EECE 340 Notes Cheat Sheets, Spring 2015

CExsye. Cheat - Shee wee FON ae _—_,. - : oy Ye. be thee te TR, xGeneral iy feed Bina, Y- (apn) FER. ys } an +Pormtel : Z£ (MAI) > —— ae ®K p «> fs0 ~ rad beclowid Lo Te HEB yhrde pmule} [pcr neeange , pire -odinse, prez ap. 24 r 2 ey! me thear ey al, & oddfoen Xe Ing- 4 Txln3 +%L-n3]J » wht= : [xIa3- ae f-n7J . A) shove ese exist prove been ey ; m ; ton “mosk ted by Mdockeon CAEP. eg as il ” mate » ae = spect —* N me ee ie xenti) ; lity fo find a ortence) + Taylor (vt) Xe Zls) x7 Ig (&)= ns = C0 a + li-w)-? 5 zn) x". > . 7 cy » @%s ax 7 . tog Lex) a Ey! aXe md Ase . a n = aoa Be * Sys fae x ' w COGS *% = a Gis 484 Caan) | ° (aay: oat : oan Toapulge Re ying> £ &La-<], + tmpulse Kesporse, feed Beward (rely te have ErR . else: ( Stele Hined-WE), +® BEG eqn: plvg Blnl fee «EY 8 Find. ch. « -_— a Ta] be x ae sysken Kachton —sy @ BK dacgean 5 baa, > i. ws Tylor expansion, Hins> Z ffo3 W (ocff of b” ish la]j ti. patiq] faction expeasion +e chagge tafe paralle} <tructo 5. (use rowan locks + Taylor repeated rests) | i convolution of findamenh| senes blocks _ Dat fosminih: “ade ae SL a LA © 319 Fos sutputs: sus. m most have two conivagle. co lex toots —4_____ ee ae oF ~ ~ enjuge . ° Gene b) (towed 0) folec's Rerwvlas esx: & +e » SIA@= <—_£- th pal Bal Aachras + Knew, blocks i wy * te €ind kOnt , Fin ding Ples B eZ" -sfind fools Go poles. Bok cate) foc molbipliers— My 1372 & > prs pe, -2. —o (EFree tot [Ci -20) (1-20) ) Conaples Siyrals Si nals j JO3 = J 03 +5 Yy. &r3. 7 Derive eyptessions fr real § tet egihaty parts . + Partie) fachion “xp aston oy 2100 412.0% ~ 2l-sa) (i270) afjA_ , 8 e aN #7 - - =— + f, 4-4% -pt 4 4lixdoy line) (i-%o) 7 EMI® U- Kay 1 a ae irre ' ' ' : ; ot * (ED [nog of safe CU) }, Yognt fe > oF C1-%0) | tp, = Xp 22. 3e fe deste " $3, yl, -->goh IR for >1 poles SY cecvmence —> vse dé eqn. ty get yenctal Foran —n prove boy taduchion 529 For Cad = S(nJ, ————————— a) Tyler series > Le dcoye F asmo* — _» fad biol by corté Om expanded bra Aro 3) Retorbubion mcthd, —— d \ ‘ z Lard) oo weeny aresys OSS: : C— Cpeeyd ‘ ( - Cpr ed / 3 (ea) Uns ah Yond —p partial Racking 5 yse. Fin damea tal blocks evpandosig Taylor iF neces. U Take E-—pe 8B v-mo. ce _ za x _ 4 wv _ — os x. ra mo Mat, => yh} = Zu xfa-1) - Z an yla-e] : Z1% of bro ConselyH@A (FY) Tn} = Zz KIKY y(n-K), Conny bHBE] eaGecrsPilC, At th bu Te a . 