Steady State Delay as Related to Aperiodic Signals the consents of phase al ervlone delay, 2s apie to ary Hoe {Gripen oem seen: of he cen, The aga spt. Ur Gaesal ses the in of ety and spec es Noles Use tie arcs ofthe sston ive ths the of ex The amplitudes conan: over Lae sagan, eis bow tht bes sheers he Uo af eatin eave a Ue dia the sec dl Meal wh the ensope dds When i tbe {ie msn abi at, the Gla eno om eign sve {tum the phase sit rhe ser set teeta el, to pines fey ite apd vss rapidly wih sone, the compan of spc datubence whi coestnds to natow suet the ‘run pera o lng tha the suing over lapping lglg ipoes faut eit nerpreation cl THE exis aplcalons of stay stte theory to Wsaswishr pa leas the emphasis ws paced on the veriation of ampitude wih fe- tyvony. The ae of hig Headed ie wade it neces oo take acon pls stort! aswel. With de development of tepastogrply and eleva, the phase caisctevade wae found to provice wef ade for dicing theoverapping of sdiecent picture laments. For these purpse: Fs oun convenient to expeess the pase character in ier thse oe envelope delay, Thave ay be cll “steady late dey!” since {hey are defined sod measured ia teas of sinusoidal dsturbanoss of ad joutle equancs. However, the sguals for wales they aye iatended ue fuaaish a Sndex ace apeinde innate Ht eeemed worth, theron toevarine more dene te teem exiting setveon “aperinli eye Sede i em of seal gnc sal ey late da, Ee fea evi the developceat of the covcept fees state delay. ity i the sady ofthe propagsion of snasoidal saves dscinetion nas mate hetween pe atl frou velacy. Thee oa patil diane Df Irsnamon the rat of this dstce ta each nf Use two veloc tay be inept delay ase with the tranisen1D the REEL Sra commurieation art, Use deve hove Bota cad pas a envelne lay, respectively: Iv he nechim eeu dispersion tay vary with ‘reqem Tel ta four attention on the condtins hougaout he rca m8 parol instn: cuvirg th tenemision ofa euscidel ceachanae We hey ete tie Ina kaye hase pean fora the put ta the foulgeL This gy Le ure ans sgl cys Uren oe tide this hiss eile ty the Frecumey, epeceed “a he seme anuvlar uote, We get the te hich wil be tect for che phase at che soto pga tas eueput, of she phase cay. Mio ‘Lay liye ore that the evivative of ais laze aif. wth repect tv feeuancy iz equa he cried i eng aloe fa tems of the group veoeity. The FFrplettraimert of Fic brad nthe eomidenaion ef tio sina saves of eqn arplnide ae elghly err: sequels Wl ta elas Ivan inverted oe most medi, ule aia inthe sate! thie altace lies exe arenes depen, Her, ip she neighborhood of eet fequensie, the phave sis varies Bp with requey, a cfter agpens <2 Ye disoutivums, ete ly che appatent dxcntiny ecg of wry rail deve of eve with frequeney, mia lena o a negative velue of envio deve, 1a the sme segio: the uasanssion varies vapid wilh Urasy, aml selesto reo Hine accu at Lie lari seanear. Tere ean he ep nod ter cf reonance in te deneata which wake xy the Ene stzccze of the "The nest slap was to diac the ie of dea fom that of velay fn taadum, ad aecociate fe wil seals tne Irv on lame Touwcen cay tke pains ota sa stem, "This we pew app ie sen to tl ste of canabcies ustvods is hich wnloem propoestion ‘cunot be rewiy visuslise. Mere too types wf rhurasteitie ear be distoguishse. One, whichis aticatel will ws yt he eae Segoe ajseme exhibits areas peas verti. gL th pase shits vl terion wth Frequency This is the ae of © aon hing nares sire. The ner, which fcemicee with “canst solamente Ue pheveteny secinee wth ncn dpe, the cage a ior a ella wae pies Ver ress iv se 2 eit Lise sean ae rete ilance, whic me the ene ‘the tapes of igh absaplicr alse tive rsreetow a the bound Ulamediin. Trapping be san det in tetres the, ec expect Uh eae bv ag ils a Halse ee keep eva fom Ae ert Scie 0 eaomart system Te camputig or massaceg Le plese aif a x aie, a» dig qency, che sents ieteriness ao fou ay Uc of vies Je ieturenrael, ‘THe soos rot aot the envelepe €eay, ith deel Ee ete svSmeAr BocMPLCAL WENA nly on the derivate, ands ths typeof dle ova be woneaized dire (e laclade ste toons charasteragse