Conn} Sapte | tt) lata cond Hen =© é a = e( 148) (esp qe Time. constant Capes) wee Preavener te: re- Ue ——— = Ee loss line “W line Ss he pelag-Lime ¥ “a af Yo, RH ' Minium phese aye fem=~ TY che dude PRE 19 RNG Non u Ato pre ta RUS pr2= sic, proparte p=Zz= Propet Te pee = (imp yop & 1p fleck of Veelp Sefect ae peameter Joxietion xeckxey i ain sh Leon Xeduces, & otacte ees | , . 4, sensitdily Stability £ Bro Tt eco bis 3 elect 6 sa deatel Tigbubonte 4 Weedoces of Fadi. = GN N EGG yp “— sensitivit 6, Wen ia wi OM = Ny J ae ae ony, Chere Ms a RGR izUP eh ct 14 Gesbtcs) 1 Die (LTE ae Af t= ato , Ed eh ep ani, ) Pp gaalite 10 Tendkhy fen touching ce, palig oa +P tore OS = Spier t eo le ah oe Ob costadke otha Rydges 1 =e Tie Mb) evk Fp re cey due 4, ctcs “4 r & “ EGgionG) _ ~G(S)XG) EAS) De Motor? 2 Coobelted Refs (i(s' (Era)s-4 (Stet vo bole ¢| Modetti Mechanical, System (van 5 lettin f) €- displacement (a) vide ~velocilyy (ols | 0 EE OG) Memn(y) Kren d B= viscous Veiction cell (asim) 4 Tobtdiq teice damping Fece F= md't _ hadv F=ft@rh) _ Puy, ae +t , te al =e ~ } String Serco f =e ve b eae. Plea 2 \ K (O44) dt AEE Ine add. Roketionall B=angb lex AS place net vad = = Arguer Velocity vad/iee ve = Angular acceleration Yay 2 pe applied “Torque (u-m\ T= Moment af, inertia. (4. m°fad) B= Wictiont coeff Now [radfoee k= bib ney sprieg Nomad Enteta Tay ve damper Toque ouet die At spring Tole Th “Ade & Ba (6-4) T= toRo-g Bre 5k, f (noatlag Mececeen ~cer creme bey Far | Aloe ~ Ceesrert G Sy Voltage (v\ chore (\ Sto (q\ R a= R L ret lhe svr0 fee! Pe Vol (ul cuvvert(i| cuyent; Voltage @ havye , Fox eeoe RAN inst fo sro tie 0) jo By condidin? "M302, inept ah slable> Ain 54s is sri fot Ula the bounded § p- the o ve a e ee Yai on | [p Meat stalole ss stable haat Vator of Bia (8) trem ot5 ps ( Ae Stable ° ‘ “Ses Stable New cortai,, Tange Bf ks pois eon K. a we thy ‘ = ms ee Ser ety 4S tq EO mee A, 4 c nt] Ay Uf Ss As a, BES a0.n0, OES ote 1 = GHG) ‘\n Rsk Column most be +ve rot be and PMs sing coely crest in bivete 5 sign Charme, ia st coleman = No ch Veet ie 4 othen a\\ poles crn located Heat outs oth opposite at B VYooks on 9, axis rk appl \c able c oly7 P* colome d whenever eax! onar cee’ ix ee io then Xe place bed (ed oben Roth aya ends ab oth Constvuct an Ae RdTlontiote ko get need coh Ye conde q chen seater Tht ein fool Stable Jing a toner | cicelllekions Yom AG AE should Ld ., ever Pol soil 1h aide tw0 . & fern ops Hervarge *k Jet Stabile ts Gcke. a. oy 7) ad=be 3 Mat alli Stable “Wind coh adebe> sta o 7 7 Maigioatlg Stable ad> be un stable SyowW= Ro} s You =RoAe HE York, =i (ud, Time Response Analisis rok) Rage es ae | g=e-t=0 soJt0 de vit Loo =0. ten Unik Ram” Lue abs YS =ad 420 =p td ae (Nelocit unit patnbole. Mea 13 Men es, 4 Occeewton 2 4 Ss ee P teo Kol 2 Kec dt =} 7 0s; cg thes let he J valve Mester Lvitet, & Pep im) = ce Ay= MS SG) 4 J Te a al. ot a\\ bile c(3) " tel hath BE shee fies . ) eae: cepphed det pole, Rayy ot 00 feed Bera valve hy vespnse Loacnit gpifp sc geste skate Hour BY Nodurel vine Nae Re ea a ( attes Sa : fea Cs (eis = (eA putt i AE reall x Xf pyroy eHS= xi -clt}-¢ tr ‘re = 7 roe +t Tolerance —> y time constants | S : = =3T7 ¢y- * M Bu u = lot £0 Ge-{ Kime Aey= eet | ponse Sor Jorious Secalls te of, Fe leleg Ht Ste p lp" Po: {- éur os 2 Ramp —c ct} e tattle * impose — cde ape et Response v Second oder om 0g? : Re) Baggs 444Sn = Matatal wen, g, = damped beg Em damping xot to hoses re, CS, = U5, Ez gs cae Responses * “Undo pea feuntshp 3 [- cosa +; Uocler dorm ped u — tHe ee st (og 8) wevitical dlarop a Sree’ Ure extf{e piae ge 6 =Tan as Cosg af : *® overdamped WM oni slep ae I= eer i pe j spe s (—-e Si = Eo ug, G2 —<) /s AL = E09, tom F6F " Polezero 5 ee rc. rh. ate =o me ARAL 10 clea pe ed Tat a pe ans bap “Pedeguad BZ Ave ¢ eet & a Real unga() overdo | 4 —veTime. 