1 F2 F1 Y1

2- In the figure below, show that if F1 and F2 are LTI, and if x1 = x2, then y1 = Y2- -Show that by convolving the impulse responses of F1, and F2, we can obtain the impulse response of an equivalent LTI system, representing the series connection of the two systems. -Assume that F1, has the impulse response fi = {1, – 2, 0.5}, and that F2, has the impulse response f2 = {5, 2}. Find the impulse response of the equivalent LTI system, representing the series connection of F1 and F2. What is the input-output relationship of this system? X2 V2 F1 F2 Y2 X1 V1 F2 F1 Y1

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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2- In the figure below, show that if F1 and F2 are LTI, and if x1 = 2, then y1 = Y2- -Show that by convolving the impulse responses of F1, and F2, we can obtain the impulse response of an equivalent LTI system, representing the series connection of the two systems. -Assume that F1, has the impulse response Л3 {1, — 2, 0.5}, and that F2, has the impulse response f2 = {5, 2}. Find the impulse response of the equivalent LTI system, representing the series connection of F1 and F2. What is the input-output relationship of this system? X2 U2 Y2 F2 F1 X1 F1 Y1 F2 Figure 1: Commutativity of the series connection of systems.
Transcribed Image Text:2- In the figure below, show that if F1 and F2 are LTI, and if x1 = 2, then y1 = Y2- -Show that by convolving the impulse responses of F1, and F2, we can obtain the impulse response of an equivalent LTI system, representing the series connection of the two systems. -Assume that F1, has the impulse response Л3 {1, — 2, 0.5}, and that F2, has the impulse response f2 = {5, 2}. Find the impulse response of the equivalent LTI system, representing the series connection of F1 and F2. What is the input-output relationship of this system? X2 U2 Y2 F2 F1 X1 F1 Y1 F2 Figure 1: Commutativity of the series connection of systems.
1-Take the following system, with the input x, and output y, у(п) — су(п — 1) + z(n) — г(п — 1). Take y(n) = 0, for n < 0. Find the output if (a) x(n) = 8(n), (b) 2(п) — 6(n) + б(п — 1). Note that c is a constant. Evaluate your results in part (a) when - (1) с %3D 0.5, (2) с — 2. Do you see similar trends in the two cases? If not, what are the critical value of the constant c, which result in different qualitative behavior of the system, i.e., discuss the stability of the system.
Transcribed Image Text:1-Take the following system, with the input x, and output y, у(п) — су(п — 1) + z(n) — г(п — 1). Take y(n) = 0, for n < 0. Find the output if (a) x(n) = 8(n), (b) 2(п) — 6(n) + б(п — 1). Note that c is a constant. Evaluate your results in part (a) when - (1) с %3D 0.5, (2) с — 2. Do you see similar trends in the two cases? If not, what are the critical value of the constant c, which result in different qualitative behavior of the system, i.e., discuss the stability of the system.
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