Consider two signals,andx(t) ==02t < 0 and t > 30 < t <3g(t) = e-t/²u(t)(a) Compute the convolution of x(t) and g(t), then sketch your result. Denotethe convolution result as y(t).(b) Compute the cross correlation of x(t) and g(t), Rx,g(t) = x(t)og(t), then sketchyour result.(c) Compute the cross correlation of g(t) and x(t), Rg,x(t) = g(t)ox(t), then sketchyour result.(d) Briefly describe how convolution and cross correlation of two signals are re-lated butvery different.

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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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Question

Consider two signals,
and
x(t) =
=
0
2
t < 0 and t > 3
0 < t <3
g(t) = e-t/²u(t)
(a) Compute the convolution of x(t) and g(t), then sketch your result. Denote
the convolution result as y(t).
(b) Compute the cross correlation of x(t) and g(t), Rx,g(t) = x(t)og(t), then sketch
your result.
(c) Compute the cross correlation of g(t) and x(t), Rg,x(t) = g(t)ox(t), then sketch
your result.
(d) Briefly describe how convolution and cross correlation of two signals are re-
lated but
very different.

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