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Problem 3. (C02) Given the signals x and y as shown below, find their convolution z = x * Y, provide it in case/branch-defined form and graph it. t +1 te (-1,0) 1 te (0, 1) 0 otherwise æ(t) = (За) { e-t te (0,1) 0 otherwise y(t) (3b) Comments: In order to compute this convolution, first express the two signals as a sum of weighted step signals and use the convolution's distributive property to simplify the problem by ending up with having to compute simpler convolutions. By the way, following this approach, the final answer will also be in the convenient form of a sum of weighted step signals.

Problem 3. (C02) Given the signals x and y as shown below, find their convolution z = x * Y, provide it in case/branch-defined form and graph it. t +1 te (-1,0) 1 te (0, 1) 0 otherwise æ(t) = (За) { e-t te (0,1) 0 otherwise y(t) (3b) Comments: In order to compute this convolution, first express the two signals as a sum of weighted step signals and use the convolution's distributive property to simplify the problem by ending up with having to compute simpler convolutions. By the way, following this approach, the final answer will also be in the convenient form of a sum of weighted step signals.

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 3. (C02) Given the signals x and y as shown below, find their convolution z 4 x * y, provide it in case/branch-defined form and graph it. t+1 te (-1,0) 1 te (0,1) 0 otherwise ¤(t) (За) e-t te (0, 1) 0 otherwise y(t) = (3b) Comments: In order to compute this convolution, first express the two signals as a sum of weighted step signals and use the convolution's distributive property to simplify the problem by ending up with having to compute simpler convolutions. By the way, following this approach, the final answer will also be in the convenient form of a sum of weighted step signals.
Transcribed Image Text:Problem 3. (C02) Given the signals x and y as shown below, find their convolution z 4 x * y, provide it in case/branch-defined form and graph it. t+1 te (-1,0) 1 te (0,1) 0 otherwise ¤(t) (За) e-t te (0, 1) 0 otherwise y(t) = (3b) Comments: In order to compute this convolution, first express the two signals as a sum of weighted step signals and use the convolution's distributive property to simplify the problem by ending up with having to compute simpler convolutions. By the way, following this approach, the final answer will also be in the convenient form of a sum of weighted step signals.
Expert Solution
Step 1

Given signal:

                   x(t)=(-1)t

The Euler identity says that

                     eiπ=-1

Replacing (-1) with eiπ  in the above signal we get the following,

                  x(t)=(eiπ)t  x(t)=eiπtx(t)=cosπt+isinπt                                          

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