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Unformatted text preview: EC ’21: T1", 1:19“ I:
I. JlU AVIJv I ' I; Solution to Exam #1 Indicated below is the regrade policy as stated in the course syllabus. Since, the Exam # 1 was returned to the class Thursday, October 28th,
no request‘for regrades will be considered after Thursday, November 4rd You must clearly indicate in your written statement where you
believe an error was made in grading. Staple your written statement
to your exam and either hand it to me after class or put it in an
envelope with my name on it and slide it under the door of my office, ENS 342A. The following is an excerpt from the course syllabus Regrade policy: All requests for regrade of a homework or inclass exam problem must be made
in writing within one week of their return to you. No verbal submissions will be considered. The
purpose of a regrade is to correct any error that was made in grading; therefore, in your written
statement you must clearly indicate where you believe an error was made in grading the problem in question. Please note that if, in the instructor’s opinion, a regrade of a problem solution is warranted, the
entire problem solution will be regraded, not just the part in question. “ring; a “n.1,” eff A WNW u 4:“ ll I My signature certiﬁes that the workon' this exam is strictly my own and that I have not reeeivedv nor utilized any
, outside infOrmation beyond the allowed formulae sheets. I Furthermore; my signature certiﬁes that I have read " I Print your name: ' __ 3 " . , , (Last name) (First name). . . and understand the instructions given below. \1 so Lion1mg; ‘ ; Your I I N THE UNIVERSITY; OF TEXAS AT AUSTIN
Department of Electrical and Computer Engineering
EE 313  TTH (16190)  Fall 2009' ' * ' :msaucaaﬁs “ n I 1 VYOu mustcircle your answers. _ _ : All'problemsieount eduallyr ._ No credit for answers» for which nosupporting work isshown, ' or for which thesupporting work is inconsistentwithvgthe answer given; ' ' ' ' _,  I ’3 4. I ' To maximize the probability of receiving part oredit; show 7
your work and provide arbrieflai few phrases Will usually do) '_ _ 5.7 V»
explanation.of.your_approach. V i i i ,
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L ' ‘ Problem (1); Supposelthe inputoutputrelaﬁonship of ’a/‘particular LTI CT systern is‘ deScribed by {he £0110ng diﬂ‘erential equation: “ ‘ ‘ ‘ I I l _ We) + Hymn? '+‘ 64y(2) = Ma) + xa) Find the zeroinput response y0(t), subject to the folloWing initial conditions y(0) =72, yw(0) = 12». lithe eigenvalues are complex, you must express the solution in the “standard form” given in class in order to 7‘ V receive'credit." “ v _
cw; ETD=5 Wu. law. 64 :— 0 m> Lh’ﬁyi: o ‘ Lam; 4“? ~9 30/ C\$;.329 v,  { 3,, (b c‘ (— Edg I 4— (lag 4. “$5353.63.
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\30, A6716. wrte (I909:— (aahdﬁ'ﬁ ‘7pr etc “25 l J: ‘Co’f‘ WKAL‘du "HACL Sckmgfcnm ' .ipéééwzbflanw , a ' ‘P‘rrobleLni (2) Consider CT SYstem characterized by an impulse’response given by,
, I ‘ V .l + 6t¥ I
ha) .— 4e um
Calculate the zerostate fesponse y(z‘) for the following eicitation . “dew #31429 8((‘\ 3" j M I
" In; MW) .   Lama: ﬂaming—4943
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><¢7~J wt—»E\:c§)ua+\ 4e. ' uti~’t3 Cit ~=> «‘—=9—:?~', gnu: ms 7:,» 9.». . ‘ .ﬁ. .91 1:45.» 37:0 It; . , . \cuXM L( (133 euka3~ Klf‘iﬂ “A ## *w H "W M ’7 A 7 H A# A N E #7 “A m “7326* " ’ Problem’(3) Find and sketch'the even and‘odd'pa‘rts ofthe following signal, ' , xm = mar) ,
, p _ . ; Wag = 4i: u t—~L—\ ‘
To receive credit (1) your sketch must be consistent with your analytical expressions for the even and
odd parts, (2)the coordinates of all important points must be carefully labeled, and (3) the numerical ' '
Values of the slopes of any straight lines must be indicated. ,  , .__._7Vl,;:..__..__;w_r ﬁtw~ﬂ~n .7 XZLAA—s J; Kate: +3 sat—4A atomiih . g
=r Vr'iquthxrheﬂitvt—ﬂ . ' 7*: 7 ~ “A v 7 A g M u ‘ W 7 ‘7 74/457 " 'kPreblyem (4) Find the energy and ’p‘owér‘of the following DT signal, ' ' ' ‘ ‘ 'x[nJ —= sellW] Numerical values of energy and power are required. \ I—nh .
v (“‘0 BEA1:55“
A V in] :y —3 Ahugni lxgmlél C} umil
7 3}“ r w
\xtv‘jlbz‘i '_E?Z V‘I:°¢3 ? CHCu—‘R «ﬂu—“M2. J: “W. —L {@4693 +444qu q " W Hsl—lo misN1 ‘ k U l A l ‘7 376W Problem (5) Carefully sketch the ﬁm'ction'cCt) where the asterisk denotes convolutien‘, ‘ ’ ca) = 527260 * comb(t/4) To receive full credit, it is essential that all important coerdinate points in you; sketch be carefully. labeled. r
5 4+? ( .3 ‘1.) We (3% => k .L,
3 '33 *n\ .39 .YS'zuob =5 WEN); _._.. ' 2 Ar SH: 54MB M=~w Ac “5 —}_—: 3 Mr H“ \
3 ~—
._~ ﬁ‘rﬁ'awglzj '5MkA5A5k ' ,/ "0“3‘47‘5Jrﬁl3‘a *— ambit/Lo  ‘
ob . pagaéfars" —_ 4 ‘ . ‘ ,1 4rd (2» 51%, 9. 4m 77 t :51»), elf fi 4" *4 " ' ” "' "Tr“C 4mg Liz). "tux—Ar t“ ‘ E‘dK‘A‘J.‘ 4e» 20 2=+H<sr<bm ~ h:ewe 4* 3/33 » ' ' lgtg'mivggi: K
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’ whemﬁn:o"l=thx_t3 :‘lévw
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'TH'EEND ...
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 Fall '07
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