Tuyen tap bao cao khoa hgc Hgi nghi Khoa hpc ky thuat Do lUdng toan qudc lan thfl IV Hd Ndi, II-2005
\MdT SO VAN DE KHI TONG HOP CAC BQ LOC SO
Nguyin Nggc Quy, Boan The Tudn Hgc vien Ky Tlwdt Qudn Su Tdm tdt:
Bdi todn xi'r ly vd tdng hep cdc bg Igc ludn la mdt vd'n de ndng bdng cho bdt ky ai quan tdm tdi cdc phep do ludng rada. Ngdy nay cd rd't nhieu pbifong phdp tdng hop cdc bd Igc s6'(BLS). Bdi bdo xin neu mdt vi du ve mgt trong nhdng phuang phdp tdng hop BIS, dd Id phuang phdp nhdt bien ddc tinh qud do xung vd trinh bdy mot sd'ddc diem khi tdng hgp cdc bg loc sd'.
Cdc loai BLS neu tren cd the sd dung de do tdn so cdc logi tin hieu dcfn sdc vd can dan sdc, nhd do cd the tdch chiing ra khoi nhieu cd pho dgc. Uu diem ca hdn cua cdc logi BLS ndy Id thuc hien ky thudt d(m gidn, do dn dinh tdn sd'cao vd viec dien chinh tdn sd f^
vd Af I khd dati gidn. Nd cdn cd khd ndng cho ta gid tri he so do vudng khd Idn.
Abstract:
The problem of processing and synthesizing digital filter has always been a complicated problem for anyone, who are interested in the methods of radiolocaitions measurements. Nowadays the are a lot of synthesizing methods of digital filter. This article suggests an example on one of above — mentioned menthod — method of once — variating impulse - transient characteristics of digital filter - synthesizing.
The above mentioned digital filter can be used for measuring frequency of monocromatic and quasimonocromatic signals, hence they can be separated from the dense spectrum. The principal advantage of these digital filter Is simple technical realisidon, high frequency stability and simlisity in leguladon off, and Af,. It can be also give us big rectangularity.
I. DAT V ^ DE
Bd Igc sd (BLS) la mdt khdu rd't quan trgng Irong he thd'ng xu ly tfn hifiu rada. So vdi bfi Igc tuong tu (BLT) nd dn dinh hon, dd chgn loc tdt hon, dd tuyfi'n inh td't hon va dfi dang hom trong vific didu chinh cdc dac tinh tdn sd va pha. Trong tuong lai vdi su phat tridn cua cdng nghe mach tich hgp vd md rdng dung lugng bfi nhd ciia cac bd vi xfl ly, vific flng dung BLS cang rfing rai hon. Han chfi' thuc hifin ky thudt BLS chu yfi'u la do yfiu cdu ti'nh tac ddng nhanh khi cdn khfi'i lugng nhd rd't ldn. Cd the phdn loai BLS thanh cdc nhdm nhu sau:
- BLS phdi hgp va BLS cdn tdi uu. Chung dugc che tao dudi dang mgt may ti'nh chuyen dung Idm vific vdi thdi gian thuc.
- BLS kifi'u rang luge va Igc dai nham dam bao cdc dac tfnh tdn sd - pha va dac ti'nh tdn s6' - bifin dd cho trudc.
- Trong cac bdi loan Id phang va nfii suy quy dao, bam sat muc tifiu, BLS dong vai trd rd't quan trgng.
Ngay nay co rd't nhidu phuong phdp tdng hgp cdc bd loc sd (BLS), chdng han: phuong phap bd't bie'n dac tinh qud dd xung, phuong phdp bifi'n ddi cdn tuyfi'n tinh bifi'n ddi Z phdi
hpp, hoac phucmg phap dat cac thuat toan ngoai suy. Xet mtft vf du: Phucmg phap bat bie'n dac tfnh qua dp xung.
Ban chat cia phucmg phap tong hpp BLS nay la nhihig thanh phan roi rac cia dac tinh xung BLS dupc lua chpn nhu the' nao dtf tuong thfch vtfi bp lpc tuong tit (BLT) cung kiiu.
