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Unformatted text preview: ECE2311 HOMEWORK # 1 B09 Name : ECE Box Number: Due date: This assignment is due Wednesday, November 4, bring to class. Make a photocopy
for your reference for fast comparison to solution set. Put all answers on the lines provided! Problem 1 , Complex algebra
Use your calculator to ﬁnd the rectangular complex representation for each of the following polar
form quantities (a) Sléég :
(b) see/4.9." 1 (a 101.715 = 'TT
{0!} 60 E” A’ = M (9» éﬂ : Problem 2 __, Complex algebra
Use your calculator to ﬁnd the polar representation for each of the following rectangular complex
quantities. Express your answer in polar form with angle in degrees, for example: 3130". (ch 31/011; 3 (b3 3 ,, j 6 1 ._.._______
(A —2 +36 :. W
{A ~: —J6 =1 M
(5‘, 6 + 7’? 1' _,__________————___ Problem 3 — Complex algebra Find the value of each of the following complex quantities. Express your ﬁnal answer each time in
polar forn’n for example: 3130". (al (?+Ja\(ev 53> = (m (2+ 553+51§93 ﬂ
CéLlﬂaXL'S’F‘B ‘————_—"—’__‘“ Problem 4 — Impedance Computations Find the value of the total impedance of each of the circuits given below. Express your ﬁnal answer
each time in polar form as in the last problem. l H Problem 5 A Sinusoids to phasors
Convert each of these sinusoids into a phasor‘ 0 29mm 20¢ +1g°§ 31 >3 Problem 6 A Phasors to sinusoids
Convert each of these phasors into a sinusoid. (a) y: 71:12") 60:30.75 Problem 7 _, System output for a given input What is the output of each of these systems given the description in terms of the “prototype” signal
x(t) when the input is as shown? 6“) ﬁfﬂeE—a 22(t—z>+1f£
Bight438% 260 7 20:): m 7H,) %@ 5 2(3255’91/16)
3%(t—D—A>)/S_j——9 97(6) Z %/+> 9 Problem 8 >7 Linearity
13 each of the following systems linear? (Show proof) “3 2m ~59 )} xg/H
W CMé?a.v~
C, \ ll C Lg, 0N8 b3 7N6 WA)E‘—9 Q(t+i).7r(+—2B C Mear‘mww—Lui” Problem 9  Time Invariance
ls each of the following systems time invariant? (Show proof) (“3 7/9 —%@ x1369) ﬁwuumfawfl‘ 3L1! /A/a c W—Cbﬁ; «N15 ([0) wt) ——§[ 5 \—">7 2(t+\\07«/t23 7i‘VL9» imwf 1N”
cmcui 0W (a3 Problem 10 ~ Signal Properties List all the properties each of the signals sketched below has taken from the set: Periodic, Aperiodic,
Causal, Anticausal, everlasting, Energy, Power. (1)
x:=t«>2e UU) Time in sec. Time in sec LC) 10 (1+2)
x:=t.93te tKt~2) Time in sec {5 4 2 TC x:=t—>cos( 100+ 1.5 cos[27rt——’ 3] v(t) in volts Fraﬂh$fe$ Ti inse. Nﬁ Time in sec. pram {7/413 v(t) in volts ...
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 Winter '08
 HAKIM

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