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1.31. In this problem, we illustrate one of the most important consequences of the prop- erties of linearity and time invariance. Specifically, once we know the response of a linear system or a linear time-invariant (LTI) system to a single input or the responses to several inputs, we can directly compute the responses to many other nput signals. Much of the remainder of this book deals with a thorough exploitation f this fact in order to develop results and techniques for analyzing and synthesizing TI systems. b) Determine and sketch the response of the system considered in part (a) to the input x3(1) shown in Figure P1.31(d). X₁ (t) 1 0 x₂ (t) 1 1 2 (a) 1 (c) 12 3 4 t 1 Y₁ (t) 2 1 0 X3 (t) 2 -1 0 T 1 (b) 1 (d) 2 2 t Figure P1.31 Note do NOT use synthetic m to solve convolution problem check with this but you must the other processes.

1.31. In this problem, we illustrate one of the most important consequences of the prop- erties of linearity and time invariance. Specifically, once we know the response of a linear system or a linear time-invariant (LTI) system to a single input or the responses to several inputs, we can directly compute the responses to many other nput signals. Much of the remainder of this book deals with a thorough exploitation f this fact in order to develop results and techniques for analyzing and synthesizing TI systems. b) Determine and sketch the response of the system considered in part (a) to the input x3(1) shown in Figure P1.31(d). X₁ (t) 1 0 x₂ (t) 1 1 2 (a) 1 (c) 12 3 4 t 1 Y₁ (t) 2 1 0 X3 (t) 2 -1 0 T 1 (b) 1 (d) 2 2 t Figure P1.31 Note do NOT use synthetic m to solve convolution problem check with this but you must the other processes.

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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1.31. In this problem, we illustrate one of the most important consequences of the prop- erties of linearity and time invariance. Specifically, once we know the response of a linear system or a linear time-invariant (LTI) system to a single input or the responses to several inputs, we can directly compute the responses to many other input signals. Much of the remainder of this book deals with a thorough exploitation of this fact in order to develop results and techniques for analyzing and synthesizing LTI systems. (b) Determine and sketch the response of the system considered in part (a) to the input x3 (1) shown in Figure P1.31(d). X₁ (t) 1 0 X₂ (t) 1 2 (a) 1 (c) 2 3 4 Y₁ (t) 2 1 0 X3 (t) 2 -1 0 1 (b) 1 (d) 2 2 t t Figure P1.31 Note do NOT use synthetic multiplication to solve convolution problems. You can check with this but you must demonstrate the other processes.
Transcribed Image Text:1.31. In this problem, we illustrate one of the most important consequences of the prop- erties of linearity and time invariance. Specifically, once we know the response of a linear system or a linear time-invariant (LTI) system to a single input or the responses to several inputs, we can directly compute the responses to many other input signals. Much of the remainder of this book deals with a thorough exploitation of this fact in order to develop results and techniques for analyzing and synthesizing LTI systems. (b) Determine and sketch the response of the system considered in part (a) to the input x3 (1) shown in Figure P1.31(d). X₁ (t) 1 0 X₂ (t) 1 2 (a) 1 (c) 2 3 4 Y₁ (t) 2 1 0 X3 (t) 2 -1 0 1 (b) 1 (d) 2 2 t t Figure P1.31 Note do NOT use synthetic multiplication to solve convolution problems. You can check with this but you must demonstrate the other processes.
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