Ta ctf thi vie't biiu thllc dac tfnh qua dtf xung cua BLT dua trtfn ham truyin sau:
h(t)= X / ? r , e x p ( ^ , / ) + 2 R e { x K +i^jh4P, + « , ) ' | ('>
IJhg vtfi nguyen ly nhat bie'n cia dac tfnh qua dtf xung can ctf dieu kien sau:
h(kTj)=h(t,},vtfi k=0,l,2,3... Khi dtf dac tfnh qua dtf xung cia nhiing khau ctf trong thanh phan thil nha't ciia bieu thiic (1), se ctf dang sau:
/,,(/. ) = & , e x p ( j 3 „ t r j (2) Co the xac dinh dugc ham truydn theo dang sau:
"^ ' z-exp(;ff,7:,) I-z-'exp(y9/) ! + fi,^,,.,
Trongdd: A„ =Rrp,B,p e x p ( | i j j (4) Mdt each tuong tu cd thd chflng minh dugc ham truydn cua cdc khdu thudc thanh
phdn thfl hai cua bidu thflc (1) cd dang:
, -. Rr , + Ur , ft-, K , 0 ) = , ~ f^^
1 - z exp( [3 J J + IX J J ) Rr, +ilr^ A^Z'' + ^ ,
cdn phdn thue: 2 Re ; 7 ^ = 1 -. (6) 1 z ' e x p ( / ? / j + r a / J fi^j^ + ^ u ^ +1
Trong dd:
.4,, = 2 exp(;?j TJ \Rr^ cos x^ T^ + Ir^ sin x^ T^ J,
A,^=2Rr^,B,^=^xp{2fi/,) (7) 5,^ =2exp(y!?,7'^)cosx,7;
Nhu vdy, ta da cd dugc cdng thflc cua BLS song song, trong dd cac hfi sd thuc cd thd xac dinh dugc. Phuong phap bd't bifi'n dac tfnh qua dd xung cdn ggi la phuong phap bifi'n ddi z - chudn. Cac phdn thuc dugc xac djnh theo bidu thflc (4) va (7).
Phflong phap bd't bie'n cua dac tfnh qua do xung cho la nhflng kfi't qua kha quan khi tdng hgp BLS. Hdm truydn cua cac BLS khdng chfla cdc "diem khdng", gdm cac loai sau day: BLS thdp tdn, BLS dai Battervort, BLS Becsen vd BLS Trebusev loai 1. Han chd chfnh ciia phuong phdp nay la khdng tdng hgp dugc BLS dai rdng.
BLS cd ddc tfnh qua do xung cd thd nfii suy dugc tfl bidu thflc sau:
K(s) = - ^ < ^ r ^ , K = K{Z-') (8) S-fi I-z-'expCsrJ ^ '
Trong vi du nay la nhdn thd'y cd hai dac didm ddc trimg cho vific tfnh loan BLS. Thfl nha't, dac tfnh tdn sd cfla BLS cd thd rd't khac vdi dac tfnh cua mdt BLT tuong duong. Ndu cd dugc gia trj sai khac du ldn d cdc tdn sd co > (Oj /2 . Thfl hai, sfl phu thudc ciia hfi sd truydn BLS vdo tdn sd rdi rac hoa coj = 2JI: / Tj. He sd truydn nay ty Ifi vdi eoj va cd thd dat tdi 10^ hoac ldn hon, vi vay can phai dua thfim hfi sd ty le nham chd'ng Iran bfi nhd khi thuc hifin cdc phep tfnh sd hgc phflc tap.
Nhfl vay, vific tdng hop BLS bang phuong phap nay se hien thuc hda BLS dugc dudi dang song song va nd vdn gifl dugc hinh dang cua dac tinh qua do xung. Cac loai BLS nay chi dung cho cac bd Igc dai hep lien tuc tdn sd thap.
