io Recio of Gy Ce Lo wih Hoiig Uig Fiie Ipe Repoe (FIR Digi Fie D. ECOOOU I. ATOIADIS Reech Ai Ai Pofeo Depe of echic Egieeig, io Techic Uiveiy of Ahe, Poyechic Cp, Zogfo, P. O. Bo 64078, 15710 GREECE. Abc: - I hi ppe eho i popoe fo he ecio of vio of o cie by p gy ce, wih hoiig of he o. The popoe eho i be o he pecoiioig of he ip o he ye by igi fieig he ip fcio. Coveio FIR o IIR fie c be e fo he pecoiioig ppoch. Siio e wee e o eoe he effecivee of hi eho. Key-Wo: - io Sppeio, Ip Pecoiioig, Digi Fie. 1 Iocio Ce e wiey e i iy poio of hevy o. The ee o wig e i op of efficiecy, o ge eve ccie. Th, eho o ece he ie ei o wig e of jo ipoce. The pobe of oeig he ye coo he o wig i o ivi pobe, epeciy whe hoiig of he o ig he oio i coiee. I hi ce he ye i oie ie-vyig. Thee popeie of he ye ke i oe iffic o eig ppopie coo eho, cpbe o ppe he ociio of he o. io ep hve bee e o coo he o wig. Ope-oop o feefow coo eho hve bee popoe, eihe i he fo of opi coo [1-3] o ig ip hpig eho [4-6]. A hee eho ffe fo he fc h he ye poee oie ie-vyig chceiic eihe ee cope ipcic eveope o hve iie obe o viio of he ye chceiic. A cobiio of ope-oop coo ig he oio coe-oop coo, ig he e of he ope-oop, h bee popoe [7-9], i eve fo, ig h eo eee c be pefoe. Ao, v viey of coe-oop coo eho hve bee popoe. A opi feebck cooe h bee eige eicy ee [10]. A pive coo eho e e ewok o pefo he ef-ig [11]. Aohe pive cooe e pee-eig pocee be o he eee of he ie of he ce ife [12]. A obeve-cooe eho h bee popoe, ig ie-vyig gi [13]. Fzzy coo eho hve bee popoe [14,15] hve bee cope wih cic cooe [14]. Thee e cei ifficie fo he pcic ipeeio of he bove eho. Thee ifficie ice he cce eee of he o poiio veociy (ice ew o i cie i ech opeio, he cce eee of he wig ge o he icee copeiy of he cooe. Of peci iee i he pee wok, e eho o coo he o wig h e be o he ip hpig ppoch [4-6]. They e ope-oop coo, h, ipify he eqiee, he co he copeiy of he pcic ipeeio. They e be o he covoio of evey biy ip o he ye wih eie of ipe kow ip hpe [16,17]. The ee ip i be o ove he ye o he e fi poiio, he biy ip, cceig he effec of he ei vio. Whie ip hpig eho pee goo pefoce i viey of ye ppicio, hei obe i iie i oc e o he ye feqecie e fo he eig of he ipe. Oy he icee of he o io of he ipe eqece c icee he obe, b hi e i eie ey i he o io of he ye oio. Epeciy whe ie-vyig ye i coiee, he obe o chge of he ye pee i of jo ipoce. I fi ep o ee he obe of he vio ppeio eho be o he covoio of he gice fcio wih eie of ipe, gee ppoch fo he ipe
eqece covoio pocee h bee popoe, eig o e of hee iffee eho fo he pope eig of he ipe eqece [18]. The ipe eqece ppoch i igificy eee, by ebihig heoeic fewok, ccoig o which he eig of ppopie gice fcio c be foe o he pope eig of coveio ow-p igi fie [19,20]. The effecivee of coveio Fiie Ipe Repoe (FIR fie fo ei vio ppeio h bee fhe ie hooghy, boh heoeicy epeiey [21]. Be o five eqiee, h ee vio ppeio wih ii ei vio eo, ho ey, icee obe, igi boy oio, yeic eig pocee h bee ioce. I i be o he cocep of Dey-Eo-Oe (DEO cve, which hve bee ioce eig oo fo eeiig he opi FIR Fie Deig Pee [21]. Pe, he vio ppeio cpbiiie of coveio Ifiie Ipe Repoe (IIR fie hve bee eie epeiey veifie [22]. A i he ce of FIR igi fie, he DEO cve hve bee e o popey eig he IIR fie. Te FIR five IIR igi fie hve bee oy coiee [21,22]. Ahogh ype of fie hve ecee vio ppeio popeie, hee of he FIR fie ioce vey ie ey pee i obe i chge of he ye' yic pee [21]. Pe, gee e, IIR fie ioce ge ey h hoe of he FIR fie. Howeve, hei ove pefoce i cei ce, veifie o epeiey, c be bee h h obie by FIR fie [22]. I hi wok he ip pecoiioig ppoch ig igi fie i e o e wih he pobe of he o wig of gy ce. Fi oe fo he ce i popoe he ecey ip o he ye e efie. The, he ip pecoiioig ppoch ig igi fie i peee. L, eic iio e e e o how he effecivee of he eho whe he ovig ice he hoiig of he o e vie ove ge ge. 2 Sye ecipio A oe of p gy ce wih veegh cbe i e i hi wok. The oe i how i Fig. 1. The chceiic of he ye e: he hoizo poiio of he oey, he egh of he cbe he ge of he cbe. Aig h he cbe i ifee e o, he eqio of oio c be wie : + 2 + ( g + i( co( = 0 (1 The cceeio of he oey, (, he cceeio of he cbe, (, e he ip o he ye. The go of he popoe eho i o ove he o o ew poiio (efie by he fi ve of, whie he wig ge i iiize. o cbe ( g ( oey ( Fig. 1. oe of he p gy ce The oigi (o-fiee ip e fo he eic iio e be o he i cceeio i veociy of he ye. If ẋ ẋ e he i cceeio veociy i he hoizo iecio i he eie ovee, he he qicke oio of he oey c be eive wih bg-bg o bg-off-bg cceeio ip. The bg-bg ip coepo o he ce whee: 2 (2 he ie i whee he wichig bewee cceeio eceeio ipe occ i: = (3 I y ohe ce he ip i bg-off-bg, he io of he cceeio he eceeio phe = i: he o io of he oio i: = + (4 (5 Eqivey, if i he i hoiig cceeio, i he i hoiig veociy i he eie hoiig, he qicke hoiig of he
o i, o, of bg-bg o bg-off-bg ype. I i pefoe wih bg-bg ip whe: 2 (6 he ie i whee he wichig bewee cceeio eceeio ipe occ i: = (7 ee he ip i bg-off-bg, he io of he cceeio he eceeio phe i: = he o io of he oio i: = + (8 (9 A epe of bg-off-bg ip ( wih coepoig veociy ( coepoig ipcee ( i how i Fig. 2. Boh he coo ip ( ( i hi wok e coiee o be of bg-bg o bg-off-bg fo. The i cceeio i he i veociy ẋ ẋ e ppie fo ech oio i eche, he co veociy oio i pefoe fiy he i eceeio i ppie i he oio op. The ie i fo ech oio h coepo o he o he op of ech cceeio o eceeio phe e fo Eq. (3, (4, (5 o Eq. (7, (8 (9. Sice ẋ, ẋ, e co epeig o he ye, he bg-bg o bg-off-bg ip fcio fo evey ove ice hoi ice c be eiy eive. Fig. 3 4 how he o wig ge fo wo iffee ove ice, whie =0. I c be obeve h, i gee, he ei o ociio iffe fo he ie oe, e o he effec of he eceeio phe. I oe ce, i Fig. 3, he ei ociio i o ccee. ( - - - 0 10 20 30 (ec 40 Fig. 3. Tie ei o ociio ( ẋ =0.2 /ec 2, ẋ =0.4 /ec, =6.22, =15 =0 ( - - - 0 10 20 30 (ec 40 Fig. 2. Acceeio, veociy ipcee of ypic bg-off-bg ip. Fig. 4. Tie ei o ociio ( ẋ =0.2 /ec 2, ẋ =0.4 /ec, =7.74, =15 =0 Fig. 5 6 how he o wig ge coepoig o he e ove ice, whie hoiig occ
