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PROBLEM 2.1*: Consider the functions x(t) = 3e−2(t−3) [u(t − 3) – u(t − 5)] and h(t) = 6[u(t − 1) – u(t − 7)]. - (a) To get your mind thinking in convolutionland, draw three different plots with "+" on the horizontal axis. (i) On the first graph, plot x(7). (Don't worry about getting the decay rate in your sketch exactly right; these sketches are just meant to aid your understanding.) (ii) On the second graph, plot h(-T). (iii) On the third graph, plot h(3-7). This should look like your plot in (ii), just shifted to the right. (b) Use "graphical convolution" to compute the convolution¹ y(t) = x(t)*h(t); let h(t) be the signal that you "flip and shift." Your answer will consist of five different cases. Although there may not always be a way to express the answer that is obviously the "simplest," simplify your answer as much as you can. PROBLEM 2.2: Check your work in part (b) of the previous problem by redoing the convolution, except this time let x(t) be the function that you "flip and shift." This is a good way of checking your work, since you should get the same answer!

PROBLEM 2.1*: Consider the functions x(t) = 3e−2(t−3) [u(t − 3) – u(t − 5)] and h(t) = 6[u(t − 1) – u(t − 7)]. - (a) To get your mind thinking in convolutionland, draw three different plots with "+" on the horizontal axis. (i) On the first graph, plot x(7). (Don't worry about getting the decay rate in your sketch exactly right; these sketches are just meant to aid your understanding.) (ii) On the second graph, plot h(-T). (iii) On the third graph, plot h(3-7). This should look like your plot in (ii), just shifted to the right. (b) Use "graphical convolution" to compute the convolution¹ y(t) = x(t)*h(t); let h(t) be the signal that you "flip and shift." Your answer will consist of five different cases. Although there may not always be a way to express the answer that is obviously the "simplest," simplify your answer as much as you can. PROBLEM 2.2: Check your work in part (b) of the previous problem by redoing the convolution, except this time let x(t) be the function that you "flip and shift." This is a good way of checking your work, since you should get the same answer!

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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PROBLEM 2.1*: Consider the functions x(t) = 3e−2(t−3) [u(t − 3) – u(t − 5)] and h(t) = 6[u(t − 1) – u(t − 7)]. - (a) To get your mind thinking in convolutionland, draw three different plots with "+" on the horizontal axis. (i) On the first graph, plot x(7). (Don't worry about getting the decay rate in your sketch exactly right; these sketches are just meant to aid your understanding.) (ii) On the second graph, plot h(-T). (iii) On the third graph, plot h(3-7). This should look like your plot in (ii), just shifted to the right. (b) Use "graphical convolution" to compute the convolution¹ y(t) = x(t)*h(t); let h(t) be the signal that you "flip and shift." Your answer will consist of five different cases. Although there may not always be a way to express the answer that is obviously the "simplest," simplify your answer as much as you can. PROBLEM 2.2: Check your work in part (b) of the previous problem by redoing the convolution, except this time let x(t) be the function that you "flip and shift." This is a good way of checking your work, since you should get the same answer!
Transcribed Image Text:PROBLEM 2.1*: Consider the functions x(t) = 3e−2(t−3) [u(t − 3) – u(t − 5)] and h(t) = 6[u(t − 1) – u(t − 7)]. - (a) To get your mind thinking in convolutionland, draw three different plots with "+" on the horizontal axis. (i) On the first graph, plot x(7). (Don't worry about getting the decay rate in your sketch exactly right; these sketches are just meant to aid your understanding.) (ii) On the second graph, plot h(-T). (iii) On the third graph, plot h(3-7). This should look like your plot in (ii), just shifted to the right. (b) Use "graphical convolution" to compute the convolution¹ y(t) = x(t)*h(t); let h(t) be the signal that you "flip and shift." Your answer will consist of five different cases. Although there may not always be a way to express the answer that is obviously the "simplest," simplify your answer as much as you can. PROBLEM 2.2: Check your work in part (b) of the previous problem by redoing the convolution, except this time let x(t) be the function that you "flip and shift." This is a good way of checking your work, since you should get the same answer!
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