Bai bdo nay chi xin trinh bay mgt s6' ddc didm khi tdng hgp cac bd igc sd. Phuong phdp bifi'n ddi tdn sd tren mat phang - Z, thuc chdt la cho trudc bam truydn K(Z) cua BLS tdn sfi thdp, cdn phai tim phep bifi'n ddi g(Z) dfi sao cho K( g(z)) cd thfi coi la ham truyen cua mdt trong nhflng loai BLS sau ddy: BLS cao tdn, BLS loai loc giai hoac loai Igc chan.
Ngoai ra, phep bie'n ddi nay phai vdn gifl nguyen dugc dang dac tfnh tdn sd cua loai BLS cung loai.
Vific tim kie'm thudt todn cua bd Igc lifin tuc trong midn rdi rac nhd phep bifi'n ddi z khdng phai luc nao cung la phuong phdp tdi tm, bdi vi khdng phai phuong phap td hgp BLS nao cung cho ta mdt mflc dn djnh nhu khi td hgp bd Igc tuong tu cung kidu. Cac BLS dugc tdng hcfp trong midn tdn sd se khdng thoa man cac dac trimg thdi gian, vi trong thuc tfi' cac dac tfnh thdi gian thudng khdng quan trgng bang cdc ddc tfnh tdn so. Vi vdy, tdng hgp BLS trong midn thdi gian cd lifin quan chat che vdi cac md ta dac trung thdi gian ciia ca BLS cung nhu cua bd Igc tuong tu d vao thdi didm lua chgn va dua tdi cac ddu vdo cua cac bd Igc, di cung mfit loai tin hifiu. Thu tuc tdng hgp BLS se nhdm td'i thieu boa sai sd trung binh binh phuong (STB). Cung can luu y vdn dd tdng hgp cac bd Igc khdng hoi quy. Thdng thucmg, bfi Igc khfing hdi quy khdng cd dugc nhiing uu didm so vdi cac bd Igc hdi quy: D6 hifin thuc boa chung, cdn cd mfit sd lugng kha ldn cac phdn tfl giu chdm va cac bd nhdn, nhung lai phat sinh v^n dd dn djnh. Cdc bd Igc hdi quy cd nhihig dac diem ma nhd dd thudng dugc sfl dung trong nhidu loai ra-da. Dac didm dd chfnh la kha nang tao dung bfi phan tich phd song song (hay bd Igc rang luge) dua trfin co sd cung cdc phdn tfl gifl chdm dd, khi sfl dung ma trdn difin trd trgng sd. Didu dd ddng nghTa vdi vific don gian boa thifi't bj rd't nhidu.
Cac bd Igc khdng hdi quy dfloc flng dung dfldi dang cac thuat toan dua vao PC khi tdng hgp cac qud trinh ngdu nhifin. Vi vific xac dinh dac tfnh qud do xung yeu cdu, cd thd thuc hifin bdng phuong phap don gian hon la khi xac djnh ham truydn cua bfi Igc hdi quy.
Vific sfl dung cdc thudt todn bidn ddi Furie nhanh se tang td'c dfi tfnh toan mdt cdch dang kd. Cdc bd Igc khdng hdi quy cd ddc tinh qud dd xung hiJu ban va ham truydn cua nd chi bao gdm cdc didm "Khdng", ma khdng cd cdc diem cue trong mat phang z. Tfnh hihi ban cua ddc ti'nh qua dd xung se ddn dfi'n su khdng ddng ddu cua dac tinh tdn sfi', su khdng ddng ddu nay se giam ddng kd ndu khi ta dua vdo mgt ham trgng sd ©(kT^J. Cd ham truydn Id
©(z). Khi dd hdm truydn cua bd Igc la phdng se dugc md ta theo ly thuyet tfch hgp ham hoac theo phep bifi'n ddi z nhu sau:
h(kT,).a,{kT,). (9)
NghTa la: K(z)= i K \ ~\a) (v)v-'dv ; (10) Viec lua chpn c^c tham stf cia ham trpng stf se lam giam tfnh khtfng dtfng diu cua
dac tfnh tin stf khi mtf rtfng dai thtfng. Nguoi ta thutfng hien thuc hoa bang each gin dung hoa ham trpng stf Dtflph-Trebusep. Viec ttfng hpp cic btf lpc khtfng htfi quy ctfn dung d i xac djnh cac he stf' cia phupng trinh:
v(k)=X !/(*-,•>(;) (11)
1 = 0
Tuy thudc vdo vific sfl dung kidu dang BLS nao. Nfi'u cho trudc h^m truyen cua BLS Id K(S) thi nhd phep bid'n ddi ngugc Laplas, ta cd dugc ddc tfnh qud dd xung tuong flng h(l)i
H()=Y^JHS)e'dS ; (12)
685
Tifi'p theo, hay Ifla chgn nhihig khoang tfnh nhfl nhau tfl: li(t)d^nli(kTj vdi k = 0,1,2..