8 Do the Hath (skp Fachoas change bounds 0 2). | yay oe a ga Cy ~ > compoting, ’) pbb; 2) Gtaphrewlly 1 Flip —» Slide aoslt badd «Kx Yad. xed qlop (erg) ce? to Mis 6m Cdr Iy a —£ = — ————————, 2-ta Ain =) C s | l KG@ic poe ain3Z ~ ROC fre€ sh £ toa ber’ ey Bike 8 Roc: check ‘o' & ‘00! then other valves far Finvk som ~ => for lgtis 3n Do st. had ¢o ° €RoC. afer ‘oe a dn fo oh wh3 ™ . ¢ pete ¥la)e 0 oe el) a HL BF ale Pt 107 ext e -—— Thea ee checK 200 - > Fintle doration: CG & check o F00~ ven = Cight- svded + extends eohwat ds it rational: wouleraosk pole. extendiag ovfwald . i favsa! + one R9C). as tte sided: exhends caward » BR rmbinar xlz):_anecmesh pole exheadhy road. (2 faatt-causaly © € RELI Repel hes Sp ee ae > + feal shifting « *Cn-N% A» X(t) ad RoC, :checK o £00. x (2) | ze 9 a + dinears'ty { a, xfoD +42 yin} —m a M2)e 2 Y(2) — ROCe MROCy E ROC scomplee sh€bs a cin) ~> X(%). Roc = tal. ROCy . + Time scale +, X£%\cl ~» X iAy ee q 9 — Ceverse 5 x C-n)} ~» Y (2°) Roc = sce ZERO, —» $e ROW oll, b 4 am yon a«{n) > -2 Skee Roly a , : convelutions = KY A> XlF)-* V2) Boke NREL CROC 4 Goajug ation x*rad as xX"(2) Roly . sSiemeubon 1 Z a rmuhion ¢ L*EeD ~» > UR) XCnJ ,- f z Xleda, D> wivitil Values xh L vey ms nd Se Final Valu - a a X [oJ = = (2-1) Xlzy . fable = at ( tohea mE ILIAC “inp == + Sing» 4 € oe ane (- we" WAS 1 No B-hans. 1 SENT me G53 + Slant —-» 2 a ¢ ohh bon - A» zsyb (etsy + a y4fsy —» ‘ € izistal. 2° a2 es +1 ' so (2- ¢0sb) 2 - fo + ~a°yf-n-} rl \ « fai ctal. fates ~ x pane la _ 27 azcosb+\ —_— Inverse E-twlS we careful f- ulnl at the end —> specrty the $ \ vse pails & pee. aSqnyloet ——= so xmage yaa Br all values 2& A~ np <cla3yl---3 (delererhed by reords of Z) . 4 nh Wy Maley g AMIE —aefase (HHS Oe Ce Soret nu ae %1 fay Mt ak NZ. Xe InJ eX fa} qear. Unilateral hans . ¥lz) = E xlo3 eT (XOXe t cassal 4 inital condrteong . # Same propetes @ yet x Inewy. SS Var ZY Klay — exh) BEV - --- gf Vive Fx laew32” celeb eg? + elweBe exCnerd Be — <u ost = pe Cx&3 et «eines a“"4---J= 2" x92? sreOiTS —— 4 THANE txtwyoe - = Whe ade -= MDE =o ( ¥le) ~h2°-xh FS - =~. = Ew} ze" 2 the form abort - ) — 2x fw-}. ~ me, Covsality syste 5 causal sf! ? 1~ hf es cavsal Wao hfaiee - 2. dH. ear yCaZ depends 07 previors X £y - 3- sys. fa: po" E ROC ‘pet conkiy posthor pers af 2 pyyiy to won't dvege— Sk bility ; (kiat] —»0 aS A Hho E> UC CROC . \ tP causal: all pales ta QOC Sae all paks most hove vel <1 P dable sided: ph mec § qs cckile ~ 0 wel <d , WH DL by blaze Fu, yR) uid + Pins GS af-n-1} Ces msde RO & q's outside}. whea sys: FA a we rational Gs stable - t. Beaded Work wovnded ovtpub —proe ANH EeS DS inthe y= FS hfer xfa-KZ wk bounded tape 47H KMax . yin) Nox Ebcey > Zz AGe% must Sefintte - 8180 Stable Stale Space. te evalvale ovkpuk +e)- Behe 503) SEa3 ~ evtteak& Fobure cpols ay LX aoe Sia . Stony —> Gai (k= — ss Oe a r fe Se > OD \ stay £Y \ xf. j { I t ~N S>. 