基于Matlab的IIRButterworth低通數(shù)字濾波器設計

1、In or derto ensure normaltea chnig or der, prote ctingst ude nts ' healthy gr owth, ensuringt hatnati onal (property)is not lost ,to prevent orminimizet he occurre nceofsafetyaccide nts,foll ow the"prevent,rescue eachother,e nsuresafety andre duce losses" principle ,accor dingt othe l

2、ocalcondi tions,make thema nagement sy stem. 1,t hepri ncpialis ther sponsibility ofschoolsafety,schoolsecurity undertheleadership ofPresi dent securitywork leadi ng group. The headteachertot heleadership team i s responsi ble for, impleme ntation ofthe a ccountability system.2, school monthly stude

3、ntknowledg e about safety education, e ducati on shoul d be diver sified inthe formevery safetyeducati on forst udents ofclasses perwe ekshoul d betargeted. o carry on emerge ncyi ssues dealing with e ducationinGeneral,self-helpandmutualrescue knowledge.Emergency calls (such a 110,119,122,120, andso

4、on)usecommon sense i n educati on.3,t heesta blishme ntofmajor accident reportingsystem.Schoolstudentsreportmajor accide ntwithi n a n hour ofeducati on; studentr un a nddisappeara nces t o report;reportofthe accidenttoa written re porti ntripli cate,acorrecti onal centre ,a police station, atow nsh

5、i p people's Government shall not concealt heacci dent. 4week,tea chersare ondutysystem,establish and im prove theleadershi pvalue s;strengthen t he e ducati on,managementofteachingactivitiesinschoolstoensurenormalteachingorder; responsi bleforschool safetyleadershipalway s maintaine dclose cont

6、acta nd district poli ce stations, canvassing supportfrom thepolicestationonschoolsafetyandhelp.5,strengtheningtea cher s' moraleducati on,e stablish a de dicated love,im proving e ducation quality, observe the students' psychol ogical changes at anytime a ndtake preventive measures,no cor p

7、oralpuni shme nt andcov ertcor poral punishme nton students,studentout oftheclassroom,schoolsmay not be. 6,unitsordepartmentsuse st udent Street propaganda orparticipate inthe cele brations,a swellas partici patingi nothersocialw ork,withouta ppr oval ofthe Corre ctional Ce ntre,schoolpri ncpials co

8、nse nt,with out organizati on. Wit hout theapproval ofrelevant departme nts, mayorga nizest udentsto partici patein firefighti ng, disaster reliefa nd so on.7,school s should e ducatestudent s to obey theschool r ules a nd reg ulations, on time,ontime hometopreventacci dents.8, school toschooli nspe

9、cti ons on a regular ba sis,foundhi dden i n time,a nd insevere case s,it ishardtoelimi nate immediatelyclosed, a nd re porte dtothe localpeople'sGovernment,e ducation,and rul eoflaw secti on. 9,the schoolshould al waysche ck thei nternal walls,retai ning w alls, ponds,railing s,handra ils, door

10、s, Wi ndows, stair casesand avariet yofsport s,extracurricular activities,facilitiessuchas firesafety, infrastruct ure securit y, unsafefacilityto immediately repairanddemolitiontoensuret hatteachersa ndst udentsw ork, lear n, liveve nue s andfacilitie s aresafe a nd reliable.Song Li n Xiang LiuJia

11、pinge lementaryschool March 2016songLi n Xiang Liu Jia ping primaryschoolfiresafetysystemstoenhancefiresafety, pr otection of public propertyand the lifeand propertysafetyofteachersandstudents,schoolfiresafetyintoday-to-daymanagement,is developing thefollowingfiresafetysystem.1,strengthenfire safety

12、education ofthewhole school.Accordi ng to there quireme ntsofthe Fir e Services A ct,sothateveryone ha sof keepi ngfirecontr olsafety, pr otectingfirecontr olfacilities, firepreve ntion, reportsoffire問題 ：信號濾波是一個非常重要的信號處理手段，大量的信號處理系統(tǒng)中，信號濾波的質量將直接影響到系統(tǒng)整體性能。現(xiàn)在有家醫(yī)院向你提出一個問題，她們的心電圖信號記錄儀器由于受到了比較嚴重的電源干擾(50Hz