Ne'u cho trudc ham truydn cua BLS thi ddc tinh qud dd xung tuong flng, cd thd tfnh dugc theo bidu thflc da biet. Cac hfi sd nhdn dflgc so bd tfl mdt trong hai phep Igc, dugc ngdt ra vd dem phdn cdn lai nhdn vdi ham trgng so, ham trgng sd Heminger cd dac tinh tdn sdla:
7tO>
w{a>) = 0,08+0,92cos^ A ^ •
Mdt phuong phap khac dung dd tdng hgp cac BLS khdng hdi quy la phuong phap lua chgn tdn sd. Khac vdi phuong phap ham trgng sd', ddc tinh tdn sd xung khdng bi ngdt quang, vific cdng cac ca'u tfl vdi cac thanh phdn con lai se lam meo dac tfnh tan sd. Bd Igc khdng hdi quy dugc long hgp theo phuong phap lua chgn tdn so chinh la mdt phdn khi ta thuc hifin ghep nd'i lifin tifi^p nhau cua bg Igc rang luge cd ham truydn la:
K ( z ) = l - z ' " ; (13) Trong dd bao gdm m didm " khdng" va cac "rang" cua bd Igc (ghep song song m bd
Igc bac nhd't)
IL PHUONG PHAP PHAN TICH CAC DIEM "KHONG" CUA MOT QUA TRINH Cac BLS dugc sfl dung rdng rai trfin co sd phdn tich cac dac tinh pha va cdc didm
"khdng" cua cdc qua trinh trong midn thdi gian. Trong sd dd, cdn lim y tdi BLS pha vd BLS dua trfin su triing lap tuong quan cua cac cue ti'nh. So vdi cac BLS kinh didn thi cac thiet bj tuong tu dugc thuc hien ky thudt don gian hon nhidu, nhung cung cd nhidu nhugc didm ddng kd.
Khao sat BLS md ta trfin hinh ve a,b ma nhd dd co thd thuc hien nguyfin tac Igc giai.
loai Igc nay cd ddc tinh Igc rang luge nhd cac giai trong sudt d cac tan so sau: fj,=kfo=kA', k=l,2.. Trong dd T- la thdi gian gifl chdm trong mdt phdn tfl. Dfi ddc cua dfldng dac tfnh tdn sd phai la dung dflng va dugc xac dinh bdng do ddc cua bd hmh thanh xung cdn dd dn dinh cua so dd kifi'n tao mach VA "AND" va bang dd dn dinh cua mach dfi'm xung dd rdng nhd.
a) u{t)
Tach stfng
"khong"
x / 2
n n
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Bd de'm (tich lOy)
Phat xung vufing [—,
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Bfi de'm II (tich luy) 1^.H. u-'--4
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Thiit lap "0" khong"
Btf tach stfng "0"
"khtfng"
u(t)
Hinh a. Bp Ipc khe; Hinh b. Bp Ipc khe tirong tir - so
Nhd bd tach sdng "khdng" va nhd bd tao xung F dd tao thanh cdc xung vuong cd dd r d n g : T / 2 ; flng vdi thdi didm dien dp vao cdt mflc 0 tinh tfl thd'p Ifin cao. Sau vific gifl chdm difin tfl khoang thdi gian T (vi du mach role) thi nhflng xung bj gifl chdm hoac khdng bj gifl chdm ddu dugc Igc nhd mach AND. Bd ddm se ghi lai sd cac xung triing nhau sau mdt thdi gian quan sdt T, nfi'u sd dfi'm nay vugt qua mdt gia trj xac dinh ihi dd chfnh la ke't qua do su cd mat tfn bifiu buu fch vdi tdn s o / , . Tinb chd'l nay cua bd Igc se khdc di nfi^u dd gifl chdm T gay ra bdi day gifl chdm.
