In this problem, we illustrate one of the most important consequences of the properties

Chapter 1, Problem 1.31

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In this problem, 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 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. (a) Consider an LTI system whose response to the signal x 1 (t) in Figure P1.31(a) is the signal y 1 ( t) illustrated in Figure P 1.31 (b). Determine and sketch carefully the response of the system to the input x2(t) depicted in Figure P1.31(c). (b) Determine and sketch the response of the system considered in part (a) to the input x 3 (t) shown in Figure P1.31(d).

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