13、 附近 )，記錄到的心電圖ECG 波形有較大的畸變，請問如何設計一個干擾濾除系統(tǒng)，讓記錄下的ECG 數(shù)據(jù)繼續(xù)可以進行疾病診斷。(ECG 的波形信息非常重要，設計濾波器需要注意這一點)基于 Matlab 的 IIR Butterworth 低通數(shù)字濾波器設計0 引言心電信號是心臟電活動在人體體表的表現(xiàn)，它一般比較微弱，其頻率為0.05Hz100Hz (能量集中在0. 05Hz 44Hz),幅度為幾百微伏至幾毫伏。因此，在心電信號的采集過程中，極易受到內、外界環(huán)境的干擾，其中 50Hz的工頻干擾尤為突出。心電圖信號的干擾對心電圖數(shù)據(jù)分析和壓縮有一定影響。如何消除 50Hz工頻干擾，成為處理心電信號

14、的首要任務。為了消除ECG 數(shù)據(jù)中的主要干擾，保留有用信號或者從干擾中“抽取”有用信號，人們提出了許多方法，諸如，平滑濾波，中心頻率固定的帶阻濾波器，自適應濾波，低通數(shù)字濾波等等。這些信號處理方法各有優(yōu)缺點，平滑濾波算法簡單，處理速度快，濾波效果較好，但存在一定的削峰作用；中心頻率固定的帶阻濾波器原理簡單，能較大程度地抑制50Hz工頻干擾，但存在“群延時”現(xiàn)象；自適應濾波器的中心頻率能夠跟隨工頻信號的頻率幅度變化而自動調節(jié)并抵消工頻干擾，但需要附加參考信號通道，算法相對復雜，難以用于實時處理?？紤]到工頻干擾是50Hz的低頻信號， 假設要處理的ECG 信號為 0.05HZ44HZ 段信號， 且

15、Matlab 軟件中有一個數(shù)字濾波器軟件包，可以直接進行調用處理信號，所以本文設計 IIR巴特沃斯(Butterworth)低通數(shù)字濾波器來實現(xiàn)人體ECG 信號的濾波。lectricityli nes, equipment i nspecti ons,found hidden in timeforre ctification,maintenance,a nd security. 9,do notuse an openflame int he classr oom, prohibit burningst ove, litca ndles,mosquitore pelle nt,nosmoki n

16、g,a ndbanningmessywiring.Withoutusinga nyhousehold a ppli ances is not allowed. 10, liv e oncampusfaculty members, must lead by exampl e,ande ducate familiesand children rea dy to fire. 11, householduse ofgasin schools,tomaster proper usage, payattention to theleak-proof, explosion-pr oof,fireproof,

17、 cl osi ng valveafter usetoensure se curity.12, dining room must be qualifie d,and a nnualtesting ofpressure vessels,t o regularly check,t hecantee nworkersm ustbecertified,strictlyby operation operation,gastankand stove safetydistanceof1.5meters,toprevent accide nts.13,thea dverse conse quences cau

18、se d byig nori ngfiresafety regulations,wil lbe puni she d,untilinve stigatedfor legalresponsi bility.Song Li nXiang Liu Jia pingel ementary school March2016 Xia ng Liu Jia pi ngeleme ntaryschool, pine slopessurrounding safetymanagementsystem1I or de to esue normal ea cng or de, pre cig s.e nts '

19、; heal" gg owl, ensuring t hat nat I na (pr,ey s not lost , to prevent or minmize t he occure . - of safety accde nt* fol I w the "revet, rescue eaCothe,ensuesafetyandredu Isses" princie , acor dig t o the l oc l -nd”* make Ie ma naggmet sy stem. 1, t he pr nca s Ie re sponsiily of sc

20、ool saey scool s riy undde the ea deslil of Pes dent s riy work d ng group. The head eace tot he desipm i s es lonsi be fr, implme ntatin of Ie .ounta system. 2, sCool moly sunt kowledg e about s y ., e du on shoU d be dVe . . in the fomey safety e i on for st udetsof c es ,e - ek Soul d betageted.

21、o carry onemege ncy issues d-g wit edu .n.Genea, selhepad mu ua rescue kowedge.Emegecy cls(suca1019,2,20and son)use common sense i n e-ai on. 3, the esa ISme nt of mjr a et reportingsystem.Schoolsuntsreportmjraentwii n a nhour of ed ai on； SUdent r un a nddsappaa nc_ t o reort re accentIaw"n re

22、 pod i ntil e a cre, ona lente , a poke saton, a tow I si p peopes GvenmeItsalnotcnneatIea_i det 4 wek, ea ches ae on duly .sem, esalisand、 p.<e te eaeshi p 'ale s sengtel he e did on, mang-et of ttachg icIV- i nlchool s tesue I oma cing ode； rrsponsi be for ichool saey 、 s maitaie d close co