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Is + LaEIN -A# ats EGO) ye = ee i vot SG NG) Ramp \fp : > 4% key x S acsatss 2 hb. ateContant Po do bo Oni sep Pawp Cenit oo be label, nt bo po Becee ot < les, & Yetas a ape cop Poles Z = prep loo ae lavanc he, tetmirate ae ee 3405 52 7 benche a et “& p>? pA le0os on Redd axis Beto at Yook focu, ee uh \ a o— (2p): \¥ re ayaf Pod ot Jug Sib jud in CE (4405/15) Find ERM. co stabil s co —7 Po} Meck A Mldition A tule X4e0 Pole jero ) ange yey to be Holle } Stable 2) Relective. Seabilitie J 2) Relative fabitity 4 | > sp mole oscittrter Sk Rang a a) Bo port shit 4) tex escittathe. 3 banging leet yo , i. oe a 5, : attotle 6) amping fe ORR BOTT Ka wldy M44) ‘ dy dh YJagt ah &) Slow ~y ; ays Ra cv iter 4eurF Ty ; | Dut, ey ck t “rape alate), Gs Kor Wve (ot) pes 2? co Beak locos Cov. pates, yee © d oo Bonk ver ey deal $B, (rode ot} 8 eo Fb Specht fey Y Ne venty Regonse Analy ee ‘f Kegense eis fee sO 1S Yin { ie " Sis Re ee chin sp 53 dp = 4sin (2L+4) A=/- kK 3. Vadfreg io Liha? Woe € £ 43Re Sorant f Teeqpeney ) “ests og B) OS =¢9. J) see" in ‘ie) ere 86 Ze otk. . ee aa i 4 = lites) erie dh = Belek igs On GM- \ (es) Odg able pied‘ stom += tt ptdlar eur ts pele ikset 1S Bo TY for Ub Myt Bw-l- Ot Mpb et 5 O85. ir 2) [Gre \vCuqh} a ae +T, f Gee Th T+ kT . Yolorio = ral, ay pe does net exist Poles fo = Indl i pM =GM= 02 deg neds Oly (p= 3dR D ame pmy eve (lable belay =~ 3) Gite pave (onstable 3) P= QM>o (magically Ste ble ) GM ms ae. 2edBldec = ChB bet soleaseu ia % ' q YedWllec= (8.4 5foct PES > 6th - 2odi{toc = ~6 AB of ; genie laa Moan A error ot Gc. 4 5- Po OA to= Ped g Dedeplst J#nzoloys6 (48 Proyees “ao Bede plot Stet “below + ; 3 Tnitiel: Slope (use le ie 08—40}sloper= shpe's ali Neto ple Final Slope (tise, j e ode= es ie inte ty Ceo Vhe ABlnet ra Magnitude otetce * Bu Eine ss delet THES fous)PPAR O(2 01, le plot aleoags oh. 4 Ger giliess 3 ne na esi Gursh ype fee eit & Gls Che _ pe VYocler~2 : gp GO= ery ae | PEpe-\/order® re aig. = Sees) ps 9 pees G(s)= Gedeaint a a Ww @= 44 ) “Ype-2 a Gls)= Aum vest) a ) Ype 2 otder-y ee Ares Ys) (Ape etder-s a=; + rt) TYpe-5 ota Als GO ea ae ‘| il =o beer Be th| ( tt encleied =! tncf at pet ez ek ote ble ’ No- oy Coclvclements th Evjjo) exit ; She. s Rap ody CODA) 4) 4s) eto af RHP at, CLTF fA) Jews th, TF eT rp (GCieg.s) = . ir det Sable syatem to TAT, $i ve | ny ak sAnc Bp S=fuk in GWACs) Oc t%< ce © Fb ATHpero ~~) No! semiok “pete —at yi Types —> 2 | + UG-ay)) = ley “Hraniltey Ce \E~afeo Wale Heal NE AEA. Or Sopaity Tab ee perp! Comtollable q. =(B Aa A°B- 4il rte obser Sonne §, = [c cé fg. cam]~ aae(4 c Ae are cw ‘| a, Kolmans text Qo= M fo Q Gilberts Lest Perlite X00 Coolum) eh a (c), Moteix the Revvespords bo “lack (Mvst\to.) ho Tedon bloc hood nok be qeto. Byertive KmAKsma, ah a Hic) totviv-tRat cebms ee (Liysl) x00 ado Seddon balge K should , \ { o = IM hoe ( ¥ Sit eoo0 (| apo wu[ clo ar v7 0.000 > 3 Se lee , 00-2 Do Se k. A) Oso do || & ON & |e] \ 9.0 0 0-30 Ks \ % |v , 0 © 00 o-¥ ¥ 0 i, v\) either Cnet MWseoorsy, YY, ¢ pensartors Fs LO \ t ( Chara cferis-tic Mead _ Fhe nd et, Delbert, Wreyt Coy A Stability Morey in OR Boy Bed A441 44,4 Sep Yay ta | &5 ver not eflected es “4 PY Gm au improved’ nt My + £, Pa Gn 954 Ss $ 4 ey l Be Cale mei | Rbet Cony lols 54 Be E Prue shuby 7 Main Stabittty i Hither Hor LpF Similar -fo Ph , fd rr “ = $. - SK ea 06 he gy To< bac € 1G ocac] = Os a> FTNetwork s @ iE a § Ven eos. ; es ®Dsink Bai iy ee Source aw velocite dpding on | ) = Source Sot ts vatid ded. Sin Deqwe off node : ~ S27 simple node (n) 872 — Principle node ( (0) min no. \eu} es M=bent] N Kel eas = np ohms las \- j Vee Hug Hye Ne VeiR ) qs ay agp k= Ph al MME LET 2 ie Loe, rE = 4Pata y de (eb Cudt) a # Sa ECidt ) Be sie Ere saws Lee, o R =0 4H can 4 * ay “olen PY: ¥qI0, rt. a deal Cayyen + Source er Wee? pee nt EO Bi lade. f HM Kae sUnthders | \n — = > md \H bil. >. ) Vv & b. Pe = ones Bee E-fpdt J E=prt TS cob-se, (Row = 3extes 7 ee - Set = Giepy At - Ep Upiat ale det = vit: RL. E = Spat = cme “ab 2 a - BE: sti = sy! a Bz (pat = = Sev! = sv * ont 2 tars ch consv sh charge Eienode eae | = YRS jet (vat jis kv) | Based on lew 4, con sequvertion 4, mts pe Oy V- iP j Ve ts y= L Cidt | ee i | ' @iaies Connection’ e Re. aa ptR; a fc vay ne ee' eu} c~ : += Gh. ceil aks bayatte | tonne clion ROR, = 2 +* La, Gd Ca Be Sete poe = ort en nee tt 4 Re = Y= oe & : He Car Reale J Abe ate od: in Sees colt of “oe g Sle cme m. Vee ae ank current e ears si Be baa = OF; wel Le sfe ean megler Lec a Poy panive we Conductance(neem Bieace ke RRS RR A ytae Lib ePReEsly re sl ) Ke! = Cee Op sy Ge oS Mos ae ee OC +G te = 2G FGyF ¢ 5 ot Bee ay G = GG ik CG, GGG as dace: ir Cobe ees te Ry ee Ba t = hee vt ) se AD L o4 ¥ a 6 & 6 are 0 G & FANN z, cc 6 (2 = Sy y PD) S$ Mesh Analysis ) - ) kvl + ohen's laed Nose when Caxrent Scutees mote than wage Soavce s (Joy Cas ealvevection) o P valid tery Planar Nfs a » whenever Cuawent Souee = encounter bjeds 2 meshe shen ik is cated spey mesh ren eit Av ead t asa one loop Aachen dapede’siatce beset lines ¢Nodal Analy sig A a J Ket + ohms lato ¥ TH ) Re 4 dame plose hen Vollage sources move thar cs Juhenever WE EACoon tex ea sect Mis nap | ts catted Supe’ Node Node Lees it as si oe as one anode pos 4 fot equation is fink bleo pendent pasameder inode Voltage | theewe ms } Ysousce Transformation | Tech ess Sa Bees | Nf 5 Kent ¢ le Dsopes Position Theoke m (\ineasackivt- Bi ita tera! | Vineasiy JHorege nity a) additivy | Nmost be moze han one source an | Sy Rowex Carmel calcolated directly (i: Not hag! eo ek Rave Specidic Sivection X voltages have curmdiats SPeeiFic Pola ttey Ite venin's theexem ere Bilaclexal) putt ott 7 ae My OCross target teaminas s 4 b Ry. 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L ~9cosg=(laq) 3 | Poramele 3 C=) Cesch=leod | iar oe 2 g R fo \ = , “Tees | Vising ys Nee’ Pp =v (4-0), Fo (<4! i. , | t ' | \ OF ; L Wel “* Meng 5 Nas Y } ff 4 to = VT fpeayl a eS { Clog} | t € [Vices$ =O , vr; d ] j YEsing 4 vi tral ¢=%o =u) (lead)eX x) | WBemes et Pe Re 3M Ys = taal (Xt ¢ eS ish, ph Cost = quoted Powers ale s-(sle) Pea? 4 = (ays v b es a Cost = A G, i pass : Tang = Bern lel-SRecay = tao" py cosg - : Asinget "Posey gle i same a (zt Z =~ abee F leads V by a0 ete a: Tant= & Sevies RLC 4 | Be Rie) tate (n-ne van (5) e cosg= DSA = Xref < nok acee, + (sl= (ree. a5 ei L zi Symmetey, P= Tan \( 8 9. \ Pica - ig —t saometircal ; Area,-f Aven yPASgenmnedaic PEL sgrmtil yf SSS spaeleicl sh ih | f y Smt Nog = af vFts dt Lae & , ~ J urgat-atioeyte ° ee — 3) Avekage valu Valve Shays! Nhu? ae + LAG pati‘ More / e Snetox SS D pear/ewst tyoter ) Simlibers Teeter BP, Eos Sens PP Mg pam v ; ‘bens ia ix) ' if Handard wavelorms sey Waa Pp e=! Vpp-A F-E=1 eee Yegea PF 19 |i) Ke, Vv, = Neo Riad Pei, n -A re SOS if ae «e = prrB (Hal) 8 of § a (PRataave Reclibies =NeNv 0) eyo Memns * NV. = ig ™ oe Fe hes PP ) Se 3% Vers F Ms ti : % BE = ihe} Sao (Fatt erg i See es Ms - Chath cycle) ) SBA ¢ xi emilee ser st ety s* Baur” =vi/n-pY } wal elements ves ri) ver tsngk € cantik : SS SeBies 2 Paratiel Kul cortvee Tesigd <> link s/chexdl Cosel 2, theset (s} <= [é} \ gle Che) 7, ot, Saiteh in wee J in ll sexie Getting chosedy 8 ope ay 9 a ere My V( pola vit) 724, { (dlikection|ee toy QD [trae ener 4 Hosed perc. ele 3 = PUK docley 2 ‘Foeng dissipated pex cycled 7 ee = Qvars Oz Pin iby Element QJec tor oe aoe Oe ore ee 0 ees Resong ‘bay oe - having Sette an i Combination 4 te a indvetoy X capaci freludi losses Modetled as Serie. | +f Yeo B lel vecest. as 7 a= ciel fo pane e Q= aS Soe Sevies Rese nance : ce At Resonance (as) 2 = Rainn) Te Xrep=© HN =X. e “TE A syhe Fe ot which bs o } i Pore sai Capacrret — te ANCE Fiven |e fee { y at whic ek th 4 iM -c ost: ee is a Pa y4 gard ni te eipR - a. S Paes ee at a Re a) ck 3) Tele aot Ba ick 5 M i pe m 4 agnetic certs = C= -/ato\ di (s\si \ sel induced Cry Leno, ode get T+ R - dey induc ta a “ups : 0 ee Z t M= RON = EQ, a, Motus! fie lacce blo L 4 i ' Elerne lp Coils. & pe