ieoy wih he oey oio. I c be obeve h he ieo eecio of he hoizo oio he hoi oio e o ecie ge o ociio. Fo hi eo, epeiece ce opeo y pefo hee wo k epey, eve wih co i ie ey. ( - - - 0 10 20 30 (ec 40 Fig. 5. Tie ei o ociio ( ẋ =0.2 /ec 2, ẋ =0.4 /ec, =6.22, =0.4 /ec 2, =0.8 /ec, =15 = -10 ( - - - 0 10 20 30 (ec 40 Fig. 6. Tie ei o ociio ( ẋ =0.2 /ec 2, ẋ =0.4 /ec, =7.74, =0.4 /ec 2, =0.8 /ec, =15 = -10 3. Ip pecoiioig 3.1. Ip pecoiioig ig FIR fie A Fiie Ipe Repoe (FIR fie i eie of co {c }, which e he fie coefficie [23]. The heic foio of fieig i covoio pocee, eig o icee fiee ig (kt S, which i obie fo oigi icee ip ig g(kt S ccoig o Eqio (10, S = S (10 =0 ( kt c g( kt T whee k i iege, T S i he pig peio of he icee ig ( k g( k, T i he pig peio of he fie {c } i eie of co of egh +1, which i ce fie oe. The z- fo of he fiee fcio U(z i ee o he z-fo of he oigi ip fcio G(z by whee: - ( ( ( = ( =0 = (11 U z F z G z c z G z F( z = - cz (12. =0 wih coepoig feqecy epoe fcio of he fo: F ( jω F ( j2 π f = - j 2π ft c e =0 = (12.b The ip pecoiioig ppoch, ig FIR igi fie, i we ebihe boh heoeicy epeiey fo Lie Tie Ivi (LTI Sye [20,21]. Accoig o he popoe pecoiioig ppoch, ie of he iec ipeeio of he oigi ip fcio ( ( i Eq. (1, coiioe gice fcio ( ( c c c be eivey e, obie by he oigi gice fcio ( ( by igi fieig, how i Eqio (13.,b: ( T ( c S = c kt S T (13. = 0 ( T ( c S = c T S T =0 (13.b Povie h he feqecy epoe fcio F(jω of he fie i zeo feqecie coiciig wih he epece feqecie of he yic ye ccoig o Eqio (12.b, hi fie i cpbe of copeey eiiig he ei vio effec. I iio, he epoe fo zeo feqecy of hi fie ho be kep eq o oe, i oe o ee he pope oio of he echic ye igi boy. I view of Eqio (12.b, hi eqiee becoe: F (0 = c = 1 (14 =0 Coieig ob ei vio ppeio, he obe popeie fo he pecoiioig pocee c be iecy e, by eeig he eqiee fo zeo feqecy epoe of he fie o oy fo iivi feqecie coiciig wih
he epece feqecie of he ye, b o fo eee e (op-b e of he fie feqecy epoe fcio F(jω, i oe o cove ow iioy he poe viio of he ye feqecie. Povie h he opb e of he fie becoe he i poe, he i poe egee of obe of he gice fcio c be ie. Ahogh hi eho h bee popoe epeiey veifie o be effecive fo LTI ye [19-21], i c be e, o, fo oie ie vyig ye, e he foowig eqiee: R.1 The pie of he o ociio i kep ig he oio of he ye, o e o ieize behvio of he ye. R.2 The fie op-b i wie eogh o cove he whoe feqecy ge of he ie-vyig feqecy of he ye. 3.2. Fie eecio A ppopie FIR fie, cpbe o ppe he ie ei vio of he ce o, hve p-b (epoe eq o 1 fo he owe feqecie op-b (epoe eq o 0 fo feqecie eq highe of he owe feqecy of he ye. Thi ype of fie i ce ow-p fie. Thee e eve eho ve o eig owp FIR fie, ch he Pk-cCe eho, he Wiow-be eho he Coie Le Sqe eho. Ech of he cce he coefficie c, ig iffee pocee, i oe o ppoie he eie feqecy epoe. De o hi ppoiio, he c feqecy epoe of fie iffe fo he eie: hee e ippe i he p-b op-b (he epoe i o ecy 1 o 0 epecivey o iio b (epoe bewee 1 0 ei bewee he p-b he op-b. The eiece of ippe i he op b peve he o cceio of he wig, howeve hey c be ece icy. A e ieiive fie cpbe o ppe he ie ei vio of he ce o, cove he foowig eqiee: R. C-off feqecy (owe ii of he op-b e h he ye' e feqecy. R.b Sop-b qie wie i feqecy i oe o ppe he vio whie he ye