Measurement of the normal acoustic impedance using beamforming method

Transcription

1 Jounal of Mechancal Scence and Technology 3 (9) 169~178 Jounal of Mechancal Scence and Technology DOI 1.17/s z Measuement of the nomal acoustc mpedance usng beamfomng method Jong Cheon Sun 1*, Chang Woo Shn 1, yung Jun Ju 1, Soon Kwon Pa and Yeon June Kang 1 1 Depatment of Mechancal and Aeospace Engneeng, Seoul Natonal Unvesty, Seoul, , Koea yunda & Ka Motos R&D Dvson, 77-1, Jangdu-Dong, waseong-s, Gyeongg-Do, , Koea (Manuscpt Receved Novembe 1, 8; Revsed Febuay 6, 9; Accepted Febuay 7, 9) Abstact A beamfomng technque s ntoduced to measue the nomal acoustc mpedance at both nomal and oblque ncdence n a fee feld. In the poposed method, mcophone aay sgnals ae decomposed nto ncdent and eflected waves usng an adaptve nullng algothm, whch s a type of beamfomng algothm. The acoustc mpedance can then be calculated fom the ato of these two sgnals. To obtan bette esults, the pessue vecto commonly used n aay sgnal pocessng s eplaced wth the tansfe functon vecto between each mcophone, and the whte Gaussan nose s suppessed by a wavelet shnage technque. Fo an accuate expemental setup, the ncdent and eflected angles ae estmated by the multple sgnal classfcaton method wth spatal smoothng. The expements conducted n a sem-anechoc oom show that the poposed method s effcent and accuate n measung the nomal acoustc mpedance of sound-absobng mateals unde a fee feld condton. Keywods: Nomal acoustc mpedance; Adaptve nullng method; MUSIC method; Fee-feld Intoducton One of the mpotant poblems n the aea of sound feld analyss of acoustc cavtes (o enclosues) s how to measue the nomal acoustc mpedance of sound absobng mateals that ae teated on the sufaces. To mpove the accuacy of an nteo sound pedcton, t would be bette to measue the nomal acoustc mpedance of an assembled component as t s, as ts nteo decoatons o tms ae often composed of layes of mateals. Among the many methods to measue the nomal acoustc mpedance, the mpedance tube method [1] s a well-nown technque, as t gves elable esults ove a wde fequency ange. oweve, ths method s lmted when measung the Ths pape was ecommended fo publcaton n evsed fom by Assocate Edto ong ee Yoo * Coespondng autho. Tel.: , Fax.: E-mal addess: sunje77@snu.ac. KSME & Spnge 9 nomal acoustc mpedance of an assembled component. Fo ths n a nomal ncdence case to be measued, unfom and ccula samples ae equed. Seveal methods fo measung nomal acoustc mpedance unde a fee feld condton have been poposed to ovecome the lmtatons of the shape and ncdence angle. Allad et al. [, 3] poposed a two - mcophone method to measue nomal acoustc mpedance n a fee feld condton. In ths method, the acoustc patcle velocty s estmated by fnte dffeentaton and the epesentatve pessue value s estmated smply by tang the mean of the measued pessue sgnals. The nomal acoustc mpedance can then be calculated fom these two values. Late, Tamua [4, 5] poposed a spatal Foue tansfom method of measung the eflecton coeffcent at oblque ncdence. oweve, ths method eques a lage aea of test mateal to tae the spatal Foue tansfom fom many measuement ponts. Recently,

