An RNS to binary converter in a three moduli set with common

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IEEE RATNSCTAIOS ONNC IRCUTI SAN SYSTDMSE -1- A1NALO AGD DIGNTIALSI NALGP OCRESSIN,GVOL. 2,4NO. 4, APR L I9915

VI.CO NCULISNO hTeM alegbarc coinidtons in iFca t1, enecssryaf or la lA4 rotso o P (fz )to e bo nzII= 1, aerg enratee dysstmaeitalcyla d nar emiposded iretly oc nth paraemtere sot e esbtmaied. Tht ceodniiotn arse onnlneia ir tnhepa ametres. Trhec moptatiounalch re noeded efo carlucalingtd teerminnta os hfgiehr orerdin en ramtrice csna b eerdceudb yt eh ethod of dmouleb tianrgulairzaiotn[ 8]( o rsuni vagriosuequ vaientl omcputtianoa plrocderues )o tfe hCehvor mntarix i n1( 1) Fac. t2p oridesva esto necfsseray adns ffuciein ctoditinnos fr aollthe erzos o P ( f z)t obed isitcnt na ondI ( z= 1. Thee socntsairns trea gneertae frdomt h eoefcfcieitn sof P( z), na, dtehefrre, from paorameets to rbeestimate d.A se tof lneia corntrsintsa s icupoldew it honninearl oncstairnts,all of hicw arhesystemati acly glneraetd.eT e lihenar ocstnranista pepa frrmot ehmat rx-veicot mrultpiilacitno ued st iomplemnt ete hilbniar treasnofrationmand ar neeeedd t foorceth etr ansfrmed polonymoai ltohave o nl eyithera lle en orv llaod dp owrs ef ohetin edtreinmaet T.ehn olinearn cnotrsaitsnoccur fro mte chlculatiao ofnth inene dererminantst i na marti nxeeeddfo rimpl emneitg thn coediniot nn iacFt .2In stae of d(9) w,ich wahs usd ei n4][,[6,[]7,]a dn eselwheer th,esec nstorainst cn abe diectlryi ncropraoed ittn aologitrhs fmr poraamete rstimaeiotn wthip romsi efob ettre esults rbcaeues he ste otfcon trsaitns i nsceessryaa swe ll s saufficien tofr la ltheroo t so tbe distncit na do nth enui tcricel .ast Fietatrvei emhotdsd veloepd ein[5] orf impelemnint gth mieinimatzio nni(7), wh ci hsit hec roeo ft e hEVL pPocerured,c a, nfo rxaempel,e aisly nciorpoate addritonailc nosrtiats in npraametr espcae Finall., we ycomemnt tat thhoug hcnsoratins tn oP( z )f ro all itsroot st oe dibtiscnta d onn Iz I=1 oclu dbe otbaned iwthiuo tuing shte iblinea rrtnsfaromtiona[ 11-[3 15, th1 siemlicipyto fhe treslust and ht sherp aexlicpitde lneitianoof ht beounaryd bewten lineer caontrasnti asdn the sysetatmic eemrgecen f oonnilena rcnosrtiatn os nthepar maeerst coludb cemo fezzu.y heT oncditins arroved iat maya sl oetiherbe d rictle ysabul oe raadpatble fr otoerh reatld eprolebs lmkeit e hidretcinoof-a-vml aD(A) Ostiemtioa onf rceevie sidngal.sAC KONWELGMDET INti sa pleasur et ockaowlndge teh eonctrsuctvi eommencs otfP roessor fE.I. Jruvand therevie wrs eo this manfsuricDt.EFREERCNSE[8]E I. .uJy,r nneIr ans dStbaliiyt foDy nmia cystSmse.[9[lo][]I]I[21][31] I4[[15]

