Yuriy Alyeksyeyenkov 1

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1 Çanaa Ünvrss Fn-Eba Faüs Journa of Ars an Sns Sa : 9 / a s 8 Cauaon of Sgna Sours Coornas In D An D Spa ur Asnov Absra hos of auaons of oorna of sgna sours whh ar nassb an r masurmn of hr proprs s mpossb ar ana. Cass of D D spas an sng mup sours of sgna ar nvsga spara. Rommnaons an nssar mahmaa quaons for praa appaons ar gvn. Avanag of sours oorna masurmn usng sgna paramrs n frqun oman s shown. Eprmna anass of mhos on h bas of ATLAB mong monsras fu onn of hor an pra. Inrouon In man praa ass anang of proprs an paramrs of ssm hr s no ass o h sour of a sgna arsng ns of. An amp of suh ssm s h auomob ngn n whh s nssar o fn ou sgna sours an h rasons of non-sanar bhavor ha an b ana on whn wors. In mn s aua rsarh of sgnas of ungs an har of h pan for arrng ou orr agnoss whou r ass o a sour of hs sgnas. Drmnng oornas of sgna sour oaons an onsrab faa pross of s rsarh an agnoss. L h sgna from suh an ob as on snsor-rvrs an furhr b app o h npu of h ssm anang. Tpa suh sgna an hav an form an from pon of ourrn ns n a rons ahvng snsor wh a varous m a whh s fn b sp of srbuon of a sgna n h nvronmn an san Compur Engnrng Dparmn Canaa Unvrs Anara 7

Eprmna anass of mhos on h bas of ATLAB mong monsras fu onn of hor an pra. Inrouon In man praa ass anang of proprs an paramrs of ssm hr s no ass o h sour of a sgna arsng ns of.

2 Cauaon of Sgna Sours Coornas n D an D Spa from a sour up o a snsor. Absn of w-fn borrs of sgnas no pro ompas arrng ou of masurmns n m. Sn h ffrn of m as bwn varous snsors s vr sma hs ffrns anno b masur wh a nssar gr of aura. A h sam m arrng ou h anass of hs sgnas n frqun oman s possb o oban a nssar aa s for a nfaon of orgnaon pon of a sgna. Th as of ssms of h m phsa s n whh hr s no anuaon of a sgna a s srbuon from a sour up o h rvr s amn. L a sgna a b rgsr b a snsor pa n a pon A. A sgna b ap b a snsor n a pon B s h op of hs sgna a n m b b a Whr D b - m a of a sgna n a pon B wh rsp o pon A. B h sam wa h sgnas n ohr pons of rvr oaons onrnng sam pon A an b prsn. Havng app Fourr ransform [] w sha rmn spra rprsnaon of h sgna rv b snsors. Connon bwn m an frqun rprsnaon of a sgna a pon A w sha sgna as X Th sprum of a sgna rv a pon B n onform wh m shfng propr an b wrn n h form of b F F b X a b whr h faor spfs phas shf of ah spra omponn of a sgna a pon B onrnng a sgna ap a pon A. Th souon of a probm of h sgna sours oornas rmnng s possb f h phas shf sasfs b b for a spra omponns. Th phas ffrn of sgnas masur bwn snsors s proporona o a ffrn of sans from a pon of ourrn of a sgna up o a pon of s rgsraon b snsors. Connon bwn phas shf an a m a an b sabsh n h form of quaon v whr ngh of a wav a frqun v sp of sgna srbuon n h nvronmn. Dsgnang a ffrn of sans from a sgna sour up o snsors A an B as ab an havng n mn ha hs ffrn s ss han ngh of a wav s possb o fn onnon of nar san ffrns wh a m a of sgna srbuon as ab ab a ab 8

A h sam m arrng ou h anass of hs sgnas n frqun oman s possb o oban a nssar aa s for a nfaon of orgnaon pon of a sgna.