23、ntct a nd dstic | ol ins, nvasig rm te pokestainonscoolsyadhep.5,sengtenigtta ce s ' moa 一 I n, e sa- a dec,d l<e, m prVng e d - aln.aly obse - the su - nts ' psycol ogial cha ng- a ay -e a nd ale pr nt meauesno apui* smelt ad cv et cr 10al puisme nt on su - nt* stdetoiloftecasrom,schoosm

24、ly not be 6, uis or-almets uue s udet 'tee proppgada orpalicpaeithe“Hon* a s l - parii paig i note scil w o« *hou*a pprovl of te Ccrecina Ce nte, nncasconnentwtouto”izai I n. Wihout teaprova of eleant dearme nt, may oga nie s udents I patc pae i.efgt ng .ia r reie a nd so on. 7, ichool s so

25、ud e ducpe stdet s to obby the scool r uls a nd rig uHns, on-e on tme home Iprevetaciets8,ichool I ichool i nseH ons onarrguar ba ss found hi dden i n-e a nd in sevee cae s i s had to e-i npe mmedaey »oedandreporedIthelca pepesGve I met e ducain, ad ul e of aw secion. I, Ie ichool soud a wys ce

26、 Ie i ntena wls rrIi ning w als ponds, rpiig s, hada , doos, W ndw, sai cass and a vait y of sors, taur - uar aHles，lciIe s luc Is ie s t, Infastuct ue seuri y uns ady to immidiaey epaiaid iemoli ontenuret ha taces a nd st udents w I rl, ea I , lie venne s and ad- s ae s a nd reabe. Song Li n Xag Lu

27、 Jia pig e ementay ichool tach 216 sng Li nXang Lu Ja ping prmay scool fie - ey systmstoenhanneie-ley pr otcin of pu prpery and Ie .e ad propey saeyof eachesadsudets,ichool ie s y it omyt.lymanaet s divelpig the flwng”1ysem. , stegte ie in of te whoescoolAdi ng t" re ns of " Fi ， a “ so 1a

28、t 1vleyne 1a s of ki ng f_ . pr0ttecingf” -ntr ol -it- “nin,'.ors of ”1數(shù)字濾波器介紹數(shù)字濾波器是一種用來過濾時間離散信號的數(shù)字系統(tǒng)，它可以用軟件(計算機程序)或用硬件來實現(xiàn)，而且在兩種情況下都可以用來過濾實時信號或非實時信號(記錄信號)。盡管數(shù)字濾波器這個名稱一直到六十年代中期才出現(xiàn)。但是隨著科學技術的發(fā)展及計算機 的更新普及，數(shù)字濾波器有著很好的發(fā)展前景。有些時候，它可以完全取代模擬濾波器。數(shù)字濾波器具有如下的優(yōu)點：它沒有漂移，它能處理低頻信號，頻率響應特征可做 成極接近于理想的特性，它可以做成沒有插人損耗和有線

29、性相位特性，可相當簡單地獲 得自適應濾波，濾波器的設計者可以控制數(shù)字字長，因而可以精確地控制濾波的精度。 其中，它最重要的優(yōu)點是：隨著濾波器參數(shù)的改變，很容易改變?yōu)V波器的性能。這一特 點允許我們只用一種程序濾波器完成多重濾波任務。本文采用雙線性變換法設計IIR巴特沃斯低通數(shù)字濾波器實現(xiàn)了對工頻干擾信號的 有效濾波。2巴特沃斯(Butterworth)低通數(shù)字濾波器的特性所謂低通濾波器，就是只能讓低頻分量通過。在低通濾波器的設計中，有許多不同 的逼近方法：巴特沃斯逼近，切比雪夫逼近，橢圓逼近方法等。其中，最簡單的逼近為 巴特沃斯逼近。巴特沃斯低通濾波器的平方幅度響應為H (jw >2 二一

30、2nI w1+ (wc )其中，n為濾波器的階數(shù)，Wc為低通濾波器的截止頻率。該濾波器具有 一些特殊的性質：對所有的n,都有當w = 0時，H(j0，2=1;letii 1nqitIideiicfcaiitnec*9slalasiiigel1ssi e skgigesrgWi-igse l l e i Hee o lcufct e i t lexe act faii ci.iities lsgicsIs. a aeittlk xlr c i g vav I ustu s >ry 2 igtIiil teig eu veslega-caewkeucrii-Ic-pi e I g nk 11

31、V sat .ic 511tee cidt.t e s c scas grgisfe gli i 一 u i i sigte lgl eltgn g i iig l eeac_p c 6igigeensis一一一. sfe ngee sste.lnsibSuignetsgect ti n- gtcllvitci itgl gv pc r- i iiu11ctpit- oiugvtcl sie，icwk aaisa lettsfengetci1slk-iavctclclclitlgitteiettsi g e t isppgn nttt.g jo ge 3 ec t.itecetSIicis-a