feqecie e vyig. R.c Repoe fo zeo feqecy eq o oe, i oe o chieve ppopie igi boy oio R. Rippe o he op-b e h pepecifie ccepbe vio eo. R.e ii poe fie ey Be o he bove eqiee, eho fo he opi fie eig hve bee popoe [21]. Accoig o h eho, he Dey-Eo-Oe (DEO cve e geee vi ieive goih ig he b Sig Poceig Toobo [24]. Thi goih i e o vy he fie eig pee ove ge ge of poe ve fo ech pi of fie oe peie vio eo he o cce he ii eive ey ioce by he fie. The he ii eive ey i poe fcio of he fie oe he peie vio eo. Bece oy wo of he IIR Fie Deig Pee c be eeie fo he DEO cve, ook-p be wee o cee ig he opiizio poce o oe he ve fo he eig pee h e o ii ey [21]. I hee epeie he ccepbe vio eo w e 5% of he vio ice by he oigi ip. Fo hi ve of he ccepbe vio eo, fo he coepoig DEO cve fo FIR fie [21], he ii fie ey w fo o be 1.25 ie he ge eigepeio of he ye. Seve ype of coveio FIR fie e be o cove he bove eqiee: fie eige wih he Coie Le Sqe eho, fie eige ig he Pk-cCe eho o fie eige ig Chebyev wiow [23]. I he eic iio peee i hi ppe, he e fie h bee e. Howeve, he bove fie hve ii e. Fo hee eic epeie, ow-p fie of oe 26 w eige ig he ofwe pckge b veio 5.1 i ig poceig oobo. The ize of he op-b ippe w e h 5% of he pie of he p-b. The eie o io of he fie w 9.72 ec, which i 1.25 ie of he ye' ge eigepeio. 4. eic iio 4.1. oio wiho hoiig. eic iio wee coce o how he effecivee of he popoe eho. A ce w coiee, hvig he foowig chceiic: i oey cceeio ẋ =0.2 /ec2 i oey veociy ẋ =0.4 /ec i hoi cceeio =0.4 /ec 2 i hoi veociy =0.8 /ec iii cbe egh =15
The oe ece i Eq. 1 w e o obi he eic e. The Rge-K eho w e fo he iegio of he iffeei eqio. ( io ie T i Oigi Fiee ove Dice ( Fig. 7. i ie vio i eio o he ove ice. 0.16 ( io i e R i Oigi Fiee ove Dice ( Fig. 8. i ei vio i eio o he ove ice. Fi, he wig ge w eie ig veice oio wiho hoiig. The ove ice w vie fo 1 o 10. The ppopie bg-bg o bg-off-bg ip w efie he pecoiioe oe w cce. The i pek-o-pek vio w cce ig he oio (ie vio fe he e of he oio (ei vio fo ech oe of he wo ip. Fig. 7 8 how he i pek-o-pek ie ei vio i eio o he ove ice. I c be eiy obeve h he ie ei vio ice by he fiee ip w vey, ege of he ove ice. Th, he eqiee R.1 w e i ecio 3.1 i e eqey. 4.2. Hoiig ig he oio. Hoiig w coiee o occ ig he oey oio. The oio ice w kep 7.5 whie he o ifig w vie fo 1 o 10. Fig. 9 how he pek-o-pek ie vio ice by he oigi he fiee ip i eio o he hoi ice. Fig. 10 pee he pek-o-pek ei vio ice by he oigi he fiee ip i eio o he hoi ice. 0.16 ( io ie T i Oigi Fiee Hoi Dice ( Fig. 9. i ie vio i eio o he hoi ice. ( io i e R i 0.20 0.16 Oigi Fiee Hoi Dice ( Fig. 10. i ei vio i eio o he hoi ice. The ie ei ociio ice by he fiee ip ppe o be vey eve whe he hoiig w 66% of he iii cbe egh. 5. Cocio Tie ei wig of gy ce o c be cooe efficiey whe coveio igi fie e e o pecoiio he ip o he ye. A w how by he eic iio e, he pecoiioe ip ece igificy boh he ie ei ociio of he o, eve whe he hoi ice of he o w ge. Thi eho i eiy ppicbe i pcic ppicio, i ipe o ipee, efficie oe o eqie peci eo o ohe eqipe. The oy co pi fo he coo of o wig i ie ey of he oio, which i eq o 1.25 ie he ge peio of he ye. Ahogh, i hi wok, hi eho i peee ope-oop coo ppoch, i c be cobie wih ipe coe-oop poiioig cooe. I hi ce,