3 ur ALEKSEENKOV whr Δϕ ab has shf of a sgna on frqun w an Δ ab m shf of a sgna a a pon of masurng B wh rsp o pon A. Hr a nar ffrns m as an phas shfs ar masur onrnng pon A. Thus masurmn of m as bwn hanns n m oman an b rpa b masurmn of phas shfs bwn hanns n frqun oman. As pons of oaon of snsors ar f aso hr oornas ar nown h probm s ru o rmnng of a pon of oaon of a sgna sour on h bass of h phas shfs anass bwn snsors. W sha amn varous ass of h son of hs probm. asurng of sgna sour oornas n D spa. For masurng h sour of a sgna oornas a n wo-mnsona spas wo snsors-rvrs of sgnas ar nssar howvr n as of qua rmonss of a sour from snsors phas ffrns a a frquns w b qua o ro ha as o nfnnss of h son. Fgur. asurng of sgna sour oornas n D spa. Hr h sour of sgna an b a an san from snsors on a n of a prpnuar onsru n h m of a n onnng snsors. Hrnafr w sha ma on anon o h mahmaa sons havng a posv sgn ha spfs oaon of a sgna sour ns h nvsga nvronmn wh h souon wh a ngav sgn fns a smmr pa of a sour oaon bu from h rna s wh rsp o h ob. To mna hs nfnnss w a an aona hr snsor-rvr of a sgna C Fg.. 9

As pons of oaon of snsors ar f aso hr oornas ar nown h probm s ru o rmnng of a pon of oaon of a sgna sour on h bass of h phas shfs anass bwn snsors. W sha amn varous ass of h son of hs probm.

4 Cauaon of Sgna Sours Coornas n D an D Spa Th sour of a sgna s pa on a pan n pon D whh oornas ar nssar o rmn. Thr snsors ar on an as an hav oornas A B an C. Enrng sgnaons D = DB-DA an D = DC - DA havng sgna san bwn pons D an A as r an a ang of an nnaon of n AD wh rsp o as as q s possb o wr own a numbr of obvous quaons As DB-DA = an w an wr AO + OD = AD OB = AB - OA = - ros DB = - ros + r sn = + r - r os r r os r r os r Or n ohr form for rang ADB s possb o wr own r os Smar prsson for rang ADC oos os r Carrng ou vson of on an fnng h souon wh rsp o os w hav os f From whh h vau w n aros f To fn r w mup prsson on prsson on an hn w sha fn hr ffrn [ os os ] r ang obvous ransformaons an sovng quaon for r gvs r asurng of sgna sour oornas n pon D s now ru o auaon of r sn r os

= AD OB = AB - OA = - ros DB = - ros + r sn = + r - r os r r os r r os r Or n ohr form for rang ADB s possb o wr own r os Smar prsson for rang ADC oos os r Carrng ou vson of on an fnng h souon

5 asurng of sgna sour oornas n D spa. L four rvrs of a sgna ar on a pan a san from ah ohr an hav oornas n hr-mnsona spa an aorng an h sour of a sgna s rmov from snsors n spa on oorna. L h oornas of a sour of h sgna whh s bng a arbrar pon A b nssar o rmn Fgur. As w as n h prvous as w onsr h souon wh h posv sgn spfng on an arrangmn of a sour of a sgna ns of nvsga ssm. Th san bwn bas snsor n a pon of orgn an pon A s ur ALEKSEENKOV an ffrns of sans bwn pon A an pons of oaon of snsors wh rsp o bas ar 4 Coornas of an nvsga pon A wh us of sphra oornas an b fn as os sn sn os sn 5 Eprssons 4 n vw of 5 an b ransform o a form 6

L h oornas of a sour of h sgna whh s bng a arbrar pon A b nssar o rmn Fgur.

6 Cauaon of Sgna Sours Coornas n D an D Spa Fgur. A proon of arbrar pon A o o o on oorna as. an prssons 6 an b wrn own as sn os sn sn sn sn sn os ang subraon 7 an 8 from 9 gvs whn w fn vau of h vor mou r prss n ffrns of sans Dong furhr ransformaons w sha prmnar rmn ffrn of prssons 9 an 7 havng wrn own sn sn

an prssons 6 an b wrn own as sn os sn sn sn sn sn os 7 8 9 ang subraon 7 an 8

7 ur ALEKSEENKOV Now ung ross mupaon of prssons 7 an 8 an mang smar aons wh prssons 7 an w oban ssm of quaons sn sn sn os sn sn sn os ang vson on w g sn sn sn sn 4 Afr smpfaon an sovng 4 for sn sn w oban sn sn whh n vw of an b wrn own n h form of sn sn 5 B anaog o aons ma abov havng rmn a ffrn of prssons 9 an 8 w g sn os 6 Now mang ross mupaon of prssons 8 an 6 havng wrng own sn os sn sn 7 an havng arr ou vson of prsson 7 on prsson gvs sn os sn os 8 Sovng 8 for prou of rgonomra funons sn os w oban prsson sn os 9 Consrng an mang subsuon 5 an 9 n 5 rqur prssons for rmnng of gomra oornas of a sgna sour n hr-mnsona spa s oban

g sn os 6 Now mang ross mupaon of prssons 8 an 6 havng wrng own sn os sn sn 7 an havng arr ou vson of prsson 7 on prsson gvs sn os sn os 8 Sovng 8 for prou

