midterm01_sol

# midterm01_sol - ECE 108 Signals and Systems Spring 2007,...

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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 closed-note" 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 _ } a9 _. E {queCTraov / we swabngan ﬂu __ .,.I__ ‘2’" DC "fer/n , .9 QHWTFJO idhsﬁfolt:o é; ngﬂﬂf ’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 Par-ab 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 .

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midterm01_sol - ECE 108 Signals and Systems Spring 2007,...

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