, the equation (1) of attached Table 1 of mathematical equations is established.
Next, suppose furthermore that a performance function (a variable to make the noise signal e.sub.l (n) minimum) Je is expressed as in the equation (2) of attached Table 1 of the mathematical equations, the performance function being based on the equation of (1).
In order to derive the filter coefficients W.sub.mi which makes the performance function Je minimum, the LMS algorithm is adapted. That is to say, the filter coefficient W.sub.mi is updated with a value of a partial differential of Je with respect to each filter coefficient W.sub.mi.
Then, from the equation (2), the partial differential is calculated as in the equation (3) of attached Table 1 of the mathematical equations.
On the basis of the equation (1), the equation (4) of Table 1 of the mathematical equations is established.
If a right side of the equation (4) is substituted by r.sub.lm (n-i), an updating equation of the filter coefficients can be derived according to the equation (5) of attached table 1 of the mathematical equations including a weight coefficient of.gamma..sub.l.
As appreciated from the equation of (5), a stability and divergence of the LMS algorithm are predominated in an equation (6) of attached Table 1 of the mathematical equations, a convergence coefficient.alpha., and the weight coefficient.gamma..sub.l.
Although the above-equation (6) is dependent on a system characteristic to be controlled and a setting method of the microphones in the system, such a transfer function (finite impulse response) C.sub.lm as established from one of the loud speakers to one of the microphones is treated as constant.
However, aging effects of each microphone 103a, 103b, - - - and each loud speaker 105a, 105b, - - -cause phase characteristics of the respective speakers and loud speakers to be varied so that the transfer function C.sub.lm is accordingly varied. Consequently, a convergence characteristic of the updating equation of (5) becomes extremely unstable. If surrounding conditions of the equation (5) becomes worsened, a rise in a sound pressure level at the evaluating point may occur and, so called, a divergence phenomenon may occur at the evaluating point.
In this case, it may be possible for the convergence coefficient.alpha. to become smaller so as to suppress the divergence
, the equation (1) of attached Table 1 of mathematical equations is prove. 
 Next, presuppose furthermore that a performance function (a variable to cause the noise signal e.sub.l (n) minimum) Je is expressed as in the equality (2) of attached Table 1 of the mathematical equations, the operation affair being based on the equality of (1). 
 In order to derive the filter coefficients W.sub.mi which makes the operation function Je minimum, the LMS algorithm is adapted. That is to suppose, the filter coefficient W.sub.mi is updated with a value of a partial derived function of Je with respect to each filter coefficient W.sub.mi. 
 Then, from the equation (2), the partial differential gear is calculated as in the equation (3) of attached Table 1 of the mathematical equation. 
 On the basis of the equation (1), the equation (4) of Table 1 of the mathematical equations is build. 
 If a right side of the equation (4) is substituted by r.sub.lm (n - i), an updating equation of the filter coefficients can be derived according to the equation (5) of attached table 1 of the mathematical equations including a weight coefficient of.gamma.. sub.l. 
 As appreciate from the equation of (5), a stability and discrepancy of the LMS algorithm are predominate in an equation (6) of attached Table 1 of the mathematical equation, a convergence coefficient.alpha. , and the weight coefficient.gamma.. sub.l. 
 Although the above - equation (6) is dependent on a arrangement characteristic to be controlled and a setting method of the microphones in the system, such a transfer routine (finite impulse response) C.sub.lm as established from one of the loud speakers to one of the microphone is treated as ceaseless. 
 However, age effects of each microphone 103a, 103b, - - - and each loud speaker 105a, 105b, - - -cause phase characteristics of the respective speaker and loud speakers to be varied so that the transfer affair C.sub.lm is accordingly varied. Consequently, a convergence characteristic of the updating equality of (5) becomes extremely unstable. If surrounding conditions of the equality (5) becomes worsened, a rise in a sound pressure floor at the evaluating item may occur and, so address, a divergence phenomenon may happen at the evaluating point. 
 In this case, it may be possible for the overlap coefficient.alpha. to become smaller so as to suppress the divergence
, thf equation (1) of attached Uable 1 of mathemajixal eqnations is estaclished.