fut, OL KS} cals in Sekies R Loe titty erm Motoaty oliog em L ly = Utlyn2 ih, be ly | € “ Motoatt x § Phos ng Ee =cols in Paxalte! . Pee: lhe Ry ce a Modtoally aj E R br C4 ly 2 Mud aI = airy uh 3 ty 2 Te io vt Urbs t2e9 PhS ig tt Ele Manet oh ReHleetiog cut pat olor bls py ts, el- & mae “Ke Ne R= eR, Ten x Xf nt, i= ben ie 2 = £2 25 Pale! eae Transients a) cet invdluiog Capacitor Kgl Adlodel (v. is sy 6) % % inductor 7 Kv & Mesh (ivis sy Memory valves axe Slate Vattahle s mermer Clements aye Lac onder ug crt Pt Re a 18* oxdes } Rte, te wire cre 19 odes Vo) = Xe (0) = V. (ot) (= ‘C= i (ot) Element — S=jud bess Complex Fre Sas Transient S=5u9 Analysis 4, 2 al R 2,2 Rn R R R Beez etohgsin ise Siysvy gg ; b4 f= 7 c os re Becee Of Tle y-. (ste be p=& B Seuse Inne Pater ; Ne ee se ave £8 a newt {Re 2? gi Seuee™’ “US- y, at : : a. ra 4) | pare’? 0) Sesies — ha Re : eR y | stet a ii =a ON, Ar) + ky, Es ae it $ Sp 3) pt eke: oe R 7 eee nes | { W)- af Ve | Py 2 Cicyy’e . mp6 tr, . t 2 t a4 3 Tae mae) H-allwil- ft ———— Ro | 3) ‘step te Shep. Bespense uf Bboxdey tL d Re Re cet ; WB= MeV AS =e vi) = is pnevalct Aas Vth TeV, vese% Hh ilbeot re vi | Wteyyete = 42% | ? . Ep Sos Lea = vy, str ~ ee R Pee ASC PL = 50/- : AR cet os | A= Toh+(r0)-Tadl@ - Dow Be Tose t he he Ste eae a) (ty ¢tlz- R \e I “ oy: vay * elt) =% 0 tay om Reb Yeyty, (1-2B= wles Lp, 5 source Wee 24 onder a) seaies RLe a Shek str — -RalRD Lt sh = RAEN (Tes xB —rbampieg fortox ’ —— = ce Sundanped Pedudl beeg CSS ips ar OS,= fte wipe 5 43 ay ) oputs if f= 09, ea ce AG 20% ie i hs Das Ve Xe. 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Roc ce TAY Ly (8) a. i) = He Sinlcheas+ a ars ape tare [RG\t Q=Toal(ispe) Tek Total) ¥sponse its = \,, Sin(at +649) ae Sca(org)e et 72) vA ui) laplace Te Xits applicetions -bo dlecteic eke Uta] = (5) = Fe Yeyat vikses Ws) vie Ms (Ber x (Yor) Bok; OVA Py sinast <9 p 5 tg? ok | Tout <5 st, tL $1 e (| Shue? orn Se ey | c { = dibs ups gh sete l <2 s oe Se FiiD\-! | Loith Z - 3 ———" if Ie : ey) 0¢2 won oe oe, eee } NF Te es oes F, iyo ok air ak a MBIT 9 ESS ug gh =? = ; Be (sc VES) =c 5, —7 9 ee di defermining ‘ehis cliNtolt \y Non -Cancnieal cet toms Parar 4 Nop ideal) ‘p like Step, Farp, Pawsbalic Ie por st eaponentis( ipl be Fillers A Sai} (s)=y Spe. Hl (sh\=o | he bass We z Y + 2 | (fp Seo +\(s) S=pe - HGS 2/0! 4 $70 HGj=0 Spee. HI SS=0 a Seo -HGS=) J Rand Beyec+ +; (fox ae He\- 1 | Vo x Gatigh Pass’ re 4 Band pass Silley TeD0 Port At fia a Trey 4 > Pee: 5 1 92 z-4, Bi ubg tat z y (se \ tree z T (7 ling patame ake ty OR ee hss FASE : 3, = Myr F953 M Y, = CYU-D a, Taverse Pte Bal ple’! a a thebxed (, era, on! 5, ely 2 en v byt ig 2D Ay cl br, t,~hy J, hy,“ CY Tnverse Wylex: a yg = o GS ~ GY This to y e WM ee io Bevelliy Rec «peect ty ZF BG z° 4y 2u~ Bs oem Meet Yer. Ap~—Be={ Ad-Be=y A he Aly'-ae=t A\y- Qi ' td Lat spe hl er, habs s Srp “hy dist “dy oelallice io |b > 8 oo at tee Bre +7 Hy Ababoal 4 4, af PP} ae . W248, 2,¢2, > Aims unbd/ ie Sets si ll cleme nts uae ee vs ay (2) not Prssible (7, e nw [y]o (3 3, oc. 17 oe\ sevies ~sewles 25 prxaie | pras\tel ¥ ce a ‘4 AR 2 = ‘fet E al "R (I= (uf) } stefes= patalte| +) Pavatel= sevies 4; : ee eh Ce AA ai 2 (a= GleThs) «J [anh a Caseaded/cha ain) Tandem ) none oma 2 Ceaph ery meshes iandeperderd eps = b-\- \ Spain ODN ney « es eas le make ageph ae) 9 Comple te oul “pn Aedes 1S ‘2 “be Teee Seb asap “havieg alt nodes, without -te%ming sae closed \oops sk da Tree odd a — te net 7s pies ) odes Kas unl (a edges Nod, dee s~ ere 18 —7 compl ek sraph el ‘ 4 Taek (fas fa Trany ee, fay) a xeduce d m cudence actsip 7 — thick Nine, on tree has art tagsco- taee > comple fnent ft tree fins x) choxels. 