2 17 J. C. Sun et al. / Jounal of Mechancal Scence and Technology 3 (9) 169~178 Lanoye et al. [6] ntoduced a new method usng a combned patcle velocty pessue senso to measue the nomal acoustc mpedance. Although the method can povde vey smple and fast measuements, t eques a senso that s able to measue the patcle velocty. In ths pape, a beamfomng technque s appled to measue the nomal acoustc mpedance at both nomal and oblque ncdence n a fee feld. In the poposed method, pessues ae measued usng thee mcophones that ae placed n a fom of an aay that s pependcula to the suface of the test mateal. Fom the measued aay sgnals, the ncdent and eflected waves ae estmated by applyng an adaptve nullng algothm [7], and the eflecton coeffcent s calculated by the ato of these two estmated waves. The nomal acoustc mpedance and absopton coeffcent can then be calculated fom the eflecton coeffcent. To obtan bette esults, the pessue vecto commonly used n aay sgnal pocessng s eplaced by a tansfe functon vecto composed of the tansfe functon between each mcophone, and the whte Gaussan nose s suppessed by usng a wavelet shnage technque. Patculaly, fo an oblque ncdent case, ncdent and eflected angles ae estmated by usng the MUSIC method [9] fo a pecse expemental setup. The elatve phase between each mcophone s also calbated b a tube method. Lastly, vaous expements ae conducted n a sem-anechoc chambe to vefy the pefomance of the poposed method, and the esults ae compaed wth the values obtaned by the mpedance tube and theoetcal method.. Beamfomng method Beamfomng s a type of spatal flte that captues sgnals fom a gven decton usng a mcophone aay. Thus, estmatons of the ncdent and eflected sgnals o angles ae possble by applyng sutable beamfomng algothms, afte whch the eflecton coeffcents can be calculated fom the ato of the estmated sgnals. Patculaly, as a numbe of beamfomng algothms may show degaded pefomance fo mutually coelated waves, caeful selecton s equed of the algothms fo a stuaton n whch the ncdent wave s fully coelated wth the eflected waves, as n ths pape. The poposed method uses an adaptve nullng method to sepaate the ncdent and eflected waves, and t uses the MUSIC method to detect the angle of ncdence fom the mcophone aay sgnals. The pefomance of the adaptve nullng method s not elated to the coelaton of each sgnal as t uses not the sgnal coss-spectal matx but a dectonal vecto coespondng to each sgnal (Secton.). Although n the MUSIC method sgnal coelatons ae an mpotant poblem as n othe beamfomng algothms, they can be mtgated by educng the coelaton wth a spatal smoothng technque (Secton.3). The poposed method can be dvded nto two steps. The fst nvolves the sepaaton of ncdent and eflected waves fom the measued aay sgnals though the applcaton of the adaptve nullng algothm to calculate the nomal acoustc mpedance. The second nvolves an estmaton of the ncdent and eflected angles usng the MUSIC method fo a pecse expemental setup..1 Geomety of the beamfomng method and nose educton Fo the geomety shown n Fg. 1, a lnea aay of M mcophones that eceve ncdent and eflected sgnals fom pevously nown dectons θ and π θ s consdeed unde plane wave condtons. In the fequency doman, the measued pessue sgnals can be expessed n tems of the phase dffeence caused by the space between each mcophone. Ths s wtten as p ( ω) 1 1 jd cosθ jd cosθ p1 ( ω) e e s ( ω) = s ( ω) j ( M 1) d cosθ j ( M 1) d cosθ pm 1( ω) e e n( ω) n1 ( ω) + n M 1( ω), (1) whee j= 1, d s the dstance between each mcophone and θ s the ncdent and the eflected angle, and s( ω), s( ω ) denote the ncdent and eflected sgnals at the fst mcophone, espectvely. Addtonally, pm( ω ) and nm ( ω ) ae the pessue value and the whte Gaussan nose at the (m+1)-th mcophone, espectvely. Fo convenence, Eq. (1) can be expessed by usng the dectonal vectos between the nput sgnals and measued aay sgnals,