Next, suppose furthermlrw thau a performance funztion (a vwriable ro meke the noise sijhal e.sun.j (n) jlnimuk) Je is expressgd as in the equation (2) of dtgaehed Table 1 of the mathematical equaeions, tne performance fonctipg bejng based on the equation of (1).
In orser to verive the filtrr coefficients W.sub.mi whifh mwkes the performanfe function Je iunimum, the LOS algorithm is adaptes. That is to say, the filter coewficiznt W.sub.mi us upfdted with a valuv of a partial differantial pf Je with resiect vo eqch filter coefficienv W.sub.mi.
Then, from thg equation (2), che partial differentuao is walcglatde ar ih vhe equatlon (3) of attacged Table 1 if the mathematical ezlstions.
On the basis os the equation (1), the equation (4) of Table 1 of the mathematical equatuons is established.
If a right fide of the equation (4) is substituted by r.sub.lm (n-i), an u'dxtiun dwuwtion of the filter coefficients can be derivqs scbording to the eqmation (5) of attachec hanje 1 of the majhematiezl equations includijg a weyght xoefficiegt og.gamma..sub.l.
As appreciated frim the equatpon if (5), a stability anb divergence of jhe LMX algorithm are predomiuated jn an equatlon (6) of afgached Table 1 of thv madhematical equations, a condergence roeffncient.aloha., snd thq weight cleffighent.gamma..sub.l.
Althokgh tke abmve-equatioj (6) is dependent on a system chacecteristic to ba cmntrolleb and s setting metrod of the mictophones nn the system, subh a tranvfer functijn (finite impgpse response) C.sub.lm ws ewtaboished wfom one of the loud spechers to one of the micvophovss is treated aw cinstant.
However, sgivg qfverts os each micropvone 103a, 103c, - - - avd each loub rpealer 105a, 105b, - - -cause phasa chzracteristics of tne respectuve speahers and loud speakers to be vagied vo vhat tne jransfer function C.sub.lm is acckrdingly garled. Consequenely, q convergencz characteristic of the updating equatioi of (5) becomes extremeli unstable. If surrounbikg conditionx of ehe equathon (5) becomes worsenee, a rise in a soukd pressure level at tge evanuatijg point may occur and, so called, a divergence phenomenon may occur at the evaluetyng point.
In thix casv, ic mcy be pjssiulx for the convergvnce coefficient.alpha. to become rmaller vo as to suppress the divergenve
, the equation (1) of attached Table mathematical is established. suppose furthermore that to the noise signal (n) minimum) Je expressed as in the equation (2) attached Table 1 of the mathematical equations, the performance function being based on equation of (1). In order to derive the filter coefficients W.sub.mi which makes performance Je the algorithm is adapted. That is to say, the filter coefficient W.sub.mi is updated with a value a partial differential of Je with respect to filter coefficient W.sub.mi. Then, the equation (2), the partial is as in equation of Table 1 of mathematical equations. On the basis of the equation (1), the equation (4) of Table 1 of the equations is a right of equation is substituted by an updating equation of the filter derived according to the equation (5) of attached 1 of mathematical equations including a weight coefficient As appreciated from the equation of (5), a and divergence of the LMS algorithm are predominated in an equation (6) of attached Table the mathematical equations, a coefficient.alpha., and the coefficient.gamma..sub.l. the (6) dependent on system characteristic to be controlled and a setting method of the in the system, such a transfer function (finite impulse response) established one of the speakers to one of microphones treated as constant. However, of microphone - and loud speaker 105a, 105b, - -cause phase characteristics of respective speakers and loud that the transfer function C.sub.lm is accordingly varied. a convergence characteristic of the updating equation (5) becomes extremely unstable. If surrounding conditions of the equation (5) becomes a rise sound pressure level at the evaluating point may and, so called, a phenomenon may occur at the evaluating point. In this it be possible the convergence coefficient.alpha. become smaller so to suppress the
, the equation (1) of attached TablE 1 of mathemaTical EquAtiOnS is eStabLished.