1 Thier fines eh del fines ——auz_cottte has b-ner link, Cveph = thee 4cotkee + ae naa + b= net b-(e') | Incidence matkex A.) gh branchdi rede axa a tein, oxdey ig nxb n=no-d, nodec , Yank ts of b= 0-4 Iskarche , Reduced matkix [Ay Rel node neglected exder is (a-)rb Jondamental logy > Closed pth having me 'n Menta ae tise Noel nee ea) = tnkS | | 4 Te sebrcurysert ot loop Gedeeae by tite dey Tesek motxiy (By oxdex — oe ABP = [oe She finks bxanche s Kank b. (n-") = ' k FI Sth bial Cuasent 2 of ae kvl =~ BYCyY=o ay cokiet One -hoig Live st tink s Ned Fp colsety Tags ¢ “A ARS eset mabe oxder= @-1eb ths Cen bgGeos faio Syston £ sh eQit a “i Hob it: J feta betes ; eve most he bounds Up. we mark vse stacey ta exponertial’s (2 1 TR= ire) Pole, io Slane fave. ep ty f chble aio cm R oo ensteet) Pts w<\g 2 k hs S$ ( 4 stal fx s 4 ~A- CS styinfty Half A Jel spetibittoled /-» .; = sF Be f je) + » 5 sn eth! , a a ONS2 ble Mex iy 3 ut De, aes ‘ Grae? of Onde bb “ue ud oh ; yee : mi [~ : | Da stabe 3 at : 2 df oe a id iNi; th it yf basenc Voltage 15 (@clele nt with : a cul se Voltarye Lovierted % guine AVEC Three phase Civcoll, bo a Te RK Nine cunsreect — Paces in Stax Reppert di meee. yA, | Pe Gitiny wil = fy Sino VARsSiy aks 3 prter . these A Saal has magnitedle W diatebten "hul- wi diet, why, ploase Rect 37 ° a(t Tey a Yn ‘alts £0 hay) ¥ (48 titty wv Ny. Hs) ¥ HS w Time & Weavehey ave dol LP cexMaethes # [(mpotse \at = step t= $B ae {step at =Vormp s molt} 4 [Ream p ak = posabolic Re tou) 185 Bae teeta) Por roy = 3 (Ramp) = S¥p « 3, Ge) = Lmpolse Reak!-atl numbers Including Nee” mol Pirkeqou, aan Basic Signals TAS Done’ sep Lovelion (utes) yxy aa ot =f eo t eo) =p téo ont Romp Sonetion vith a Jat 26 b 4 slope =® yH4e0 —— \ Wt st) ier odd-y dadled, fgrem dees eet Euensinnpolse, Since, Weombtc Ad \4) YB} wa | is xt Sine: *)55 Rectangles Siagoel @ Senclio ny weel=1 Us 'y Pleing tect (t) Fh Te tl sath Ah ie a J Bey maplit { \ p, 5 Bien angola “prse Aevelion -.,. Ast} = I-\ey Wey “A inte! =o ra Ee e =4 Lonctio sae Ct} . aes \ nes EEA S& = D < 0 fs eek a eS “a GO odd se t iy Seagyt) WS-20- a 8s incAunetion t enc Lh tet — voted doe Asine(l} = Asin je or =1¢ F * | sine IE S a en ne sued ; Sad SAM Y bole sei $ 50)> 3 Sg} = - 54 } foad\ 2\ In case of hidden seme eveneodd t hole | AWererctiation Kelation ship tit! Me) Peay d He dy \ { rt) Bounded seed ave “catted Bounded 5 ‘a : ne ae vel) ti (ES sin cM, i Sle) Buk SAY nok boorded . Er ¥fB, 5 ow unboonded S Mintle dune dwetion $ gral Hthe purelion 4 Sanel we Finite then i is carted Linite uation: | 2) Goosian undien TTR eee gee. kt ee (3) Sioscidal Sigpel key = Asw/nt +4) 1) Reot Xeol_ exponent nontial) , oe zr bil = net ee Rex xy. er s A BP (5l4to) HES Sere cE { ait) |" i) Complee exfoneetial signal XY - est S=ItIRte <0 | { aS es S=S+i\p Teo S=o+jp Tx Pe LRA ee Aah iss Modelos eft) lx\ wee / jx Loo MA =K+cy piserete ont Shep Avacd of ‘ola)= f n2z0 =o Nilo Ap discxete Sorel & pee eee ato cotegtion cloey not EBS OnE OLN = 4S (6 olor Ula} =S/n}+ fe ‘) adusceete un vat “‘mpulse mapulse Sr) gtk) 1s ARG (n: S(ny=i J a=o \ fe => {nto “see a (nt) Un) =SO\tSirje SP) off) = a = i closilicti on ‘4 Signa th SaLLN —~- ) Cordinvous signal cir domain) Bene |e ERLARG ER Continvans ot -Gme | > », biweveke sol oop cael Sampled version rr: Lime domain sare otKp axis coil Anke onl integers not Pel bl Waris P lat ge i) 3) digital Sign wayis discvettsed hy aes quanti 3° cated quanti i gactton . | Sb = ST, \ f Taj samp \ peeled ) CT Bomain Angeles He ) br General teiw Yum cosust tcontinvois Casnt— diseye te ‘ ect § rosiagal erly, one nth pasatenefer a fy tod — Bienensions = Ato. af iodpdt poameleig Sop signdd ware than one prameter Sry) 9 piss sir ST bein eQ- eles J T= Jonctamertell me period oF Vr Wy "Keg DP ACY - st N *Inkeges taltigies af re OAD, han ionics. t foun Poperts (oh wigs A doriotic Sacal’s be periodic Signal must be deorn 06 to 00 py soni periodic ig either -rotog Holos |! “ 84Slematio manner. Ey Tv Can bet Aroltiples + ilege xis 7 S493 3 Pombexs T= Vy, 3/4 \weige, motile Ar \T= 1am A Ratton 5 MOHiples ah Ar=\1 bea Y/, = oF 0g d analy AS, Lin 4ia0 oot \ 4oy ~ Ray Srime Shing. ~ 2h ee 2B 9) time Scall oe ae peer ect Linear Combidcetion, oth buroals, EY