b09hwk2sol

b09hwk2sol - ECE2311 HOMEWORK 2 B09 Name ECE Box Number Due...

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Unformatted text preview: ECE2311 HOMEWORK # 2 B09 Name : ECE Box Number: _ Due date: This assignment is due Wednesday, November 11, bring to class. Make a photocopy for your reference for fast comparison to solution set. Put all answers on the lines provided! Problem 1 e Signal energy For the following functions, compute the signal energy (show the integration work) and provide the answer in Joules (assumes usual 1 9 load interpretation of energy). (a) 23(t) : t - u(t) — t - u(t — 2) w ’1. < 1 C 'l _ 3 1 _. 8 ,ve 0 0 Problem 2 ~* Signal power For the following functions, compute the signal energy and provide the answer in Watts (assumes usual 1 9 load interpretation of energy). (a) $(t) is an everlasting periodic signal with period 2 seconds. The function which describes it over one whole period over the interval 0 g t < 2 is: $(t) : Se”t — u(t — 2)] l9 2 \ "L 'L 2 b‘ ‘ ‘tf C I _ VX T; 24901 3 (Se +3 ah? (I) a L "29‘ .14: ‘ 2; it a Z ' e 6‘ : Egg ( | ~Q~ 3 wag/5*! (b) : 4cos(20t + ~ 2 603(7rt) Tm mmsaié‘s 2;; 00th Reviewed“ LAM; , f 32 I 2 v 1 ‘71 PX i" ( 3 : r“, (0 mafia? ’L L 2 ’i Problem 3 — Even/ Odd Signals The function 113(t) : e“u(t + 2) is not even or odd. But every function can be expressed as a sum of an even and an odd function, x(t) : 3380) + 2:0(t). a) Find 236(t). A: ,L *7 .- mm; 5’9 ups-n) +2e W JC+2> F 4 s 1 _L I 1 J J 2 1 i ' I L KelL-k) 71‘ I i I T j v / 9 \" w r r I F * " A L w 1 T f L “H T + t a A k I L. i L f i J i T f i L 1 r 4 ‘1 i r T } J T i s i i s g ‘ if ‘ E i‘ ’* f 1 ’ ‘ ' i L—' *7: L l 4 A 1 I T i l T I 4— J .4 4 I L L T .1 T 4 F T { T q ‘ " 4 + r L i 1 i i 1 r 1 + Mac)” L Problem 4 ~ Unit Step functions Write the function 35(2t) shown in the graph as a linear combination of delayed unit step functions. I 74:1. '* 1'r* f* f" ' (ML 1i} x i ’ I l i ; 1 L { quwbi’ u(Jc+\§ ~;éu(£-l\ 4- ?u(t 4) (b) Write the function y(t) which results from differentiation of x(t) by using Dirac impulse functions as needed to represent differentiation over a discontinuity. ‘99:): 'thf’c’r”) 4’ 8(+’+\§~68(e~l\ +Z<C(+»Z) Problem 5 — Dirac Impulse function evaluations Evaluate the following integrals (a) [00 2005(30t ~ 7r/3) . 6(t + 2)dt Wow vi 2 003(10 (.13 r ma) : «z M (4,0 WE) : _ 0.42 (b) 00 2 .[ 5%‘th—n—25a—2nm Vet atz 343 3 — & 8 Z’ til .621 -l -3 2Q °-2Q 3’: 0,6é7 Problem 6 e Convolution by Table Solve the following convolution by using the table in the book on page 177. Note: the * is the convolution operator and not multiplication in this and the following problem. y(t) = [3 te‘2tu(t) + 2e-3tu(t)] * 2e-tu(t) Anya Lam? M4 JianN/o («m 412 m 4&- am: awe-chewe'tuzu +4-e'1‘tumaxe um Jmk ‘/ /0" a Cl 06"? #4 \ c 4 ,x\ 3" te’HWHV 6 “Um I' L e“”-€'t c’ :_ ,_.______.. alt) Al 1, [\L ' «2 +1 gt "2* v \) ’1‘}: I + Q’WT- u 6 ‘e.u(+\; L(evt—- Quy‘é‘) (1.2+W ‘ V L _-t - + (’8 - e 2 —2':'6 “lam Problem 7 — Convolution by Integration Solve the following convolution by performing the actual integration. Be very careful to give the complete form of the solution for y(t), that is, valid for any 15. lZe‘ (“Gout—‘3 y(t) : [Mt — l) — u(t - 2)] >|< 2 e’(t‘1)u(t — l) 00 i t (—e+v\ 2[u(‘cv\\-u(rv1\]6‘ “medium 1? ~90 PM“ 5?th NW W 4%);0 V4,» 1542 For 4: 04L V\—Q9—-yo\ lw+fiflrcjtja fir.“ 2‘4 $-21 HM t>7 we M 44 téhawEQ/mm létéz 4.". ) t" ) at ‘c _ _t+ 26th? 1} (l't+z)p(1\ 5 1 g" “L _/ lngtwc 0’60 '1 l l 1 ’2 o 8(1’t)1 , e __ l L 13 emit-wild,t _ L («(12+t) ; Z 6(1__t\— €14: \ ("K IA . . J) U’m "-1 W \x r‘\ < .. \. _.w_’._—— W 0 < QM : am -eh‘t Q§’“¢lél* Problem 7 —» Matlab graphing Read pages 53—60 of the textbook if you have not yet done so (it was in the reading assignments). Matlab is installed 011 ECE and school—Wide (CCC) computers on campus. You should either find an icon for Matlab on the desktops of these computers or in a submenu of the Windows Start menu. Launch Matlab as you would any program. Once Matlab has launched and initialized itself, you will find a >> prompt awaiting your commands. You can either use Matlab like a calculator, typing and executing each command manually, or you can use its built in editor to create scripts that can be saved and executed again at a future date. You should try entering all the commands in the textbook section mentioned above if you are not yet familiar with Matlab to get some experience with it. Also see the many tutorials that I have placed in the “resources” section of the course website to get additional clues as to how to do basic tasks. (a) Do problem 13.22 in the textbook. Attach your plots to this homework (yes7 with a staple) (b) Do problem B23 in the textbook. Again attach your plot. 11/11/09 11:27 AM M:\ECE2311\bO9\Hwk2Plots.m 1 of 1 t=[—3:0.01:3]: xlzreal(2*exp((—l+j*2*pi)*t)); x2=imag(3—exp((l~j*2*pi)*t)); x3=3—imag(exp((l—j*2*pi)*t)); figure(l); plot(t,x1); figure(2); plot(t,x2); figure(3) plot(t,x3); 50 —% “K 2T 10— -2 10 ——————T— -10_ -15_ 15——-—r -10._ -15 r 1! ._. _| _ 3 ...
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This note was uploaded on 04/21/2010 for the course ECE 2311 taught by Professor Hakim during the Winter '08 term at WPI.

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b09hwk2sol - ECE2311 HOMEWORK 2 B09 Name ECE Box Number Due...

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