of ubitory welts. To give ar fac memng tn pve ely sme convertion wd ave he aczpunt for decerining lols if uy, alle of 2 tobe added to tho ems pose lor the Faquaney in question. Ayurely ae such convention box boon agra yon obich i of genen! wicaon. Rar daaxpod pesos sich rani Trequenie dowa to ery Lie eustomary > wire ie phase svi phe ao at ae requerey, wl [ow higher fequences, toa) ultipls al 2r oo dhat tae pase dis res soinwoaty wt sequen. Th ten, # is nope phase shit, brave ~ wand e, vo ray repre tent the onatnaoualy aspng poate sil oy B 2a Whee me i re tree of iacontauities fF whic lave sce chiminated i pang fon ero tho tequeney in stan, Tho hewn lay roy he be dined as _ Btn @ Dy Any simile sowvmaten fer e2zzat systems sl To less simple, al ‘Snes oy wl snr Ii, paeee dey hes Te Leary om apedidic ‘Sons it seme ure to stsemps to forall such @ ceavention hee Sy nme! wth steady ete delay, let none caine Lia cay of em apetilic evel 1F the sigal is tananlted sibout dtorton the eam Cept of delay’ af se signe whole snp 1, becmape of ee, {Pe seal vecived signals ace elena L we may’ sti agree upon come Temata Sasi ot eich ae determining he Use of occurence, the “stn in consicerable eels ay vy qealy ita te dings ‘lsracatiaie beeen, For exenpir it depends on the Eebavier of cor wonwncs high feeqaenoy the dak aay he ute een frm oat Je depeads ov thier ho. Te the Exes eee she sl wel be ie fMfected i, before tarsminsn, uke gach were se rg ghee flee and in the second, Hit ent trough low mas te Teac ease fre mene a sly estate with w ditrianee which cmprisce ony thoee Fourier raat of the sins) which vont paticuler limited Inoge of fequeany. We any cong thi dea “aethr aad make go of « ‘rey nore un pas flee, Dy mirying ste ifeegucuey of tai fond tye cbtan ray wich is a funecion of frees. Tis alae, et any Fogaency, Ci uiy, ae defred by cur cnaveuton, of © dicubeace Sshicrsexpubds to the pat of the spctraza ofthe sigeal wie i fr the irvmalia ueighborkcod of the ‘eyes ix quetio, Our prebler then bo ad sccog'eahle fares ofa lturbarce ofthis kad ih bal, Dun Uiey ane asd oe exter of ray, the result cea be rete dinetly To the se ue envelpe dele os iene in len sof peindic distarbanes Compared wilt the pair of rqu sinusoid used in the deximition of STRADY STATE DBLAY AND APERIODIC StGwAtS Be caveloe delay, this dstusbence dirs in tain any finite cange of fre fqueney, cere tre en Isinty of slusos, the amplltdes of which nae tot all he che same, Tor simlisty, we same te accual ker to be replaced iy sn ied one in which there is ro dscortion within the base Aiud no Lavamibsion oats it.I he sgn] wae waoie be represented 2p 8 Fourier ing ve may chin the dese? lsurbance, for an angular requeney, ay by Sategrating from my ~ 5 tows} 2. "Tae dieurbsnce may be seprescnteé by f= reiyst tat [amin bslt Pla, 0) wer ia ent hee he se {aU ae hoa ey aon dae pe cipal tin oe ye a ta nor trai nn en xe he rng at feet fm Yo et Since we ar interested only in emall valuce af « xe may replace « by shure a af te the values of ad ‘We deine an instant, Pb sand tine, by Sbstitating these in 2) ane peforing he inegraion, we get sinh 20) = ro part of 28 exp lane — Oy — 08) ewe inte te angle, ae we tan = sod task (ot sre tan suid tke the reil pt, we act {ermB snd) (inh Bt com. . naa 2 exe cesar — Os — a) 19 si Lec us conser fist the exten wn ete the epectmam of UE sgl — a Vig. BsnctaySatcnace worming i on sme of he sete ‘ifr ia spline 9 he nelgiboehood! of oy 20 that of fezer. ‘Thon J) = 2840 en (09 EB con fur =O ald.) ‘ere the anita neues a const faevor which proportional to the bardith, 26, snl he agniande, 3 expe, at Ube Feequency, shuardaFirstin of linea plat of hick ies in Fig 1. Thi funtion Corsies of a roi’ navel Seaquezeyjc the clio vars with tine, re ervey Iwing symm eooat the instars, 2. AL whic iL maim. Ta, the Hine of maxinuan cove, hem 8 Unique inetast whe ie stale o> deine the treat whi the dae ‘urease occu. T ieterminel ley Phe slope uf the pase eequeney fare forthe sperm, ‘The ins, may be intexpete, in accordance with the prince cf setcnany