he ip pecoiioig ppoch c be e o povie efeece ip o he cooe, which oe o ecie vio. Th, he hocoig of opeoop coo c be voie, wiho he ee of cope epeive coe-oop coo ye. Refeece: [1] Skw, Y., Shi, Y., Opi Coo of Coie Ce, Aoic, o. 18, 1982, p. 257-266. [2] Aeig, J.W., Toge, H., Tie opi coo of ovehe ce wih hoiig of he o, Aoic, o. 23, 1987, p. 437-446. [3] of, K.A.F. Ebei, A.., oie oeig Coo of Ovehe Ce Lo Swy, Jo of Dyic Sye, eee Coo, o. 110, 1988, p. 266-271. [4] Cho, J., Pk, Y., io Recio i Fee Sye Uig Tie-vyig Ipe Seqece, Roboic, oe 13, p 3, 1998, p. 305-313. [5] Sige. C., Sighoe W. Kiikk E., (1997, "A Ip Shpig Cooe Ebig Ce o ove Wiho Swy", Poceeig of he 1997 AS Topic eeig o Roboic Reoe Sye, Ag, GA. [6] Sighoe, W., Poe L., Keio,., Kiik, E., Effec of hoiig o he ip hpig coo of gy ce, Coo Egieeig Pcice, o. 8, 2000, p. 1159-1165. [7] Skw, Y. Shio, y., Opi Coo of Coie Ce, Aoic, vo. 18, 1982, p. 257-266. [8] So, K., Skw, Y., oeig Coo of Fee Roy Ce, Ieio Jo of Coo, vo. 48, 2085-2105. [9] Skw, Y., So, H., oie oe Lie Rob Coo of Ovehe Tveig Ce, oie Ayi, Theoy, eho & Appicio, vo. 30, o. 4, 1997, p. 2197-2207. [10] A-Gi, A.Z., of, K.A.F., izi, S.S.A.K.J., Opi Coo of Ovehe Ce, Coo Egieeig Pcice, o. 3, o. 9, 1995, p. 1277-1284. [11] oeo, L., Aco, L., eez, J.A., Toe, S., Hio, A., ich, G.., A Sef-ig eoophic Cooe : Appicio o he Ce Pobe, Coo Egieeig Pcice, o. 6, 1998, p. 1475-1483. [12] Tk, S., Koo, S., Aoic eee Coo of he Aie of Ce Life: Life-ie eee Coo, Coo Egieeig Pcice, o. 6, 1998, p. 1099-1107. [13] Gi, A., Sez, C., Ui, G., Obeve- Cooe Deig fo Ce vi Lypov Eqivece, Aoic, o. 35, 1999, p. 669-678. [14] Behijeb, A., Giige, G.L., Fzzy Coo of Ovehe Ce Pefoce Copio wih Cic Cooe, Coo Egieeig Pcice, o. 3, o. 12, 1995, p. 1687-1696. [15] Lig, Y.C., Koh, K.K., Cocie Ai-wig Appoch fo Fzzy Ce Coo, Eecoic Lee, o. 33, o. 2, 1997, p. 167-168. [16] Sige.C. Seeig W.P., (1990, "Pehpig Co Ip o Rece Sye io", ASE Jo of Dyic Sye, eee Coo, 112, 76-82. [17] Sighoe W.E., Poe L.J., Te T.D., Sige.C., (1997, "io Recio Uig i- Hp Ip Shpe", ASE Jo of Dyic Sye, eee Coo, 119, 320-326. [18] Aoii I., (1999, "Gice Pecoiioig by Ipe Seqece fo Rob Rei io Sppeio", Shock io, o. 6, p. 133-145. [19] Aoii I. Ecooo D., Rob Rei io Sppeio by Digi Fieig he Gice Fcio, Poceeig of 3 io Coge o Copio echic, Je 24-26, 1999, oo, Geece. [20] Aoii I., Ecooo D., Rob ei vio ppeio fo ie ie ivi ye by igi fieig of he gice fcio, o ppe, echic Sye Sig poceig, 2001. [21] Ecooo D, Lee C, voii C. & Aoii I., iy Rob Ip Pecoiioig fo Rei io Sppeio Uig Low-P FIR Digi Fie, bie fo pbicio i he ASE Jo of Dyic Sye, eee Coo, Jy 2000. [22] Ecooo D., voii C. Aoii I., Rob io Sppeio i Fee Sye Uig Ifiie Ipe Repoe (IIR Digi Fie, bie fo pbicio i he ASE Jo of io Acoic, Jy 2001. [23] Poki J. G. oki D. G., Iocio o Digi Sig Poceig, ci Pbihig Copy, 1988. [24] The hwok Ic., Sig Poceig Toobo, fo Ue wih ATLAB-Ue Gie, v.5.2, ick, A, 1998.