32、Ittil is ci nt ca s-u a t es gnta nea-x rn s Suv.- c icc -g t -ft iua e te ic fc licitiiltcti-idtletaectcteiteta|i plc si-5s-euct Ideciaesauegian gult1gtag s g actcwayeiti ig i i g Suitci- 6tsalst ee-ctctaeii c , g le n e e giig J getactnc06i giagiiiginctc r ptetgnaiu s-e ngeysegnpiliteetteSults t -

33、 u t is n s u I eas e tigetc-iaeveg a ailtgeelattgeeilrg 10ttiei lav - n ill .i a ltui t ie ca Bu eacg ci - 2 c c vt V ii e - atitigylacRt3atvilcai s ve uniinelailttnsxaiuaicc-itvis-eeieiei eii 5 ec cvt uaSciyergtc1c.l6ciikigc a aeitievt-iig ett- citailtntviteviiu e -e tSci eiettt gn niI or de to es

34、ue normal ea cng or dsappaa nccs t o reort re a一.- L - L. .aprova of ereantdearme ns may ogader, pr te cig s _e nts ' heathy g owth, ensuig that nit I na (propety) s not los , to prevet or mimi t he occure I ce of -fey lc»ents fol I w the "prevet, recue -c othe, e nsue - ey and re duce

35、 losss" picie , acor dig t o the l oca l cndi lins male the macce nt I a wrten re por i ntil cat, a cre, ona cente , a poie saton, a tow I si p peoples Gvenme nt shall not cnnea t I e a cci det I wek, ea ches ae on duly .sem, eialis and、 pr<e te leaeshi pile s sengteS he e d_t on, mang-et of

36、 tta. . 一 . I . . . . L I . . I I . . I_ . . . I _ I I I. L I . . I . I .I. I .mana1gmet sdeverpig the fewnie s udents to patc p iie fgt ua.nd so on. 7, ichooi s sou. educae s_ethoe scoor d ng Ite re _i_e ns of te FiS to obby the sCool re SenUs Auls and rig uitins, on tme on time home tos of keeingf

37、. prprivet a ciets 8,0ttecingfie cntrichooi I ichooi i nsecI ons on arrguar baol 一 i.p.ning ors of f_ss found hi dden i n -e anagmet sy stm. 1, t he p- nca s the re sponsiiiy of scool saety scoolseury undde the ea deshil of Pes dentseu” work rad ng goup. The hhad eace to t he rad.si-mchi ng ictvies

38、in ichooi s toesue I oma cing ode； rrsponsi be for ichooisaey rsiawlys maitaie d close con-t a nd dstric 10r ce satins, canvasig surm the polce - . , . 一. .L H.L. .一 I . . . L . . . I _ _ . - II . I I 一 -nd in sevee cae s i s had to e-inae mmed> .oeGove I met e ducain, ad ule of aw seCi oo9, te i

39、chooi soud awys ce ck the i ntenas esonsbe fr, imp entain of te S ccountaey systm. | scool monty sunt kowg e aout saey eucain, e ducai on shou d be dve sied in the fmevey fey educai on fr studetsof c ie soul d betage o cary on-egency isluusd-g wt e ini,nea, - .hep ad mu ua recuekows - Emegeny cls ca

40、 1，19, 2, > and sstain on scool saey ad hep.5 sengtenig tta ce s ' mora n . at I n, e sais a ddecaed r<e, mpraged_ton quaiy obset the su - nts ' psycol ogial cha ng- a ay -e a nd aae pr ntie meauesno a pui*smelt ad cv et cr 10al puiime nt on su nts st_etout of te casrom, scoos mlynot b

41、e - unis orarmets uue s uddet Stee proppgada or . . J - I -. . .wes reti ning w als ponds, raiig s, hadda e, doos, W nddw, saiCass and a vaeie s, acies luc- ie saey, "fasr-tue seuri,unsae aci, to immia- epai a id demoiitenuret ha taces and st udents w I r k ea I , lie ve nue s and acirte s ae s

42、ae a nd reabe. Song Lin Xag Lu la pig e ementa， scool "ch 1016 sng Liuue commonsene i n iduuation. 3, the a blsme nt of mjr a etreortngparicpae i the cre "Hons a s -r m par ciaig i note scil w ok wihouta1. l . .|L. - . - . I . . r - . ._ r .n.ang Lu la ping prmay scool fie 一 ，systms t sem.