KSA ES A AY am EA Fu lk} X Ch at hort, tele | €(tap) = Riget shit ddr ar dompesion b4 1 O6K21=4 ERpansion bef %. ct method gre nethod ey en. Ried Y % t Linea Combination 4 he 2 os hab es 2 oo petiedic Sanats need 7, ~ ¥ Te = nk not he periodic - PAT he fee oh 5 # Signal tp be! periodic T= (Lemna tg T ast only, i either Arslan 1s (Cem valve ; Mex \s ey terms of Tes fate (4) -m Should Not be tm terms Aw: 3 * ee teygai- bertsob tf * Raste tens on Sigal’ “Stine Revered (lasing gperien o Soe op tk ‘ Res J Ampitade Seti net) axl \ a (fap - Wht shirt of ete, j aeadding 2s.) tng pltalaed by * signet fleet Addition lp Cae: intend % HF e ye 7 ex ¥ (es be 1 pl si cotati! t ee ee ® ripe ak event fime ¢ L B= afd re Hexen Serome og! A dh : e3 vie) = rae iL stage Qvo dyn ) C b 4 = even tigoals tot CxS Dongenpeelss, (a) Rexam’ 2 : icons is rh = ~e(4) ® "i tty x4 seat voating thay | IBS + Ba X38 © 8) os . © |g) Hicker, _Sammetiic signal 4 wy ~Evut onltg to ode signals zs i « B= pay be e 4 Bud symmetiic » vent er 25 vert We: ‘au ma Widder | bk clamp mer free conglude VEN veh ode Mee) ~ D) Ptcele, 5 we abt ‘ { he Component 1, odd Signa | it becomes Widder pt ate tho, Cvem nk oe. ~ \¢) Hatecnve Hon praiils ek we * . ett} =e [+ 2)Hota bait ak bath Ape fe Reverse anplitode NereE Otwkea tw ‘stanals are added oveutt wange i (LMA Th fndividunt Signal karqe, i Deohen tie Siqnals caro woltiplied over alt tara, Vb inferdection “ah, individual siaral Konqes: | # REE = Xe X a5 BAS xl rece) CE) = HCY —eb) s| MD Conpler signs.” = i (0) = Keg} ¥ (0) ea Cornpler Sqoometrg. o &(o\ RUS Fe Ka Xen) ee oma we Bact Cotwse on reff ag ok Sheration ey ines” Sarals ate vsed = 2) cavsal Signal tt} olt-3} aE x=o0 5 £0 fo.) ¥{nj= 0 PI Neo 13) Ankicavsel slink ntlise dre, al. ha | bein 7070" | ty) ‘Aton Corsa be ; ' Er Nrerthey Covsal nov Aphicousal Nile At peiedic: z ‘siqrals are Non CH pers ad fs . xeBEE og En BUM 3, iqoals e te) power X ESeRS SQA ft Dean Get he Tee +f : en | 9 ie DT n> bette 4 pe 2° et * p= N/o Rens =(P, ( Mole Oe i TD Lr ipetesictateers, OL Creaiesss dt- ie q te he © 1 fpotedielat =» © (Mpetodelt - i as a , Bh tole hoc pere XEH0 HS pore RS } |9) vceZ we ARKO =S Enea SQ" " > BP tgp Neitter power od ee “6 f eOi gy, YR= 07 . Soe: el} = TAS Rell s AEBS én = ah is oe 1/13 ; Woe dal ' ety s (i thy fe FH) tha sevall s PAIN periodic signals axe pooer Siqnat s f ma Att Ge burction Signals a signal * an oBounced Signals ase nether ps ver E Bounded Signals Uh Constart am plitude (olf X ibs cletarged sats) Ani’ le ceurllies One power Stqval s i ® Rovacded Signals ath eb onential de ean Signals A nyantte cuiction aye eels : & nals: inl Strength, (5 cbubled then endo af4 / tnNoTE.’ ~ Est ps = ps- x Sal CENND © DT boinain - Decimation Mr) < x(a) - RIS ele M>| (Enteg es) Tn sexf 2 a) bes Bice ats cah'ich cleperds iss Siles ‘ OA” Sequence. : Metbines hy e200 ay wt) Aveta acl Bate yates Inler polation Gaon =\ ine A B Decimetion . ‘Jinterpeletie of Kay’ a Reversal ' aps x (e a ClassWicetion a systems ecimation / Cex fe Rte on Scale Lineal aw Hadditivily ~ Anderpoleti of Static A basamic (eect: Leo] hem Ting charges) } ds on present 7 itp -then “geen | is stotic ASA& post ® ns valves Beaten HS by Evdiy Kiierertial) potas ane dynamic ts ve we Sha \s = ceti te -then is buamic> at one ee tie : ae baaen 2) ws age Xen meat Vineat . “faeplitede eid a\et [x, det ¥(n \ <| Convoltion TON ropes te i Genel proherkien o Pavoiative —7 2B hE = chet} enh = eit fave Rental he ARM shi a Associative — 7 x(G « [hlehe byl] 3s sini feb di * pishi kobe 4 ey 4 j Ree. pn 4 re Lineacet eet 2A +3 Ene =s a 6 eS: Bis) « Ha) = (oe Scalin thot) « blot} = ray 868) -i¢ fot =e ei CMOS at ete coy eh- e “ty Dat ve cla moltWS 4 0(¢5 < # Pc =i 4 =o f # OMe oY > Mhirees ts He Basso ® veck fphatrveck Ul) = = No ah nvolytioNn ——— fi ae ce ae ule a ole) =\(n)+ vp) & Th , i ac) z OG Fo =5H Cor qe ef _k(ph(o-*) Brig c V\nea Mineat convelirtion a Merveelay, periodic Gi yet a