4 | ~ N (2) ty Su toin) | SuSnri ° -~-—--*O 4 ° ane v A =< ~+ 12 ~4, J v t 4 fi 6) 9° _ IS = (by baw, boa-betnr ,--~, bi bo dy) Sin - be efa} « Yr Sun fan}> Syl} -- ~ Qln3= Ca}. Sw fae} = by inspection F Oy SLA - Gyr KIA) -- —- -% Sw ta} - Vyfny = by mspecheas ou etipe—— 4 & Se fa} be Su fans — subshhk exp. & Sufari] . foget y WW : ry Sar] SASCa} + & ia} > Starid= A sfo¥ + ate xla-c} , Yty = Cstaz + Daz. ) ast Y= CA S34 £ CAB Canc} #Drfa) , 2-HaasQu~ Stayz Car-ay' @x(2) rk CO = — = ?. (Cis -! 2 ve ~ Sy ves < & (ar-ay'B 540) X(2) te find poles check (@z-Ay' 22x. a ; Y ds — an vee _ , r. ae At ~> (grea) = Co (22-4 —> -A) are pole, rom NS me) atapay ame eehdee A eee Ee —_ det (@r-Ay= ay hy —»reots ar peleg. . a fev sal Si ced Mm lay Zsa “ey. ( Joilaea| Nobe yEnerz msy laud sayin z= xfe). ee ce (LY ey 2 6-246 )-3 C2 Fey- ey) 2 VO = XQ) XG) - : Rey © BYET “CEE eyady los Hse re Ee Soe a zsR ere _ Lae Continuous [Me scr ga fen” art always § ST mole. ind A ond . : it, oss BH Impulse * ‘- 7 a ee {22 se - % w lk Be AY a 4 He UL % « * ~ a : I o We &.- » Slt) is distribsfion ; fhe % 2. __)_s .. a ( S: 70) _ fie. J sofin dpe fic) = (3) a Su) ; in ot Af Susdee § Oo tM, t bev eee = | . Fog ibs fox tee — J sine ae it sul) . o| () G4) = 9) SL4) - . oe —_ 4.9 ug | ; ee 4 ie 9 OY) Cte o\ > SLE on a yen - Sta ht-tolde p mma os 2 oe it jel as =A al dthde = iggy. D+ 4+ SAILS gute) Sttte) ‘Sapo ‘BEAD | oa hol yas: Zn - Pia, fit i” rage a \ | o Operators © Feat wee he che - - - pera. : fe ta dey tation, _ Lands. . hl) = 2 Coates . ef ults a a df fereatia tiod . Block Diag . At 7 2a | | Fon domeat Bho "order - <- - > SR: et alt) . Find poles= oe A — s' | Betfer Qatalle| a i oe, poly us) | as for cc Orks A ‘ re ; k Jecoupos‘tion es reer — pel) ct ull) - e find ols . Cossolufion. ‘ soper position vy lt) * SCt-to\ " xy U-te) “be a sigan Heb combiqubva’ oe @ gig" : thd ‘ Taek kiecila | -fiip ove oF the cones «take ceftaeae tro” AA | hie beck Hil hea S 20 ove rkep. ot y = bake infetvals He account Se chaages in shapes ator variation of wegen t\. fr) -u/hu NK 12, ced (E) 2 alter) ult T) . Limifs of the integral afte. i- fixed from fixed curve - - varia Sie fom slid ty Cute + a _ a —— a Laplace “V imaashrm Fis) = Ste dt - 4 ROC. set sh SLitalle *ldt £90 — gah =e no 7 | ve dae 1 Uaillerd Yess fue ge © ROG, oatip. tht) ~ é Xs) PCy Ste" H —Duniqieness 0 Cav te | Inxlty e0 he bo > §2e3 ¢ ROC - | oetty ys X(sex) Rot hip by -* (- ay — b a wl uf OS: + Juclyte Be ua se aid. "¢ xl) KES) -ROC. Phen o Tey-Sale Sa -.