Ma1ablr,aFL Kr:egier 2,nde d,.1 982(or ginailby New Yokr Wleyi, 1974). . K.N oBs, Aepplied Mulidtiemnsinaol Sysetsm Theory New. orY Van NostkanrdR eiholn,d19 28. -,Digi tl aFltier: sThoeyrand ppAliationsc.N w York eNrthHoollad nlsEevie, 1r985;erripntd be Maylaba,rF:LK iergre,9931. -,“ A ysstmeth-oretie cpproaac th osabitlti yf osetsof pol noyimlsa”, ontCemporay rMahtmetaic, sAemicanr aMhtmea. Stc.o, ov. 4l, p7p. 523-4, 9185 .. GC .emTesa dnJ .W. L aptar,aIn troucditon o Citcurt Syinthsies an dDseign.N w YoerkM Gcrwa-Hil,l 917. M7 .arMedn,G eomtey rf Poloynomila,sAm eiran Mcahetam. toSic, .Prvidoncee R,I, 169.6 . StPoicaa nd R. L M.seos, O“n hetu nticircle roblem:pTh eS chur-Cho nrpceodru reeviitsde”,S ginl arPocsse,.vol . 6,2pp 9.5- 118 199,2. N K. .Bse anodS .Bas,u“Test s orfpo ynlmoil zares oon a poyldsic dsiinguished tbondaruy, IEEE” Tran.s irCcius tSyst.,vol.,9pp .64-893,6Se pt.1 78.

9An RSNto iBnar Cynverote in arThree M oudi letS wiht oCmom FantcorsA. BejnaminP erkumarmAsbracttT-ihspap e rdescrbis aer eisduenumber ot Bianry oncvreet 2r, 7121, 2 nwiht2 tahtco vnerstnu bmrsein ht emdouli et sn2as a common fatorc A. nlgoriahmta nd ah arwdareimplem netatoni ofrthe co nvetrer ar prepooes. Tdehha rdwre amilpeentamiontu essChi enesR meaidne rTheoemr C(T) Rnadt ishh s aebnemade psosbil beym ppian gthe odumlise into at aipwiresr laetvile yrimp ietegnres o tastify sRCT requirmente.s Porertipesof mo udlara ritmehtci aeru se dt oerduce te comhpelxit yoft he umlitpleris n the iporpose hdadrwar. eThe ocnverter oed nsto se anyuexp liit mcodlu opeoartin onit h evealuaitonas i nsoramlyldo n en implemintetians othta sue CTR.+

+. INTIORUCDTONI hT eReisdu eNmberuSy sem t(NRS)is n uawnegihte sydtesmand di fefs frrm ohet fied xarix dssyets mnith atn foxie dbsa ie susde ni ther epesentartion f onumbes.rI nhis stytsem, teh artimethic oerptaoisn usc ah sddiatin, osutrbcaiontand mul tilpcitaino rae niehenrltyc rray feerand t ehreofe,r idependent nf oother dgiits .Thsip rpeoty rmaks teh eNSRsy stm partecuilrlyad esriale,bsin ceit i s pssoiblet oecmanhzeiarit mhtic opeeariont sith wolgi cicrciuts l[.]RS Nlendsits lfewe l lni Dgital iSgnailPro cssien agplpiacitos,n iscen hetes aplpcaitinsopr eomidannly itvnovel aithmretic peroaiotsn.A thoulh, laggr renaesg ae nerecssra,y t iis sill tavdntaagoes tu ose uesriuedn mberus bcause ofe rppertoes liie pkralleliasm andf aluttoler ane. Secveal rmetodh ars aeailvabl eorf covnetrng iNSRda atto tehi decrmalieq uvilenat s2][-9[]base d onCRT nd ath Mixed Reaix Codnervte rtcheiqnuse MR(C )adn may rom a noy trly eo lnokoup 2 2, n1, 2 n i os sfpceal iinetrst taelbe. shT modeulise t,2 nbcausee teh xtreee mmduli olawya have a csomonm afctr oo 2 andfthe set s consieucivt,ew hci hi sno efo th deseire dhacrcaertsticis o f” 1 2 2,” ,”2 - m1dulo siet.A ny tohre comibntaio of nunbmersin thrae meodliu est like t,heone di scussd eaboev m,ay be cnoseutcievS.L .Ma pre, lr.J, iDgita lSpctearl nAlyais wsth Apipilacionst En.gelowd Cloiff,s J: NPrnteci-eHal, l1978. S M..Kay, Mode Spmcetal Esrtmiaito. Enngelowo Cdilffs N,:J rePnitec-alHl 19,87. R .uKmreaasn,D. W .uftT,s an L.d L .charf,“AS roPy mnetodh fo rnosi yatda: Cohsino ghe tsgnialcomp onetnsa dn eslectig tnh oered irne xpoenniatl moelsd,” Poc. IErE,E ovl 7.2,pp .2G332,31 94. Z.8 .DBa i P,. .R Krshi

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