HW01S12solutions - GEORGiA INSTITUTE OF TECHNOLOGY SCHOOL of ELECTRICAL and COMPUTER ENGIMEERENG ECE 2025 — Spring 2012 Probiem Set#1 Assigneci

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Unformatted text preview: GEORGiA INSTITUTE OF TECHNOLOGY SCHOOL of ELECTRICAL and COMPUTER ENGIMEERENG ECE 2025 — Spring 2012 Probiem Set #1 Assigneci: 94311-12 Due Date: Week of 16-Jan-12 PROBLEM 11*: Convert the foiiowifig {9 130131“ 11231111: V {a} = -—z {c} = —: (e) 2 {6,—4.5} {33) L = {5 _j5)_2 (d) = (fir? {if} z = -(.2 ~13}: Give numaricai valuas far the magnitude, and {he angina {or phase) in radians. '?T (a) 3: TreJ -2 .7.— -n do) gzg’s‘JE-e”) 233—055 -21 cc) 5,: 2-3-13 -13 7: 351 (d) 3—: Ore”) :We 2. . 5 _' 35 ., +0.,“ J o. 64 _ 3 J m 27 ...’_' :_5(i—1— :7,S€ cash/7J1“ 7 5J5) 12 . . .60“ __.. I. I 7é ' - J m 5 _ I J (at) :..(4—q—‘);z)= 5+J12=I5€ "-156 §3ROBLEM 12*: Caravan the mile-Wing to rattangular fOI‘fll (by using Euier’s founula}: {a} :=27refi:‘7"’13) (c) z=—zz£(29¢zi3} (b) flaw-“3)” (d) .22284—132} Give numerical values for the real and 1111a ginary parts; - F, . CQ> é: 2W3“ ‘J? = 7r ’JW j 277? _ 'lT r — .. T ._ :5. _. J. _' .1 _ \ 60% 5— We ——Tre ~—W(2 Jaw—2H5} ' ~ e“ .rlT Cb) 080 gaff—in?) = _? “325 2 —'5T 5,256Jll:_3€ i3ROBL£M 13*: Evaiuate the faliowing and give the answer in 130311 raciangtflar aflci 3301Mme In all cages, 2153111116 that {he compiex numbers aye :1 = —'1 — j and :2 = Bejmwi. "l '3 (a) .21:2 (3)} 2;“ (C) +2371 {(1) 53;" (6:) Ezii’zzlz: Note: :2 is the. “coajugate” of :. Part (6) i3 "336 mag};Wage-squared, which can 3130 be wrifien as {he product of the mmpiex number and its compiex cenjugate. . fl __ ' fl . 571' 9- - J a 2 ~ J 3 _ — 3 m) 5.5z= twp-(3e ) = c-.-J><‘7e J—wzeJT ei - 77)" = w em" = 950.36%?) +j9stwZé _—; -5127421-1 (2,2?4-2 ~2221 ,_2_ri_ 3 - -M«2 I -—— _ was} (aw) :76” ieJ =g—(—;L+J§—) H :7 :_. a 0.0556 +J 0.0‘262 cc)*"—_ .L-Jg LLB—-5 Ea. 3‘I+};" I+J+ae :‘H'Ji’aéz U2 ‘ “((+6) =—o_33;; .4.) ¢_2.88’7 = /€a4é €32 [44.8 J 3n ‘"3 ’3’?” ‘J'i r F 5%" C)j§f:'3éjflsl:%e _€3=__;__128 PROBLEM 1.4: Plot two periods of the following sinusoids over the time-interval -T E r E T , where T is the period: (a) A cosine wave with a period of 6 secs, an amplitude of 2, and a phase of «radians. (b) x(:) = J; cos(0.7m — 0.32:) (c) x(1‘) = 3 cos(2 0:1"(1’ — 0.02)} c6) ’Xl-t>= 30m (297.- (t—om) T: 9.1 mm PROBLEM 1.5*: The wavefonns in the following figures can be expl'eseed as : C + Acos-(coo (r — rd : C + A 003(m0f + g5) : C + Aooserfof + 95) From the waveforms. determine C, A, mmfi), rd: and fit. Choose the value of fit such that —a' < (11:: 71'. Make a careful note that the time axis is ill units of second. @) 1.5 1 .7 0.5 U -0.5 4 -1.5 . —0.01 0 0.01 0.02 0.03 0.04 0.05 CR) T: 3%: 12,0 gm 1%: [2° w,=2497r '6J=.o $20 C20 A=L5 ' (b) 0 Di AAAAA _ ,2—aoé (b) T: o : 0.02 gm 74:50 HZ w.=lDDTJ' ...
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This note was uploaded on 02/07/2012 for the course ECE 2025 taught by Professor Juang during the Spring '08 term at Georgia Institute of Technology.

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HW01S12solutions - GEORGiA INSTITUTE OF TECHNOLOGY SCHOOL of ELECTRICAL and COMPUTER ENGIMEERENG ECE 2025 — Spring 2012 Probiem Set#1 Assigneci

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