leah ot ron Lim-) ins hin] 2M k(n) = {3.607 * Len) 2 Mex(t ) Nirh)= nos Meer as a Rleci)= 7136 i .. Loy adpee zee ta “4 d. = hist) Ex'— Countess - i n) 7 Hn tar ea & tf Exe Registers a ole bP. fo = for i 4 Lines fy CWE volar ah PAA ab © els)= eae 3,641 “3 Nia} = J fies - =(Mer}on te L 4 Chast 3 7 Ae oaks iF Ov P49 FT RS Max (a(n), Wa) ya) =s = L- <7 Cs ce et ty 5 (F fhe 1-4 Ae4 44 # Som a, loeoer (writs of fant of Uh * iow UME [toni-ts of BAY A KELS 1S Upper tonite af KES & the ahove Loo points aw valid Loy BT bomain F Convelvtion a r Rectang ts Jonebion 3 a voequel durations esol “Tppegoicad Sige ® Convdulion a 9 Reclanqolas Joncfions of equ dutotions vesults Tango Sigel - # LeE X(t} Ay Ney At, Aye AyAt, es ee is Pp Veshonse 5 (3 q i at is sep Bren vespense ' Skep Xesporte iT homain or Somatn = Babe {(0)= Xinhien) @ a= Ula AB 5B WIEE= vias = Uejehe) SO = Sindy Serie 0) EAC) cp bee oll hay {en} = 8) -$(n-) LES RHA js lores | ~ | Note ~ chen “As m connected in caxcacde the Overall Tmpulse Kes ponse 1s Convolution of individ impulse WU ponseg t ANeaqency Raia a, frat ‘ pied sqnals Anal Ki 5| les spec fem 15 colin a Tine Korat Yicen, fn on set i wi 2 Dias tae i : \ xt ‘ Scontiavory periodic } 2) continvous + Aperiedic comlinvong -time |, Oo 3 Wanshetm a t- “a | s)piscrede + periodic bTET (iscuele tine | euier sei) | 4) Sis cxe le Fapmiedtc bret Az-Tfe pele ef | Table , Time Komain Veeqbercy Horror eo a ve * mh s cominvows eo? Abérindic - 3B) Kiscvele «<7 paiodic x x SV piodle <9 bce x 4 Ajeriodic &——_ cortinuonsFourie series ( hp Phtsenads on) dc eked Tyigenomedai ¢ er beri. Snts callad j 8 ) x (tS = = Sot seas rit 4 ban rinkt) a= aa = “2 kibeoriat . t Efe Sin TINS tok polars ce =A &, Boe t +6) Cem 240, ay 6 =n (e Exponential Vs) 4 a oh Pie £ ehh ef ierne >y Cntied orm vp a fee in) (xe) _ at << xt = x, a OK erraket ne rr \ nt} - as x tet F vse TES i ee paiodic shoals pipe mee Ere gh iNs . : «ashe tee Dis . calculate fhe Magni-terte phae spec byoms- alien |) Caan Saad Teget Be An bn ale, Com) Qe 4a, cosine Ht ay. Be One dake given en [%! ee _piepetin AP ' c ae mye (= elt . \J Yaeo xk exists Gros ‘ ; Te Whee. So-hs-1, | >): ¢) 6= ta (BO corr =F x= % (455 b, eto B) Magnitude 18 alongs even, ps does rot ee: 4). BA) consists th plore vlves eye 1 Pa Lt ; ¥(k) is old 3 gales th, Haase ¢) @ =e (e =2% a y Pre X a =e : : “ jae Wideyh\h 4) by ewtats, 2 %) M5 even a) ps 1s odd consist 42% NoTE™= TE be compontat exists then ts ae _ Hidden Seve beg Siegrel- = ey Ts Neither eyen novodel ) a= erists wo r (x on) (a On) (x, xf) eeaists DMs is even Nps odd \ consists A ) sf atleaut one Valve eth et tha >To) +2 _prveoblenn solving 1) calculate Re ae : P ci ° ponent al Sanat dent even Semmetry of a sme, ah, Siar Xealevlete x7 valves d 3) ay step © veal e axprl hidden sammety (oy making ave ampiids ie = Ve ample l ealevicte & valves. | ~ ia +) Apply Hos (ie PY Raping AVE Amps -veam’) & cenclode * pele} uer- ‘ Flas with vebain odd tharmonic S| Ge cancel, ven % ‘ Propestion of louienseries ) Vineet) ax (abe (4 —ax,+br,, %) Time, shee kor Faerie oT Yn omalt, Else) Ky, RED xk eX, 4) inne S Colin RYO Ry Time Comp rewsion= Fn oA Rethay, Mey Expansion SN -xime pilleentiation a ess Say @% akC)etina_sobepiction » Yr abl rH et Kn eo r, Sects HER?” Sonne e.. ‘| on {ot MS , Tae oh . . i xy ona f Porseval’s Ahecvem’’ ty sat Pie Vet b ool x i bats = tyne BLE ORees) oe 2 EFS = Rez, le Be a thes theovem Stetes hat Powe» A TIME Homan Di \ powers in ey Soman i shipti — nN Vel Cue, Rete ke 1 tie With Finite, a there Nocke Muchas stl i : Were 5 by © fy MS re ches , | ae No change No the ; Chava Cheat 8 2 \ eink, 4 reek Ps cha Fam) * phorge Reversed charge |e r (ma) | C3 afm op don | Peclnge te chomp | noc4 Diwchelet conditions: Prose caitt nok effect: pruer So oe cam divecth apy Wr 8b uot in detderte od Sg 2 grave te expand xe MS wc tl ye power 8 enemy inthe ue sqre| * ps “ Senet, ‘ a Fourier aransheim (ed wep of, ontirn PRS ails H ET FT = X(ie9) = Ceayetotas 0 LF = tS = |; (es) Olt J «tte Sheuid not have Ane i > Lit has total mah tn most be Pinete « Anpltdes af -those Aiscontinvitio, most be Lirtle ie atinile ogo Maxima \ Primima (A vex VnideLime interval. 