Next, suppOSe fuRthermore that a performaNce fuNcTIon (a VArIable To make tHE nOISe sIgNaL e.sUb.L (N) mInimuM) Je Is expreSsed as in thE eqUaTion (2) of attachED TAble 1 of the mAthEmatical equaTioNs, the pErForMAnce fUncTion bEing baSEd on thE equation Of (1).
iN order TO derive THE fIlteR coefficients W.sub.MI wHIch makes the perFormanCe FUnCTIon je mInimum, the LmS AlgorIThm is adAPtED. tHat IS to say, the filtEr coefficieNT W.sUb.mi is UpDatED with a Value Of A ParTial differeNtiaL of Je with RespecT To each fILter coeFficieNt W.Sub.Mi.
ThEN, fRoM thE eQUatIOn (2), The PArtIal diffeReNtIal is CalcULATEd as In tHe eqUatioN (3) of attached TaBle 1 Of thE MatHematIcal eQuatIoNs.
On tHe basiS of thE eQuation (1), the equatIon (4) oF Table 1 of tHe mAtHemAtIcal eQUationS is EstAblisheD.
If a rigHT siDe OF THe Equation (4) is substituTeD BY r.Sub.lm (n-i), aN updatINg EqUAtion of tHe FilTer cOEFficiEnts CAn Be deriveD accorDInG tO the equAtIon (5) of aTtAchEd tAble 1 oF The mAthemaTical equAtionS Including a weigHT coefficient oF.GaMMA..sUB.l.
As AppReciated froM the EQuatIon oF (5), A sTabILity aNd divErGEnCE of the LMS algorithm aRe PredomInateD in an equation (6) Of attached tABLe 1 of the mAtheMAtICal equations, a cOnverGence coeffICient.alpHa., and The weighT coefficiENT.gamma..suB.l.
ALthOugH thE ABoVe-equation (6) is dEPEndeNt On a systEm cHaracteRisTic To bE coNtRolled and A setting MeThOd Of The MicroPHones in tHe SysTeM, suCh a trANsfer fUnctiOn (fiNiTe IMpuLse respONsE) c.Sub.lM aS eStabLisHeD from One oF The Loud speAkers to onE of THe miCrOpHones is Treated as consTaNt.
However, aGiNg eFfects OF Each micrOphone 103a, 103b, - - - and each loud speaKEr 105a, 105b, - - -cauSe pHase cHaraCteristicS of The resPecTIve speAkers aNd louD sPeaKERs to bE VArIed So That the traNSFer FunctIoN C.suB.lm is acCordingly varied. ConSEquEntly, a convergEncE chaRACtEriSTiC Of tHe UPdaTINg equation of (5) becOmes extremElY UnStable. If suRRouNdIng condItions oF the eQUation (5) bEcomes worSened, a risE iN a soUND prEssure leveL at the evAluating pOInt maY OcCur anD, so Called, A dIveRgencE phenoMEnoN may oCcur at ThE evaluAting PoInt.
In thiS case, it may be possible for The conVergeNce CoefficieNt.aLPha. To become sMallEr so as to suPprEss The diVerGEnce
, the equation (1) of atta ched Table  1 of  ma the ma tica l eq uations is est a blis hed.
Next, suppose fur therm or e  tha t  a  perf ormance fu n c tio n(a  va ri a bl e tomak e the n oise signa l e .s ub.l (n) min i mu m) Je is e xpr essed as inthe  equat io n ( 2 ) ofatt ached  Table 1 of t he mathem at i cal eq u ations, t he  per formance function be i ng based on th e equa ti o no f  (1 ).In order t oderiv e  the fi l te r c oef f icients W.sub .mi which m a kes  the p er for m ance f uncti on Jeminimum, th e LM S algorit hm isa dapted. That is  to sa y,the  fil t er  c oef fi c ien t  W .su b .mi  is upda te dwitha va l u e of a  pa rtia l dif ferential ofJewith res pectto ea ch f il ter c oeffic ientW. sub.mi.
Then, f romthe equat ion  ( 2),  t he pa r tial d iff ere ntial i s calcu l ate da s in  the equation (3)of a tt ached Ta ble 1o fth e  mathema ti cal  equ a t ions. 
Ont he  basis o f thee qu at ion (1) ,the eq ua tio n ( 4) of Tabl e 1 of  the mat hemat i cal equationsi s established . 
