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Material Type: Quiz; Professor: Ebel; Class: Signals; Subject: Biomedical Engineering; University: Saint Louis University; Term: Fall 2007;
Typology: Quizzes
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Instructions: This quiz is OPEN BOOK. You have 25 minutes to work this quiz.
val.
a. Find the coefficients.
b. Plot the magnitude and phase on the plots below
x ˜^ ( ) t [ – 2 , 2 ]
x t ( )
t
3
X (^) n
Magnitude
f
Phase
f
over the time interval seconds. Over this time interval, these basis functions are mutually orthogonal and each are normalized.
a. Find the Generalized Fourier Series of the signal over. That is, find the coefficients and. You may assume that the basis functions are orthogonal and normalized.
b. Plot the signal as a point in the signal space given at the right
ϕ 0 ( ) t Π t
= ⎛^ ⎞ ϕ 1 ( ) t^ Π^ t^
x ˜^ ( ) t = X 0 ϕ 0 ( ) t + X 1 ϕ 1 ( ) t x t ( ) t 2 = [ 0 2, ] X 0 X 1
ϕ 0 ( ) t
ϕ 1 ( ) t x ˜^ ( ) t
