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Unformatted text preview: ECE 108 Signals and Systems
Spring 2007, Instructors: Prof. Tiffany Jing Li
Midterm (50 minutes, March 14, 9:19~10:003m) a You are aliowed to bring one piece (doublewsided 0k) of lettepsize note“ Otherwise, the
exam is closed—book and closednote" 0 Disclaimer: By signing below, I testify that the work in the turned pages is my inde—
pendent work. I did not cheat in any form. Name: ID: 50 {%+Q§w§ Date: Signature: 
—


— I. (30 points) Givsn (D2 + 4D 4» 3)y(t) = (D + 5)f(t), calculate the impuise response
W) (SHOPPEWB, m2 ; P(p):p+5,m=1. O
Abe); w (7t_>+[lp(D) afﬁx/{FAME} (32(..)\)1_/\1+¢)\+3 I (.A'fUMﬁjw $3; All. / owl/Margy; modes 6 “T / e “3%
‘ m— art ,_ t, I, "rt ...
(‘ ﬁnli)ﬂcle +628 3 J iﬁhfi)zwcf‘e ""362ij ~ _ _ %‘ known r‘n I'frcM
9“ { 3‘9) 1 I COMNLQ‘M 5; W “33’ 9'1 U, 1:”) C’ESA
’;”Cr“‘3ﬁm (21.2»;
2; 914%): 3L (3 “mt” Qwre) ._ int.. —‘—‘“*{:
WEEQ +.3a3t{~§g Mt éeaujfﬂx) 2” (40 points) (a) (26 points) Find the compact Trigonometric Fourier series for an evermlasting pe
riodic: signal ﬁt) whose period is To m 27:, and whose value is ﬁt) = for
0 S t S 27?.
hints: fsin(am)d:c = ~§ 003(am), cos(a.:c)d:c m isinhm),
fxsin(a33)d3: = 31.1;(sin(aa:) — amoos(a:c)),
fmcos(a$)dm = ﬁ(cos(cm:) + a3: sin(a,a:)), EDI meamdm m 717093 “" 1)“ A "Jihﬁ ~ M “721171.: “\wc‘hif. W
{(1)3a0‘9 Z) (Ca/1039141: +5913?” htr
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’7’ '3 “game; @5727, awn/«€754? ‘ “,3. if \_
bn’m O _§rm(fn't)6ﬂf :bﬁiz (b) (14 points) Sketch the amplitude and phase spectra. (c) (30 points) Prove the timemonvolution property: .f1(t) * f2“) Q FNUUPEW) %a><+/5W# [77,65 3. (10 Bonus points) True or False:
CAUTION: You earn 2 bonus points for each correct answer, and lose 1 point for each incorrect answer. (3) Consider = 3(t) «1*» g(t), where 5(t) and g(t) are all real signals. Let
X (m), .5'(w) and G (11;) be their respective Fourier transform,
° iX(w)l W 15(w l+lG'(w)i ( F)
o 1X(w) = 48(111) § 4G(w) ( F ) (b) The Fourier transform of the signal :c(t) is X(w) = j26(w — 2) —~ j26(w + 2)
o we) must be odd( 7‘ )
o must be periodic( ) 0 33(16 mustbeaeemeseiéeieﬁmetim( )
) Facet T ’ X( m) rs Parab hawker/c #00”, ...
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This note was uploaded on 08/06/2008 for the course ECE 108 taught by Professor Li during the Spring '08 term at Lehigh University .
 Spring '08
 Li

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