HW01S12solutions

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

This preview shows pages 1–4. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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' ...
View Full Document

## 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.

### Page1 / 4

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

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online