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Unformatted text preview: Name Exam 3 363M CM 1. (25 points) Finding the energy in a given bandwidth For the signal x(t) with spectrum shown below: . _ . _ _ _ _ _ _ _. . _ . _ _ _ _ . _ . _ . _ _ . g O
100 £0 60 40 20 0 20 4O 60 80 100
Frequency (radians/sec) Determine the percentage of the total energy in x(t) between 20 and 60 radians/ sec. R AID .no '20 L”) Sro
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Lawué 1" 810 q: i 7f? Name CM 2. (30 points) System analysis with the Fourier Transform
Consider a linear time invariant system with impulse response given by h(t) = 3—sinc 22: 27:
with input x(t) = 3 sinc2 cos(t — 3)
Jr 71' The output of the system is y(t) . Show all of your work and draw a BOX around your
ﬁnal answer. a) Determine X (m) . b) Sketch the spectrum of X ((0) (magnitude and phase) accurately labeling the axes
and important points. c) Determine H (w) . d) Sketch the spectrum of H ((0) (magnitude and phase) accurately labeling the axes
and important points. w 2'3“)
6) Determine y(t), the output of the system. Z I‘ 3
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The following set of questions refer to the signal below (a) What is the fundamental frequency of x(t) in (rad/s)? (b) Find an expression for the Fourier Series Coefﬁ
answer as much as possible. cients, ck, of x(t). Simplify your @ 7; .5ng w” 7 7:2 ’ r 2
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signal, X(co), is also real and even. (7/ a m i ’33 K m new
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This note was uploaded on 11/04/2008 for the course ECE 300 taught by Professor Throne during the Fall '07 term at RoseHulman.
 Fall '07
 Throne

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