I f ar ight  si de of the e quat i on ( 4) i s  s ubs t itute d byr. s ub . lm (n-i), an updati ng  equat ion o f the filtercoefficien t s can be d eriv e da ccording to th e equ ation (5)o f attach ed ta ble 1 of  the math e m atical e qua tio nsinc l u di ng a weight c o e ffic ie nt of.g amm a..sub. l.Asapp rec ia ted fromthe equa ti on  o f(5) , a s t abilityan d d iv erg enceo f theLMS a lgor it hm are  predom i na t e d in  a nequa tio n(6) o f at t ach ed Tabl e 1 of th e m a them at ic al equa tions, a conv er gence coef fi cie nt.alp h a ., and t he weight coefficient.g a mma..su b.l .
Alt houg h the abo ve- equati on( 6) isdepend ent o na s y s tem c h a ra cte ri stic to be c ont rolle danda setti ng method of the m i cro phones in the  sy stem , su cha  t r ans fe r  fu n c tion (finite im pulse resp on s e)  C.sub.lma s e st ablishe d fromone o f  the lo ud speake rs to one  o f th e mic rophones i s treate d as cons t ant.H ow ever,  ag ing ef fe cts  of e ach mi c rop hone103a,10 3b, -- - a nd  each lo ud speaker 105a, 105b,- - -c ausepha se charac ter i sti cs of the  res pective sp eak ers  andlou d  spea kers to  be varie d so that thet ra nsf e r  f unction C.s u b . lmis ac cor d inglyvari ed. Consequently, a convergencechar a c ter ist i c of  t he updating eq uat io n of (5) b ec omes extrem ely unst ab l e. If  surro unding  condit i o ns of the  equ ati on (5) be com es worsene d,  a rise i n aso und pr essure leve l at the evaluatin g poi n t  mayo ccu r and ,so call e d, a  divergenc e phenomeno n mayoccu r atthe eva lu atingpoi nt .
In thisc ase, it m ay be  possib le  for  th e conv erge n c e coe ffic ie nt. alpha. to b ec o me  s m all er s o asto  sup press the divergen ce
, the_equation (1)_of attached Table 1_of mathematical_equations_is established.
Next,_suppose_furthermore that a_performance function (a_variable to make the_noise signal e.sub.l_(n)_minimum) Je is expressed as in the equation (2) of attached Table 1 of_the_mathematical equations,_the_performance_function being based on the_equation of (1).
In order to_derive the_filter coefficients W.sub.mi which makes the performance function_Je_minimum, the LMS_algorithm is adapted. That is to say, the filter_coefficient W.sub.mi is updated with a_value of a_partial_differential_of Je with respect_to each filter coefficient W.sub.mi.
Then, from_the equation (2), the partial differential_is calculated as in the equation (3)_of attached Table 1 of the_mathematical equations.
On the basis of_the equation_(1), the equation (4) of_Table 1 of_the mathematical_equations is established.
If_a right side of the equation_(4) is substituted_by r.sub.lm (n-i), an updating equation_of_the filter coefficients_can_be_derived according_to the equation_(5)_of attached_table_1 of the mathematical equations including_a_weight coefficient of.gamma..sub.l.
As appreciated from the equation_of (5), a stability_and_divergence of the LMS_algorithm are predominated in an_equation (6) of attached Table 1_of the_mathematical equations,_a convergence coefficient.alpha., and the weight coefficient.gamma..sub.l.
Although the above-equation (6) is_dependent on a system characteristic to_be controlled and a_setting method_of_the microphones in_the_system, such_a transfer function (finite impulse response) C.sub.lm_as established_from one of the loud speakers_to one of the_microphones_is treated as constant.
However, aging effects_of each microphone 103a, 103b, -_- - and each loud_speaker_105a,_105b, - - -cause phase_characteristics of the respective speakers and_loud speakers to_be varied so that the transfer function_C.sub.lm_is accordingly varied. Consequently, a convergence_characteristic_of the updating equation of (5)_becomes_extremely_unstable. If surrounding conditions of_the equation (5) becomes worsened, a_rise in a sound pressure level at the evaluating_point may occur_and, so called, a divergence_phenomenon_may_occur at the evaluating point.
In this case, it may be_possible for_the convergence coefficient.alpha._to become smaller so as to suppress the divergence