phase the one hich Lie easel components of foe at near inte some pee, and hve he as deste ter FREEUENEY (o fezence. ‘This soliton ill Inkl when the ostanareons phase angle chong least ply wis Cegaenty, Ua iy when Rone fom which Theanale, 8, ~ eal, in (6), ives the pase of she save ne the insta, 1, whet Ra civehpe sa asiinen. The berceation of this ele wl bo iced by che genetic soagirution af Fig 2 hich ie sn to thet ms bese S¥Sreur YACHONICAL FOURNAL feploye for phase and group veel". The abscicar are value of Sin the ordinates ate values of phe in rlians. portion of the futon, fin the neighborhood of ig bow. Theditaace, OB, iss. The lope tthe tangent, (it, ts Gi carve at A ie. The dstarce, CB, i wu CCoasequenty, OC, or the intercept of tie tangeat on the Base ws, fan li xv alan in he Be, the sbeotte vale of this interey {2 greater i wwe ray teuloan {6} tom oem in which che angle lass tom 9 by the substitation = breath Bae, a vee sc ategr nd lel<e Th Pig. 2, mis and isthe distance DC. (6) then heron f= mt oy) 2H ctor = 9 aud pf the eednnry pls lag of saws, live to an oxg f time five by the instant of masinun envelope ‘We iy ein asthe inlant st wich Te discsharce aecuss oe Ty as whieh the envelope i a naninum, bat 7, a whish the istancancoas ‘ave of the function sie eas ablate volue. Since 8's small Comiare wit, thie wil occur very tel atthe smallest ste value Sie ler ubich ia — e} isl, This wll occur or eS mn “Saved, sual for wn -rey cha Teves rom (2, (and (7, tt he t nue ea tego sue) shat P< annatth <5, “The signfcane of thie case oan fra ig, 3. Here ination to che @ furve of Hg. 2, tere aoe plot Seis oF eaves whose online der ‘tam, ‘Hounalyonic" Ces, res 1016p. ST from it by multiple of = Ino ‘ar as anyone purely sinusoidal exmponent of te dstucbance concerned, wales af lave eternal y Ue twee hie ier ya even valle af ld he fisting. Aiteing by an ad musiple would repreext a reversal of siz, Let at tw ers tha cuve Sr whic the tanger ab inttrects the an le eat the origin, and elit #-} Br. Since, for the case dra, vel <5, st were greater we should have ba tnt 135 chen obvious shat he Lief sani absante value, Ty is glven by theeope ofthe line OF, Telfer rors Phy he derence in slope 0: the lines Ol and ‘We nove ta ced mn Ske epeccram ofthe éstusbane te tire of cecurrnce n term of twa deitions of the ater The nest step isto fumnpare ‘bee time for Ce int and oatpae and determine the come Sponaing dehy, Tec us onsier fst the rave where ie attenuation indepencent af cient f er in The own signal also. We nay then cafe vas acorsion t Eee sae, e. Tet deepen is alae Ae pat by ft the phase wt of the sytem by A. "Then at tbe Guipnt il 92 exeal t9 Ff BT we take the tire of accureace as Stein by the asimmum etvelpe, these times eb ad eutput Tank Tham “The aly ie then We Ty Pym By chic sy leon the envelop day af tho eyetem, ‘fee ie she me ov arene bused on tke mesma alse value, we ave, at the input, Denes At the opt, where STRADY STATE DELAY AND APRRIODIC SIGNALS mL ‘The delay, Wile theres. sypercial siaity ecco: his and Lae phase delay), ft fe of fit eral sizineane; ix C2, ia uetennined br Le eggrnae Increase in-phase sift with Srequarcy, shed in deter naire bye te of socrease aéw:. Mi exciple ux staien fo shch the two delays fre very eset, Is fucnshed! by & wave gue shen Ue fecuancy only Jit exer the ctol. "Phe pase deni hea smet seco wile she ate Uf edacge ps hit with requste is very lg. ‘Thus the delay haves on maim ateninr value depends on eth the ave lela anc the phise sit ot te ster, but ot on the phase ‘day. There romaine to eximite this cepencence fn more detall. The ‘alu of & depends on the spect of te igual as wel a the characte ofthe eystem. Tt of inovst to See i 1 ca Lemley a panty ceived trom the system characteristic ala: The west ovine Ping lay fea celsy whieh ie derives fom she pase sit of dhe syste i the terse deve sn Cas of the signal epootram. Tai wile pabohe, shee eee aes Toe dieser ewes this al the aperini iy baton ate salto Dem Do = Ele, Beet t= 49. Sion 8 thr en ingen stn “Femtac§ De= DB. =.