ps-4 - QAZDM ( 51’.- ztILLQJWSJ-aingfaft-fi"...

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Unformatted text preview: QAZDM ( 51’.- ztILLQJWSJ-aingfaft-fi" “[4)“: A cos (wot-i: . mournsdfllbwu 3mg... . r$ - , ._W,{é'mhil‘égggggg' 51424619 x; 5043'»; 4&4) _' W... 1:03. ( 511+ 3 cos. 5'1: 417/ 1+) iOpts a) Find the signal obtained by summing KG) and ya), whore, k6)“: 6005(20t+5) and y(t)=§3$in(20t). Is the resuit periodic? If 30, find its period and frequency. 5pts b) Write y(t) of part (a) in terms of superposition of oompiex exponential functions. La) “H: gcmaws) (3H): g§,\1(gaf]= g ego/flOfigg—J A signal-ma) is defined as: x36) m 3j + cos(3t+e:) + 8cos(10t+7r/3)+je“16‘ 15pts 3) Find the speeirum of xa(t). Present your answer both as a table and a plot. Spts b) Is not) periodic? If so, find its period and frequency. . 5pts 0) Thegvaiiabie of xafi) is tinfie‘in seconds. X305) is sampled with a sampling period of '1} == 0.4 sec. to obtain a discrete signal x[n] 2 xa(nTs). Find x[n]. lspts d) x[n.j is cofivefied to an analog signai y(t) by an ideal D/C converter with fSEUTS_ Find. ya). - - 2- a) 55M. wfllfi .__,U+)__: M. .l ' Semen-em 7} owe“ KNumiJg; (y) WJLH £10m gm“? aomioOM—QwaLa; $9! CM “Wig Hz; aaoéfier cork: “NHL (ire-7‘gflik 2:7: # m4 Ox GLOW/5K gnaw-c1»? affix. f“? “fight w \ffl S (X Q ) (glafiacfli c , _ FI’QW.O{GLUV"CLU£'W~’€ {lit/€23 J “9'” “we” 2 / F (AC "' “'1‘ "‘ Mfr/awe. h. _H , /_ZAZ_\ :; I T‘Giefifil M gfiecwm hL] 4?- R .3: ' | 4 t 01. M M-L‘l 0'4 r-— P (hr _: ..— C ‘- 9v.”- 3 flak—$15132 ()1 f O u f éf-r-u era-W v: 1 I.“flimflflncgaifinglwxflg=.n..15_:+:._.Zcos(l?_t+TF/A) +. sin (STE-t) 9 gird “Prue. . ILNaca‘uistLah-ECanhfium....aom?1.h3__$rec1ueng Buoron’rgcs. Perfect . q ,ceaonsthruafian)_¥on.fifia_-.sriBnQ‘.-..__im.. un‘r’rs. of; . .Hcfli... Br’mflH gay-again flour gnaw .LJS :h.....2.co$. Cl.2_t...+ We) .+_. smfia‘trrt)... __‘___ ‘ h, .,__.._..___;E‘_::__O . ...091=.1Z z: LJJS = . =._Zfi$3 . __ __'if17:;i;iii"‘;mm> " 4?: -- --%s=-4 Hr- ._..~.._wm..gmux. . . gufiquxst z; .Zfimx 1.2.g3 .1: .3 . . a; “mMiL-cufimchmqflnlm and c5; Kat;zm__:_:__f iii—“LII” $0 = Q miqgrgsg w ~_"l.,4—_._.\.__...H.L_._.:..:."0.4.1__::~4=-_r_:.h_.._ .__‘___-.?.2. “ii , .hgcmcmigm______. _. 33.. 2.5, ___.mm_m_fl__.______m.m____-_..__.-_..%.Js_3tfihm b.qzcmo_nlg_. ._..___.__ mm_ “$3.499 r— 5 + “.1315; (spurt) + -m.Q351L.Jc;__ .___.--____,H.m..M______ ‘wtrt '—‘3zm "35111: 43.5w: ____.__m____...._ MALE-gi_E,.+nMfiig__mg?3__.___i_-__.__._-__%__. _. ._. ._,_'___k.,—.__.Q__k_—._é._-___k5_=.e___._._k= }.m_______lg-.