Dudng bao cua mdi "rang" cua dac tinh tdn sd se giam theo quy ludt: 1/k , k=l,2.. khi tang tdn sd f . Do rdng giai thdng cua mdi rang ( khi z « T) se bdng:
Af=fn,x-fmin=-^ - = / ' ' ,^k^; (14) T-r T T{T-T) T^
cdn dd pham chd^t khdng phu thufic vao k va se bdng:
Q k - f k | A / , = 7 ' | r ;
Khi dua thfim vao bd Igc mdt so dd "Dao" NOR (trfin hinh ve a ky hieu bang dudng net dflt) bd Igc se bifi'n thanh bd Igc chan, luc nay thay vi khai nifim "dai trong sudt" se la
"giai cho qua"
Nfi^u BLS nay dugc sfl dung nhfl BLS mdt giai thdng, chi vdi mdt hai tdn s6'/o ta cd thd thuc hien mdt ldi vao phu bdng mdt bd Igc cd giai thdng AF ,va dugc chgn tfl didu kien sau: A/", < AF < 2 / ^ - A/j / 2 va cd tdn sd trung tdm l a / o . Liic nay ddc tfnh tdn so bidn dfi se khfing doi hdi yfiu cdu cao iSm, chi cdn sao cho dac tfnh pha tdn sd cua nd tuyfi'n tinh trong gidi han giai tdn Af,.
BLS vfla khao sat tren ddy it duge flng dung. Ne'u trong thanh phdn phd cua qud trinh ddu vao xua't hifin cdc dao ddng cd tdn sd khdng tnmg vdi giai: Af,; nhung lai cd bifin dd
\6n hon tin hifiu hflu ich, thi sd' lieu thdng ke cac didm "khdng" cua qua trinh ddu vao se khdng tuong thfch vdi sd lifiu thd'ng kfi cdc didm "khdng" cua tin hifiu dugc Igc. Nhu vdy, phai tifi'n hanh chfi' dp tin hifiu yfi'u vdi tin hieu manh. Nhd bd Igc giai phu dat d ddu vao cua bd Igc nay ma hifiu flng chfi' dp phat huy tac dung.
Do cd sai sd thidt bj (vf du nhu su md't dn djnh cua T va T / 2 ) nfin dac tfnh tdn sd cua bd Igc xd'u di mdt each dang dang ke. Dd khdng dn djnh phai chi ct mflc, sao cho:
A T < T / n , trong dd: n > l , A T / T < l / n Q . VI khi f=300kz, T=3,33ps ; T / 2 = 5 ns;
Af,= Ikz ; Q=330; n=2; A T / T < 0,15%, do ti'nh khfing dn djnh cua T v a T / 2 cd thd dua thfim vao nhimg xung tuong flng nhd cac so dd tao xung sd . Bd de'm 1 thay cho so dd gifl chdm difin tfl D va Iam nhifim vu bie'n ddi ma thanh nhitng khoang thdi gian. Bd dfi'm 2 dung dd tao xung T . Luc dd T=nT3 , T = m T , , trong dd T, la chu ky cua cdc xung didm da'u; n = 1,2, ...; m=l,2,...; n » m . Thfl tu cua cdc xung tfl cac cfla ra 1 vd 2 cua mdy phat didm dd'u se djch chuydn so vdi nhau vdi trj sd T3/2. Qua trinh ddu vao dugc dua tdi bfi tach song "khdng", xung "khdng" se quy khdng cho bd de'm 2 va md khoa 2 bao gdm triger T, va so dd A N D , • Cac xung tfl ddu ra 2 cua may phat diem dd'u nd'i tifi^p nhau vdi chu ky T3 se la'p ddy bd dfi'm 2 vd md khoa 3 (T3 va AND,). Tin hifiu la'p ddy bd dfi'm 2 mcr khod 3 v^