3 J. C. Sun et al. / Jounal of Mechancal Scence and Technology 3 (9) 169~ Fg. 1. Schematc llustaton of the beamfomng method. as shown below. p( ω) = [ g g ] s( ω) + n ( ω). () ee p ( ω) s the pessue vecto, s ( ω) s nput sgnal vecto and g, g, column vectos of the matx n ght hand sde of Eq. (1), ae the dectonal vectos o beam vectos coespondng to the nput sgnals s ( ω ) and s ( ω ), and n ( ω) s the nose vecto. Fo smplcty, the fequency agument ω s omtted fom ths pont. If thee s only one ncdent sgnal and f the eflected sgnals ae caused by ncdent sgnal, the tansfe functons between each mcophone wll have detemnstc values because of the fully coheent sound feld. Theefoe, the pessue vecto can be eplaced by a modfed pessue vecto that conssts of the tansfe functons between the fst and second pessue sgnals. That s, 1 1 jd cosθ jd cosθ 1 e e s ' = s ' j ( M 1) d cosθ j ( M 1) d cosθ M 1 e e (3) n p n1 p + nm 1 p o p = [ g g ] s + n, (4) p whee m s the tansfe functon between the fst and the (m+1)-th pessue sgnals as pm m =, (5) p p and s ae the modfed pessue and sgnal vectos and s ' and s ' ae s p and s p, espectvely. ee, the dectonal vectos n Eq. (3) and (4) ae dentcal wth those n Eqs. (1) and (), although thee s some change n the pessue and sgnal vectos. Eqs. (3) and (4) may be moe effcent than Eqs. (1) and () as they povde fast measuement and educton of computatonal loads fo pactcal measuement. Fo example, f Eqs. (1) and () ae used to estmate the nomal acoustc mpedance, the computatons must be epeated tmes fo measuements. The nomal acoustc mpedance can be calculated by aveagng the obtaned values. oweve, the use of Eqs. (3) and (4) wll eque only one computaton, as each tansfe functon whch s the element of those equatons can be aveaged by tself. Consdeng that all measuements ae conducted unde a fee feld condton, the sgnal-to-nose ato of the measued tansfe functons may be elatvely poo compaed to that n the mpedance tube. Fo an enhancement of the obtaned values, educng the whte Gaussan nose s often an mpotant ssue. In ths pape, a wavelet shnage technque was adapted to educe the whte Gaussan nose of the tansfe functons. The wavelet whch used n ths pape was the Symlet wavelet, and ts decomposton level was fve. An ovevew of the wavelet shnage pocess s omtted hee, as the applcatons of these technques fo de-nosng have been wdely vefed n many papes [1-1]. oweve, n Secton 3, t s possble to confm that thee was a meanngful dffeence between esults wth and wthout wavelet shnage n the expements. Fo convenence, the nose tem s omtted though the followng deployment n ths and the next sectons; howeve, t s consdeed agan n Secton.3.. Calculaton of the nomal acoustc mpedance To estmate the ncdent sgnal s and the eflected sgnal s, an adaptve nullng method s utlzed fom the vaous beamfomng algothms. Ths s an algothm that estmates the sought-afte values by maxmzng the sgnals fom the ncdent o eflected angles whle othe dectons ae mantaned at zeo. The adaptve nullng algothm fnds the beam steeng vecto q that satsfes the next two condtons fo an estmaton of the ncdent sgnal [7]. Maxmze q g, (6) subject to q = 1, (7) q g =. (8) ee, q s the beam steeng vecto that detemnes