—.: .__._.__._-___._.. .u .____W_m,.mafl..-.;5_._m_uéw;_gg_g__%__._____..Hq¥_.-=_ci _ “MC-m).-. .3 _~é-.!:5__HL._._..,.,:T§. m-..Zl-Lr—5.._EEC__.....__M._.; ._ .___ . .___ _. .‘—_?(_ED_]_E_X.<_V\T§;].;_»5.$*“.%Q$_‘.%anamrt. _ _ ._. ._ . m... .. . ..... ._.._._.__..,._ . mmmm____M_____¢_______._;M.m:f§.__ ' . “5 A discrete—time system is defined as y[n] w (nw1)x[n]+x{n—1} . 20pts 3) Is this; System linear? Is it time—invariant? Is it causal? \ (H ntflxfgmq+9< Yul—I7 =al$ld1 J: 3>q) (X: .1 T K I q i?( V f ) 75%} (aviyxz w“? 2 “‘“1 “31 _ {bx-437439114, (xlfqflf‘12‘a3m) - A diserete~time linear and time-invariant FIR system has an impulse response Mn] = 5[n+1]+35[n]+6[n»1]. 20pm a) If x[11] $11M} is applied as an input to this system, Where u[n] is the unit step function, find and plot its output. (Provide numerical results for each eiement of the output.) Indicate the transient and steady state ranges of the output. Spts b) Is this system causal? @ 1.,D a. dis-ace- ie_:hm= girstgml,:\:b: authtw-flfigugjsumgfljbéfige M..._.._._-m.....*._,.__ ._ 3933;424:311 m____.._ __ wwwtafipjfiwxglm __ Mann. .. .. ........................... .. ___ . Answ.:___mn_\ mam: _ xfififl 47—9- B‘Eflgr—a 0" “0t mum“ _____M.m.xlxngflhiggngrijétmj,_____.___,.,.._._\ .. __ _.._._._.___m___ . ,_ ______ mEyA-x-wmw : 415': . " 1:: ::_:.’;Tg._1::gQ:“Egg—[.QflQQfiQQQg.;;§.j_pg;;=mx:m: _@M 1.0 “a cum-{gates}.ng gm. wm_lg_ihe_dl@¥£rmm_to‘udim4__mm .. ____n. _____..—5_\Z_Q;L:_3_>§_Lu3...:Lx_Ll:xg_:r_ps_En:;}._-_w... _.m_...._.. .__...... _____ ._Ls_‘t\m-__.sgsi’c:m.Jame.imqumorwndtzfllust1¥3flom_mfimar;__ NQi‘. tinng bumm_.___._ .Anamxr..L:flmc.._m3mg _ or- net firth “\nVfiT'IQfT'; . -. _ ea . ._m____.. mgmmmmasjm_m§3§mm fin}:_}$£:h3"is_ficm .u.gg}ifl3.,_m “lingimn-.. xLLGgrgAE-zén 31);] .. .‘anlucs_.§3hflm55 an.d§h1$$b3..._b5._..m_.uq?r Mmgomfmfii‘LfileLKLLmrfigshmis iima..um57m3-, ....__u....__w_. _. .. mgfiéhigflbg_bguirihmu ....Pgsswflnmugh ...:;55i7m.;. . .. .. -. . . .. : .. . .. _._. _J%3Ln§;;j;-_2§Ln:m1_:_2,2$.\_:l:2n 31%] 11.): [m—.n9.-.-..3].. h... , .. . _-_._-%LCSL_PQ5&.:H1CM13}3-.fthe__»§£$‘fe.m,.:’chegn_§h3¥if.f’ike..flui‘{xfli_b3_nq:. .j. .. -. .. .. ........... _____;_5_2<_En:.qa_:w21erL:mfl:hnag .+.. gbmors]. m... .._ WEh13i£ Biwflmo] .5313 is flat "hm 3nmr'\ont~ 'EO;Winfi .‘Tl'wo Seaman-Ger: aha-l ‘>\o‘t Hour answar, T,“W...-..__._h{fll,;mmm"w- Wm.” .. , _ KEG]: l *5—2-40123456 __:.__‘.w.r.,..._T MM, .. . ,. .. .5 ‘BLnjg-b xin] _--_. _. 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