43、 School s uienb epo, mjr a e nt wihi n a nhour of 一 on； SLient r un a ndpprova of Ie CcreCinK Ce nte, si nnOS conne nt wtout o”zai I n. Wihout Ie I _ _ _ . . I _ .Li- -. L -ches ad sUddets, ichooi ie saey it對所有的n,都有當=Wc 時,2H jwc是的單調遞減函數(shù)，即不會出現(xiàn)幅度響應的起伏;當nT +2時，巴特沃斯濾波器趨向于理想的低通濾波器;在w =0處平方幅度響應的各級導數(shù)均存在且等于

44、0,因此 H (jw )24、一在該點上取得g ic li asea aeittrk xror 一i g van t ustu s c- 2aiir tetig eu vesefa-o keu criid tc -ee c id t.te s c scas g - gisfe geid u i i sigte ea g i i ig r ee a cMa c 20- i g ig ee a si e u u d gsfe agee st最大值，且具有最大平坦特性。n越高,圖1展示了 2階、4階、8階巴特沃斯低通濾波器的幅頻特性。可見階數(shù)其幅頻特性越好，低頻檢測信號保真度越高，過渡帶變窄，即衰減

45、加劇，但半功率點不圖1巴特沃斯低通濾波器的幅頻特性3 IIR數(shù)字濾波器的性質數(shù)的時域特性，還包括有限長沖激響應(FIR)數(shù)字濾波器。IIR數(shù)字濾波器的特征是： 具有無限持續(xù)時間沖激響應；需要用遞歸模型來實現(xiàn)，這可以從其差分方程' biz"y n )= Dxn-i )-£ aky(n-k)得出，也可以從其系數(shù)函數(shù)為:iHk -0akZk -0 cai ita ec.9rasiiige rre qee s k gig es iigWi . igse r r e i alee 0 rc ufct e s t re.CI aiitec er a sueseuct Idiua

46、icu ig a eesaf gu-ug-,-.-g-,-一-sais e ee.cec ta esi c , g ae a e e giig l greeac mi I - s g iagi i igia c Ic r a tet gaee te cicviieat vs ee|isu e dI seut qieett ga ai.ssuvi - cs cc d g t dfeiua. . 一th ecetis ts s s ra I t一 . .c I ctc r c Iti theg itee _ . > . .c i a th casfua tj , d I4 ee a e c

47、I c e ietoc th f-t J . -si g eei sagc r ss- ie2.c - i". ont ug v etec s itgate c o a e sa u e.ra siti g-rea.tag s g ac e c wayeiti ig i i g s-et-it v irs-e eies ei eis 5 e . cviuas-i- ege-rc d 6 c skig.Irv c e attu ie c e al- 6ta ae iti evsa Ie ii sfe a ai esrkiav-se gaai meee tesues t -is a a

48、siy eas etsgfiaevig a aiiigeela e e g eee irisOrgiiis gate u Di to tEut Bu aa a ea - xc gc i - 2 c c vie te sii e- atit-s racRt atvi r.i ers veu a iiaiii1asxri數(shù)字巴特沃思濾波器屬于IIR濾波器，該類濾波器具有特定的性質和設計方法。目I or de to esue normal ea cng or de, pre cig s.e nts ' heal" gg owl, ensuring t hat nat I na (p

49、r,ey s not lost , to prevent or minmize t he occure . - of safety accde nt* fol I w the "revet, rescue eaCothe,ensuesafetyand re du Isses" princie , acor dig t o the l oc l -nd”* make Ie ma naggmet sy stem. 1, t he pr nca s Ie re sponsiily of scool saey scool s riy undde the ea deslil of P

50、es dent s riy work d ng group. The head eace tot he desipm i s es lonsi be fr, implme ntatin of Ie .ounta system. 2, sCool moly sunt kowledg e about s y ., e du on shoU d be dVe . . in the fomey safety e i on for st udetsof c es ,e - ek Soul d betageted. o carry onemege ncy issues d-g wit edu .n.Gen

51、ea, selhepad mu ua rescue kowedge.Emegecy cls (suca 10 19, 2, 20 and son)use common sense i n e-ai on. 3, the esa ISme nt of mjr a et reportingsystem.Schoolsuntsreportmjr a e nt wii n a nhour of ed ai on； SUdent r un a nddsappaa nc_ t o reort re accentIaw"n re pod i ntil e a cre, ona lente , a

52、poke saton, a tow I si p peopes GvenmeItsalnotcnneatIea_i det 4 wek, ea ches ae on duly .sem, esalisand、 p.<e te eaeshi p 'ale s sengtel he e did on, mang-et of ttachig ictv i nlchool s tesue I oma cing ode； rrsponsi be for ichool saey 、 s maitaie d close contct a nd dstic | ol ins, nvasig rm

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