基于Matlab的IIRButterworth低通数字滤波器设计

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问题 ：信号滤波是一个非常重要的信号处理手段，大量的信号处理系统中，信号滤波的质量将直接影响到系统整体性能。现在有家医院向你提出一个问题，她们的心电图信号记录仪器由于受到了比较严重的电源干扰(50Hz

13、 附近 )，记录到的心电图ECG 波形有较大的畸变，请问如何设计一个干扰滤除系统，让记录下的ECG 数据继续可以进行疾病诊断。(ECG 的波形信息非常重要，设计滤波器需要注意这一点)基于 Matlab 的 IIR Butterworth 低通数字滤波器设计0 引言心电信号是心脏电活动在人体体表的表现，它一般比较微弱，其频率为0.05Hz100Hz (能量集中在0. 05Hz 44Hz),幅度为几百微伏至几毫伏。因此，在心电信号的采集过程中，极易受到内、外界环境的干扰，其中 50Hz的工频干扰尤为突出。心电图信号的干扰对心电图数据分析和压缩有一定影响。如何消除 50Hz工频干扰，成为处理心电信号

14、的首要任务。为了消除ECG 数据中的主要干扰，保留有用信号或者从干扰中“抽取”有用信号，人们提出了许多方法，诸如，平滑滤波，中心频率固定的带阻滤波器，自适应滤波，低通数字滤波等等。这些信号处理方法各有优缺点，平滑滤波算法简单，处理速度快，滤波效果较好，但存在一定的削峰作用；中心频率固定的带阻滤波器原理简单，能较大程度地抑制50Hz工频干扰，但存在“群延时”现象；自适应滤波器的中心频率能够跟随工频信号的频率幅度变化而自动调节并抵消工频干扰，但需要附加参考信号通道，算法相对复杂，难以用于实时处理。考虑到工频干扰是50Hz的低频信号， 假设要处理的ECG 信号为 0.05HZ44HZ 段信号， 且

15、Matlab 软件中有一个数字滤波器软件包，可以直接进行调用处理信号，所以本文设计 IIR巴特沃斯(Butterworth)低通数字滤波器来实现人体ECG 信号的滤波。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数字滤波器介绍数字滤波器是一种用来过滤时间离散信号的数字系统，它可以用软件(计算机程序)或用硬件来实现，而且在两种情况下都可以用来过滤实时信号或非实时信号(记录信号)。尽管数字滤波器这个名称一直到六十年代中期才出现。但是随着科学技术的发展及计算机 的更新普及，数字滤波器有着很好的发展前景。有些时候，它可以完全取代模拟滤波器。数字滤波器具有如下的优点：它没有漂移，它能处理低频信号，频率响应特征可做 成极接近于理想的特性，它可以做成没有插人损耗和有线

29、性相位特性，可相当简单地获 得自适应滤波，滤波器的设计者可以控制数字字长，因而可以精确地控制滤波的精度。 其中，它最重要的优点是：随着滤波器参数的改变，很容易改变滤波器的性能。这一特 点允许我们只用一种程序滤波器完成多重滤波任务。本文采用双线性变换法设计IIR巴特沃斯低通数字滤波器实现了对工频干扰信号的 有效滤波。2巴特沃斯(Butterworth)低通数字滤波器的特性所谓低通滤波器，就是只能让低频分量通过。在低通滤波器的设计中，有许多不同 的逼近方法：巴特沃斯逼近，切比雪夫逼近，椭圆逼近方法等。其中，最简单的逼近为 巴特沃斯逼近。巴特沃斯低通滤波器的平方幅度响应为H (jw >2 二一

30、2nI w1+ (wc )其中，n为滤波器的阶数，Wc为低通滤波器的截止频率。该滤波器具有 一些特殊的性质：对所有的n,都有当w = 0时，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对所有的n,都有当=Wc 时,2H jwc是的单调递减函数，即不会出现幅度响应的起伏;当nT +2时，巴特沃斯滤波器趋向于理想的低通滤波器;在w =0处平方幅度响应的各级导数均存在且等于

44、0,因此 H (jw )24、一在该点上取得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,图1展示了 2阶、4阶、8阶巴特沃斯低通滤波器的幅频特性。可见阶数其幅频特性越好，低频检测信号保真度越高，过渡带变窄，即衰减

45、加剧，但半功率点不图1巴特沃斯低通滤波器的幅频特性3 IIR数字滤波器的性质数的时域特性，还包括有限长冲激响应(FIR)数字滤波器。IIR数字滤波器的特征是： 具有无限持续时间冲激响应；需要用递归模型来实现，这可以从其差分方程' biz"y n )= Dxn-i )-£ aky(n-k)得出，也可以从其系数函数为: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数字巴特沃思滤波器属于IIR滤波器，该类滤波器具有特定的性质和设计方法。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

53、 te pokestainonscoolsyadhep.5,sengtenig tta 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,schoosmly not be 6, uis or-almets uue s u

54、det 'tee proppgada orpalicpaei the “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 t patc pae i.efgt ng .ia r reie a nd so on. 7, ichool s soud e ducae stdet s to obby the s

55、cool r uls a nd rig uains, on-e on tme home tprevetaciets8, ichool t 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 nae mmedaey »oedandreporedtthelca pepesGve I met e ducain, ad ul e of aw secion. I, te ichool soud a wys ce te i ntena wls rrti ning w al