- ST ey. > % (4) ciguh-sGed > ROC aights ad Rol. tes 2 oy} , double sided ROC onc stip - ool ™ 1 Soitial 4 Final Wales —— el { au) Faile doedag 2 Coker BLT. ; xt ro sls). Roc, CROC © if lh has to empslse at zero - » Xley cationgl —> ROC determined 4y pls. faode om J xls) fev arent ~ (ot) = & 5X6) £14) cavsal > ROC, cight-sided 8 foo} € ROC 4 a (ime € | BCE) acrli-rausal-7 RoC lef-sided §U--7EROC | * (x yu) aon Xb)" oXls\ (ranescwrc’® sf ~tt) Peet? ae | lat) ~ “Ma axPOl, nelne) = — oXls) - at y) hain — : a, ee _ + ea 5 > ( i, Saffial Coaof hens, site?" a-t eae A ry bor S bars” this the Zs) aoe r = e Fh we 79 (5) = sf Me i #AStQo ad tea an 3 Net * | + BSR FG) be col sf - aR | vr Eigen fas & Valves BS csqon! = Hue &” { Eo atyec** {a [}-S yok Hen). poseee | yShele-Spare--§ (. SF) 2 As) 4 Qxlt).. . Yih) SU Cle e-— o\ Sly... . --—— = . ---- oO bo Buy = Estey Ol ; sl eo ae =29 Ms, 4 ~ pict aT Tt { ‘ aoe SU Y , : ‘ ‘ - er} | “ao osc — 2 F be S febilf bsoldie. om He Me - 5 fbf abseldle, hia 7s oatpak gees bo -gesb : TH, st. [at] K Ny. ; ; ’ fir ne capuk § ae 73 Ny at, yl < Ny St - M4 aii te “ny intial condifia oo, “> absalofe . ¢m © Tm daplice Doman! == ws axis CROC. REBPT CO j Ref teh O° | ties ann ED>o E<o ~ cttaulh - ba (ty. Roth “Hcwita- Ho. fr’ Caoser| Systems. Qs) = aS" HiqsSh- tases, > F meek ach ke es. aot stable. iano Swtshtle UF reves, Ee vated cow-leagth . : a by = hal Oa) Garter ‘Ga s} (px ‘bales atet ~Ba-SPQn 2 Baye t - ' | dook of £* Colas Perec. a» elemey|s —>prles on fr-awid. "8 4 = sign Charges > pales mot om LHP. => Stable: No “y changes Nor Zefo clement fs NN 1 Column = aol fables ' fect (ak) + rect( bt) a cL ( $04) 1 ls . | “< ) -arl 4) | ult) Ys Ristdo sta ) 1, <-?ie at ¢" At Reiado | on sintlies tT 28C6)~ S(e- LY rai] sit! C’eoew Fence r 2 fa a ye i a _art “ (i) oe Taste) Sees) StI] in bt b reside | ogee a zy Sinl2mid spe of 3 Le cap y abhun) S etre” gu Tle AY bos « enée a) é “Se ft _ a pe a Sd Spay Joo ET baci SALT. ne “ Patent nee ene, Lem) Sqn le) p 1 646 ae ' ny ¢ | = Thee G—-> i, . | > a NA ‘ ; = — es —Latl P i - tye Bo (9 kein er WES l= Ui ve Comblt) j Hee mech Sede farce de | Kisaye F Lr lj Bay G(r it +), FIs Aime ont eae, g San | Ce Xe (j Pee)? ‘ \ ri . | | nn J fiv4 ) ‘ - Goaloge “Sakegte nO 5 G Wei dy x z Res | erat, 4c) $ 4 titide ROC ples. of Fease «lar 2%! dbase aside C+ fad Res If, a! s Res 146 a Gs fa) = & Cas ay Ca-a)"! & Ge th, Caede — a is pole of ordef’ on 2 #) Resif, al ~ bo Ce-a\ fez) . tO z2z2!'oe2 | fire oo 3 eye -a\™ * 7 | ) Resifal = cai ¢ if aa 3] . Hey ~ Ze LB BIE aadlyhre ‘ a" se 7~_ Me) ee petra oz. | Pecede find Flvye Xl2y2"" cars | aie db Reo —» he pales ~ devide mberoals oP alerk~ Fez) ~ wa | ale > 08a bub a mebinc + change mod ro ee _ a =a — — Sanna a We keys 2 Ole fry Count c= deeomnintor alnnys on ths Bom — S=—._ eh we ra dprle Fdeyne 2 wh7~ L- (42 (nara refa Jolan)e"y Ca) | 7-24 aie Br ao 0 pk of degte. (-04) 2 op ba) ~ - tf td on a ia Yam Aathes = ga & Tt fir » aS & i aot 2 annem: a* (ent) aA ¢+2> = Car) A* ufone -Can) a ulary - take vahes