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1) Here we illustrate one of the most important consequences of the properties 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 responses to several inputs, we can directly compute the responses to many other input signals. a) Consider an LTI system whose response to the signal x1(t) shown below is the signal y1(t). Determine and sketch carefully the response of the system to the input x2(t). b) Determine and sketch the response of the system in part (a) to the input x3(t). X1 (t) y (t) 2- 1 1 2 (a) (b) X2 (t) X3 (t) 1 2 3 -1 0 1 (c) (d)

1) Here we illustrate one of the most important consequences of the properties 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 responses to several inputs, we can directly compute the responses to many other input signals. a) Consider an LTI system whose response to the signal x1(t) shown below is the signal y1(t). Determine and sketch carefully the response of the system to the input x2(t). b) Determine and sketch the response of the system in part (a) to the input x3(t). X1 (t) y (t) 2- 1 1 2 (a) (b) X2 (t) X3 (t) 1 2 3 -1 0 1 (c) (d)

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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1) Here we illustrate one of the most important consequences of the properties 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 responses to several inputs, we can directly compute the responses to many other input signals. a) Consider an LTI system whose response to the signal x1(t) shown below is the signal y1(t). Determine and sketch carefully the response of the system to the input x2(t). b) Determine and sketch the response of the system in part (a) to the input x3(t). X1 (t) Y1 (t) 2 1 1 0 1 (a) (b) X2 (t) X3 (t) 2 1 1 1 2 3 4 -1 0 2 (c) (d)
Transcribed Image Text:1) Here we illustrate one of the most important consequences of the properties 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 responses to several inputs, we can directly compute the responses to many other input signals. a) Consider an LTI system whose response to the signal x1(t) shown below is the signal y1(t). Determine and sketch carefully the response of the system to the input x2(t). b) Determine and sketch the response of the system in part (a) to the input x3(t). X1 (t) Y1 (t) 2 1 1 0 1 (a) (b) X2 (t) X3 (t) 2 1 1 1 2 3 4 -1 0 2 (c) (d)
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