Midterm_2_Solutions

Midterm_2_Solutions - BME 513 Midterm #2 4/11/06 This test...

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Unformatted text preview: BME 513 Midterm #2 4/11/06 This test is closed notes, closed books. No calculators allowed. Show all work. Write your name on all pages NOW. Include your name on any extra pages you may require. A table of formulas is included. Name I have neither given nor received aid in completion of this exam. Signature Name 1. Show that time integration of a function x(t) and convolution of x(t) with a unit step function u(t) are equivalent operations (15 points). (I) Twine WES m‘H—GM 0'? O\ ’pLWkCH—OM X (It) t 3 1%th t U5,“ 3 Eu VifJ/ TYLLMS‘i’O Wm warm—m 0 HWLE WLCEI “Li—‘77“ @ LL”) 1; Mao) EL») 500 @ Co mvotutrm of XCJC) WFHA Wt) Mt) 7% um) (:3 Moo) - UPC“) : xtm- C“ M”) *33) : ESQ—W) + "(T XCO) £3047) JR} Hath 9“th Pwoem‘g‘ r. H @ xg @ 0km can-\oiudeai‘; Name 2. Assuming that an LT] system has an impulse response h(t) 2 u(t)_. find the time domain and frequency representations of the output when the input is (40 points): @ M0 = 64110) @ x2 (1‘) = 005(20711) (33 x30) : cos(20m‘)u(t) 6') 354(1): 5(t_to)—5(r+to) For inputs >90) and X4(t), sketch the magnitude of the Fourier transform of the output. Clearly label any pertinent values (10 points). @ L193 Wm aways at we) owl act) _ m Xfig) :: if: I H'(S)‘— S a J— -J-— = (9 3H) ; 1% i 1(8)} : ate) r e—quti) Njefml-JUQH USVME} We Pfopeflh ‘GVowt ’ rt St E'tUCZMlZ : Sate Zolz :. Q *8 >uUc) ’00 prelolew :L: “scram-ti @ Hm) : ngthS‘L—J :J {W Wm : WWW am) W}— Name . a. 1 q. \H(w:10fi)\ : ’\S 13921.. 1 “\f 1+4?o:r Gm)” Ll-OUTF Lug“ :flww lon'fillo) Amwé"? : WEED" l ~—QO° 344g): (_ OSLDJDTT-t-QOD) -‘~ \I ‘35: {MCD-O‘T‘E) er"; Yup) : Wm” 5n LSCQHOM —$Cw—1DTT)J L W; "——// ——-- .. 2/ __‘ x : ® Ms). Hts) H mm, 3/... MAW $8) l 850:): 1" H3691 :. g“ Smclofit) Mat) "’7/ ——-—~ @ muchwcc): S“ gate) ugz) At- :1 é:('t+tn)ULL—C)g\t _OC. Name 3. What is an adequate sampling frequency for x1(t) in problem 2‘? Explain why you think this is an adequate sampling frequency. (10 points) I NEPM —‘e 0% m; wowmnm rie‘ *1“ \OO " Mm woay'uMe' Map; +0 0~Ol . \JP/Ezonl 1:; \lgrds=0*0l Ciprlmrflaw) DOT—WOO Vomit/S Of : 139%. '2, H32. PM qubucs‘r SOJA—‘Dlmg {,VRCVTKK'D he. SahI‘FEL We naeél .{S :D‘le;39\ H1": ___..._// _________ Name 4. Sketch a sampled version of x1(t) in problem 2 and its corresponding discrete Fourier transform. Specify all pertinent values and their relationship between discrete time domain and discrete frequency domain. (25 points) l N £5 :3th cm pwblw'ig =—-:> T: = 0.03 gecmol mast) Jr .Q °—_ox0\ :5 To :. QHCE‘E : M000) “Kl/fig“ mam; m’r we Mom "on SocmplQ Query A H2— 7“ mem\ “(/1007 ...
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Midterm_2_Solutions - BME 513 Midterm #2 4/11/06 This test...

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