of 4 & fnd derivable. wurth lmih g End a ceewtrence_telabio = 7 zune > fle) = — < ——_ lie ae”) (e-e)™" = s ' a* nye Ye wre ame entire oe ( a : . j 4 : Ke; a*u lay rat] — . = (at Kaylan edt, ( i Jara ff) R>U_ Ft ie a~fuye ae ade: nF atlaseo —- AdxI-K ow other thang . | Cae) F amuko —> pelecto sferdee me-(aren), | ~Res(foye —— SF lea\8), oa. | infeed = ctieaye do laze | a (aya eLay*a®: met ae-K . / ©) % lue\—-- Lena\a" nat-n , | 2 (-y% (en J aX au Cue} — y z ™ Perye 2° a4 cassa( + m% | | “ae hes (Hr Yz) 2 2 2 wh «(hy ¥ ean el/y ) me, west“ = pha” 5) ae Res(¢ -4 tart? ° w40o iW) = ~ (+4) fay . A ee — lee. cc 2 ake er met otgey is of interest . Gt cn to: : pHi - Wee), = 43: : . ovr — Hye) on aoe Z Hye i phase . a ae) ; - - He Jls I] e peace) | Pots, KX (3-20) (3-2) - ~ (jos _ = : Bode ; a Hess & Spd hee ‘i <i 1je-e y" | Zig) 2 Le 2 L Wet) <°L Wje-pe) | Dido deg 1 Hoey) = al © 29 de Lag ye-8 = Za0day Wy =p,l we * ityte « | a) LAG) = + AY oe-2) - ZL Gi). rahe’ Drawing for ave zelges! mag: af 71, Sbpe pncrense. by 20 fecal : sil woh "phase a? ot 2p) slope incheuse by 15/ deca de - oe lasts Lent, won] | So x ree of cee) a at fo 2» slop decheuse by 5 *Jdecade ") chiage F go...” 7 | _ oe re emey: at F , ‘slope dechecse. by do to Vien be. , itha pe ie Eo “phase afou Pus slope dectense by us/decade f effect (asls [oy eh] ast cep « y ( ON ah to PL yg, sti ee, te) “leeds. chee. iP 96 Fores’ ea 9) —> XG > Su etd. os Xess, a £€ 20 oF ¥kc) incla deg | yY- CS — | Hhog pues als iy Lo» et diy. ; is | fy impolsive petiodic.. | Tp! lt. he 3 god ty Fast ulees \ wae aoea mpl { * Moet» XGjtmema) 1. = af MGenehs | @ Sty —t. aid an Mt ede n> Ft i fc a : e, ts ite 2NSG9) wee only — X59) Le Xp) = fade J ] e we LFYK =X) * “Zz . 7 ' @reatlp’ as emc(2) ro 5 “Rar Lal) C—— | by nel. “K a KOS en s 3 ko at\\+ ) 4-H e xl 2 XQ) ts Rea). | poeete~ as t+ ue ° aD) > seks) | xl) Coal —> Xtyade ¥ ‘as Se ‘sing er. fet + talt og Dosti pean * He he vie ULH +ul-t) 4. -> Ue, T Ses ~ yey a Sco), | vee testa Usd gs ‘ ytd = > Xty)> YGe)s Guy — 27 gl-s~). y Lay * (idee, Yd Xtjor lay” ~{ v | o a(t), ‘st ome t “ Noni} [ fencer tent (acer tainty a ae “ \ with (A ¥ auth) oan . - <isph igus} | as | O, foslat)= > 4 C8 tar) e Besos 4 : © SM (wot) —D FE Serene Glas AS] 03 iy elites Pas Sj fn St de= aa “Fo C “orale fon 7 fro l rm oben fait = L "Feat" fo: Lf Woslay i sexe i te) *Hieew)| ar’ | Svatler foc Bey SAWS « ; wee, ofl vay. 2 fajesee>) a06'( =D os HF ewkiny 2 inshacas of she fo. eg Sot Let (—_ or Lynd" de. be xed CMY oda vy Sia Gah pe aa < Sir a aC PER es cum 3 Fg F 5 HE a wii ez ae . is) Ge? i 2 xt}. ome Lye ier = bee “ea a _ “ ara a3 btw tn) Fea ¥< sal: ale enh nex Le Kye . ; Pees G += 2 zee ae . ae — ae ‘i & ie La —