quy khfing bd dfi'm 1 vd md khoa 1 (T, va AND,), sau dd cac xung tfl ldi ra 1 cua may phat die'm dd'u se Id'p ddy b6 dem 1. Ne'u chu ky dao dfing ddu vao trung vdi thdi gian Id'p ddy bd dfi'm 1, thi d ddu ra cua so dd AND 3, se xud't hien mdt xung de'm. Nhd bd dfi'm 3 ma cdc xung dfi'm dugc tfch luy ddn. Nfi'u sau khoang thdi gian T, ti'ch luy dugc sd xung N > ko mdt xung dfi'm, trong dd k^ la ngudng dd bdt ddu de'm va dd chi'nh la tfn hifiu da dugc tdch ra. Vific dua vao bd dfi'm 3 bd ma sau ddy: A„i = M,„ ~k^+\, trong dd M,„ la dung Iugng cua bd de'm 3, vdi dung Iugng nay se dam bao thie't Idp dugc ngudng dfi'm. Hoan loan tuong
tu, cd thd thidt lap dd rdng xung T = nT^ va x = mTj bdng each dua vao cac bd de'm 1 va 2 cac ma sau ddy: A, =M, -n + \, A„ - M„ - m + 1 .
Nfi'u thdi gian chuydn tin hieu khdng co cdch nao bifi't dugc thi thay vl bd dfi'm 3, cd the sfl dung thifi't bj lam viec nhu mdt bd la phdng kidu ham mu hoac dflng thanh ghi, ghi lai dd dich chuydn dd, cfla vao va cfla ra cua chung dugc nd'i tuong thfch vdi cac bd cdng va cac bd trfl ciia cac bd dfi'm dao.
Do cd do Ifich pha ngdu nhifin gifla cac tdn sd cua mdy phdt didm dd'u va dao dfing ddu vao se xuat hien xung de'm cua so d6 ANDj va sau dd trong mdt vai giai tdn se xudt hifin tfnh ngdu nhien. Mdt do cua xac xud't sfl kien ngdu nhien nay trong hdm tdn sd md ta tren hlnh 2. Khi cf ddu ra cua BLS xud't hifin sfl tfch luy sd lieu bd de'm 3 (thi dudng dac tinh (0, (f) tren hinh 2, cd thd ngoai suy nhu mdt dac tinh tdn sd).
Co Ihd chflng minh nhu sau:
/ , ' ^ / = ' ,,/ = - ^ , /
J mini rri f \ ' -' min i T" /^ i . ...\ -' msx, T" I._ , \ ' J ina T,(n^my ^"'"^ T^(n-\ + mY'"'^' T,(n-\) Tfl bidu thflc cd thd tim dflgc cac tham sd cua BLS nhfl sau:
• Tdn sd'trung tdm:
1 T,n'
h
• Gidi thdng:
• Gidi llidiig ddy du:
A / ' = / ™ , - / „ , . , = 2 « - l - l - « 27;n(H-I-l-m)
m-\
• 1 - l - m ) '
r3 (« - l)(n -(- m ) ' i He so'cdt:
IL.
He sd'dd vudng:
K = Af\/Af, : 1 + m)(n ^ (m-lXn-lX'" + ") m . KET LUAN
Cac loai BLS neu tren c6 thd sfl dung dd do tdn sd cdc loai tin hieu don sdc va cdn don sdc, nhd dd cd the tach chung ra khdi nhifiu cd phd ddc. uu didm co ban cua cac loai BLS nay Id thuc hifin ky thudt don gian, dfi dn dinh tdn sd cao va vific didu chinh tdn sd f(, va Af, khd don gian. Nd cdn cd kha ndng cho ta gid tri hfi sfi' do vudng kha Idn.
Tdi lieu tham khdo:
A.V. Likharev.
Cdc phuang phdp xd ly sd vd thie't bi radar sd
Moskova "SOVRADIO" 1973.
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