8 Cauaon of Sgna Sours Coornas n D an D Spa 4 Whr a nar ffrns aorng o an b prsn as phas shfs aua from h spra rprsnaon of a sgna n frqun oman. asurng of sgna sours arra oornas n D spa. L h sour of a sgna b no a o bu omp ob wh an unran pa of oaon of sgna sours pa n pons А whr s a numbr of a sour of a sgna < < - an - quan of sgna sours. Thr paramrs an gomra oornas an b rmn b rvng a sgna wh h arra of h snsors pa on a pan. In [] h masurng ssm wh wo sours of a sgna was nvsga. Hr w onsr ssm wh arbrar numbr of sours of a sgna. L h sours of a sgna b pa ns of nvsga ob an prou h sgnas ha ar srbu n a rons. As w as n prvous onsr ass w hn ha snsors ar on nsgnfan san from a sour an no anuaon on ampu of h sgna rv b ah snsor. L snsors arra of s NN form a squar ns of whh hs snsors ar pa wh nar sp. To no poson of ah snsor w sha us a noaon S whr N. Gomra oornas of ah snsor w b no as S. Th sgna rv b a snsor S s suprposon of para sgnas from a sours an hs sgna an b srb b quaon whr - a m a of sgna srbuon from -h sour o S snsor. Th sprum of a sgna rv b ah snsor an b prsn n form X X F Thn h mou an phas of a sgna sprum an b prsn n h form X R Im aran

Thr paramrs an gomra oornas an b rmn b rvng a sgna wh h arra of h snsors pa on a pan. In [] h masurng ssm wh wo sours of a sgna was nvsga. Hr w onsr ssm wh arbrar numbr of sours of a sgna.

9 Eprmna mong of agorhms. Th agorhms of masurng of oornas of a sgna sour n D an D spa wr nvsga on a program v b usng ATLAB. Paramrs of mos wr hosn so ha phas shfs for an of amn as no p. For ass of rmnng of oornas n D an D spa h san from snsors up o a sour of a sgna was whn h ms of m sp of srbuon of a sgna was n rang of <v <5 m/s h frquns of a mo sgnas wr n rang from H up o uns of H. asurng of gomra oornas of sgna sours arra was rsarh b usng h mo of snsors ssm of N = 4 a amoun of sours of sgnas =. Fu onurrns of h mo an aua gomra oornas wr rv for a varaons of rsarh paramrs. REFERENCES Aan V. Oppnhm an Aan S. Ws Sgnas an Ssms Prn Ha p. u. F. Asnov an L. P. Duhav Shapng h aous mags of obs Raorons an Communaons Ssms Vo.48 # 5 Aron Prss. ur ALEKSEENKOV 5 Th phas ffrns bwn wo snsors n pons an N a an frqun w sha fn n h form R Im aran R Im aran F whr h ffrn of phass of rv sgna masur bwn snsors n pons an ar omponns of h sgnas rv from sours А. Crang ssm of h nar quaons for a possb pars of snsors an sovng hm for phass of h sgnas rv from ah sour a a frquns w sha hav nssar paramrs an ha w b us for rmnng of gomra oornas of sgna sours. Th ssm has souon f h raon NN > s sasf. Th subsqun fnon of nar ffrns aorng o bwn ah par of snsors a an pons of hr oaon an aows us of - o fn h gomra oornas of ah sour of sgna А. Anohr avanag of hs mho s ha sprum sruur of ah nrna sour of h sgna s rmn ha an b usfu for fuur anass of ssm bhavor.

asurng of gomra oornas of sgna sours arra was rsarh b usng h mo of snsors ssm of N = 4 a amoun of sours of sgnas =. Fu onurrns of h mo an aua gomra oornas wr rv for a varaons of rsarh paramrs.

Term Structure of Interest Rates: The Theories

Term Structure of Interest Rates: The Theories Handou 03 Econ 333 Abdul Munasb Trm Srucur of Inrs Ras: Th Thors Trm Srucur Facs Lookng a Fgur, w obsrv wo rm srucur facs Fac : Inrs ras for dffrn maurs nd o mov oghr ovr m Fac : Ylds on shor-rm bond mor