2\ el} omost be absebte integrable £00, 03 te ( Lecgil dt Kloshr, (us 8) Ss enesy shite ok Herr *Gleo..s\h Ca KG (cores? \ gf Heeqveney Nillerentiotien ER xinA (xt¢)) » = to) Con\ ection W Veen ie teqialion oe x (es ) As a) Xr CHeo t7. io Sewst NSE ouctinate 2 Sawula : Fans) it ee a Xe) = t “eae oy Ay Wo) = £ Ay LU st = Me onde al Second often Atmel Hi) ax (to) eM £0) = aH) Xs eshales ALA Founla Tappiele dey nil Arcos tt «4h Aue cos( br 6,4) Aysio(ube 4) [ee csnfce cares - = erthety a ae = Lai a hy = Lalas ag = [ala ‘Santi thee Sole amar trey Sal 4 Criss] - T Sampttag Hee \, 2 Vmax — ove é ey f= Par Emel Pai: 4, (atyayist he ‘ae Ponda tt Mee "aE om ilphtey isk OUR, soning . then olp Samaplea axe a1 Nore ) when 8 sigovseieel sigeals ae po Cot big re Snag * mat (45, -%) a, ae | Bake "e Sinusoidal signals axe motliplied ss i Ju eet " orn if ‘ 3) re cos 244-f rite ; ab Def Asin 14 non 2 sh thencn’ Steugdel Signals at Convolved -H.. pny = inh, St © Nyquist itera ot pevod 7 je a i Laplace Te(Fd vp corto, @ i exindlc sants to Sty’ X(s fh eet ae glare inde ie ) ti RES Ff Od Exist [iLs)f 0 : | Piiperdien of Roe - 1) Ree ts qy step barattel te jut! axis 2) Roe should Aot contain an Polex bey, ot poles systen doo, act exist WRee sit altrays PHEE Tt Svcceysive po’ Poke Ter dirt) ve: ae ; eter x (ss. mer Pel Wet E Roles 7 | Ret 28 pore Rels> Se Set} ey - Re {s <-a dah Ger cath £, tes 5 oan. tothe _sta Gra}Fua? J ne es fds ested) cost ae ] g tah” - } Role-¥ Taser anc * yR he Apserse alice the SPR Role wtey ik Voots au Keo!) R distinct ») So, Role pto.y \ the Yoots axe imaginay | Cp | D Abily Rule wo,3 i the Kooks cre ye 2 W) Arty Rule Noy ib rts) NT S) evpreved intem th!Nore | cil. - ‘ — a tuo TS AYE Same hei Reece ame ‘ ow § Upileterat cy Ms) = Sete Fut sed . Caceybes $(qnal » ays Z- Tonslame (Fp vep % digcweh = roe Oo ice Co Sgalt tn ste; t X@) eke" Xin) e4 X epee e z= nr Ep Resides Hote LiN=F (ray) Taa| Xt) ; x2) | | propertion rf Rec Mthe Roc a Conce mse Bing mn ‘2'plane centered aein rs Rec cannot comtain An poles ‘ Sa} x(n) isa caved Sequence athe Yoe s entre yt plane except ot gee | ANS ete) 15 a apts (ot) Non cavsall san the He Roc tS endive 2-plane “except ten sj ay ray) Ts dinete duration tao gicledt Sequence then oc ts erie '2' Hane 2-0: 2 ) TE xh) isan intincte dwation {wo Scotts Seq, hen Yor witt Seeks e CPA Kinny, 0) ~ plane: ie a ene, Te s-toble ening nee ge 8) Roe must be acornected Kegien. ad propertie, of 2 TIF . Linea ‘| 2fa tela b xg) 4 ax, 2) *bk, (2 See of,7 ime Shut shti Ne \ 2 sa a aoe i dee AN xen’) 880%) or it Reversal i Tree a(t) te os oO veo Ry (| yay ede ae tech on i © ¢)convel ti ip si ae 2s) = fl ye) = x2jn(2) > He brie expansion Ken} =F (rp\ n's mstiied & k - | 0 n isnot + % | Con| coasts Seay oe ‘ § © 8) Seifiel valve theokem | Xe LE X(ey 7 Jad waloe te sven Le E lh] = il = & @ Mrrep Zentifcetion x Titers 9 ) ti (cies) 5 fuvem)| tp ¢ ‘ BS HCE )) « nce) “oot sNY Ce) = (a lem| sar ase Gaur 5) ce oa = Man Atl pus Mapp a Spore 2 ~ bine thts inside le —1 stable Rants S okside ole —yendeble on Dmaavis ON Ent ole __y ‘nally shoblle . ON ead ws Ht) BSB H x echt} Sinc(t) Since ce) 3) ei Siwec ff) Sine™ pe) me 4) Sine EB week (1) xect( 8) 5) Cosa i (Ft yes(ety} Nilesat. ‘ 2 & (us Fet)| ’) Sint, loa hes) [sls Swed een ts eh t vee) oert + ed ty 46“) t Bi : (a +jant* & xjass® ae eth T80) “5 seh xe lent oe Pee vate rer 2S ; | ulf-oft§ -ve ; ge c vs “ i Nato Kennese! on 1S Same ina Xm, ep tye nomber s eet 5%" Ne a F * Po opertion, Goss XS ent o}sigh bit ey lension i) hiviston ba 2 Sm er Hy only YS Comp hay vviyve Kepresertetion Ap by 9 ope Ro. Range ttes ee f i sign Tae mon * rs 7, a" f Same trical 8) ! XS onap Pa. 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