4 17 J. C. Sun et al. / Jounal of Mechancal Scence and Technology 3 (9) 169~178 the ncdent sgnal. Ths beam steeng vecto q can be easly found by usng the othogonal popety of the vectos. Assumng that the beam steeng vecto s expessed as a lnea combnaton of egenvectos coespondng to the nd to the M-th egenvalues of the matx gg, the followng equaton holds: M = a = q e, (9) whee e s the -th egenvecto of gg and a s unnown complex constant. As gg s a matx wth only one egenvalue, g s clealy othogonal to the beam steeng vecto q defned by Eq. (9). Theefoe, the second condton of Eq. (8) can be fulflled by ths othogonal popety. To fnd the complex constant a that satsfes Eq. (6), the nne poduct s utlzed wth q and g, M ( a ) q g = e g = a b. (1) = ee, a s a vecto, the element of whch s a, and b s also a vecto consstng of the element e g. It s clea that the nne poduct of Eq. (1) has a maxmum value when vecto a s paallel to vecto b. Theefoe, f a s defned as the next equaton, the fst condton of Eq. (6) s also satsfed. a = b = e g. (11) Fnally, by applyng the Eq. (7) wth Eq. (9) and (11), the beam steeng vecto q can be detemned by q = M ( ) = M ( ) = e g e e g e. (1) The ncdent sgnal can be estmated by tang the nne poduct wth the beam steeng vecto q and the modfed pessue vecto of Eq. (4). q p = q [ g g] s = ( q g) s = cs '. (13) ee, c s the complex constant q g. Addtonally, the eflected sgnal s elmnated by the beam steeng vecto q, and the ncdent sgnal s amplfed by the complex constant c n Eq. (13) n spte of the full coelaton between each sgnal. The modfed ncdent sgnal s can then be estmated by the followng pocedue: ( ) ( ) s = s p = q p q g. (14) The modfed eflected sgnal s can be also estmated by a epetton of the pocedues fom Eq. (6) to Eq. (14). ( ) ( ) s = s p = q p q g. (15) ee, q s a beam steeng vecto that s calculated fom the two condtons, Eqs. (6) and (8) eplaced g wth g. Fom Eqs. (14) and (15), the eflecton coeffcent s calculated fom the ato of the modfed ncdent and eflected sgnals. s jxcosθ s jxcosθ R( θ ) = e = e, (16) s s whee x s the dstance fom the suface of the mateal to the poston of the fst mcophone. In Eq. (16), the phase tem expessed as the exponental functon s a facto that calbates the phase dffeence caused by the measuement at the locaton apat fom the suface of the test mateal. Fnally, the nomal specfc acoustc mpedance and absopton coeffcent ae calculated fom the obtaned eflecton coeffcent, Z( θ ) R( θ ) z( θ ) = =, (17) ρ c cosθ 1 R( θ) = R θ, (18) α( θ) 1 ( ) whee Z( θ ) s the nomal acoustc mpedance and ρ and c ae the a densty and the speed of sound n a, espectvely..3 Estmaton of the ncdent and eflected angle In the pocess of measung the nomal acoustc mpedance, the speae must be located fa fom the test mateal to satsfy the plane wave condton. Theefoe, t may be dffcult to set the speae wth the pecse angle of ncdence. Fo a pecse expemental setup, the MUSIC method was utlzed to estmate the angles of ncdence and eflecton. As the pefomance of MUSIC may be seously degaded by the sgnal coelaton, a spatal smoothng technque was adapted n ode to educe the coheence. In ths secton, an ovevew of the MUSIC method wth spatal smoothng s befly pesented. A moe detaled account can be found n the lteatue (see efs. 8, 15, 16). A coss spectal matx of a modfed pessue vecto n Eq. (4) s consdeed such that R = E[ ] = [ g g ] R [ g g ] + σ I, (19) ss n whee notaton E s the expectaton opeato, R ss s the sgnal coss-spectal matx E[ ss ] and σ s n

5 J. C. Sun et al. / Jounal of Mechancal Scence and Technology 3 (9) 169~ σ n P when σ n = Enn [ ] and P = E[ pp ]. ee, R ss must be sngula as the ncdent sgnal s fully coelated wth the eflected sgnals geneated by t. In futhe pocessng, ths sngula condton wll pevent egenvalue goupng coespondng to sgnal-plus-nose and nose subspace segmentaton. To succeed wth the pocess of the MUSIC method, the coheence between two sgnals must be educed by vaous sgnal pocessng technques. In ths pape, spatal smoothng was employed to do ths. Spatal smoothng educes the coheence by aveagng the coss-spectal matces computed fo seveal sub-aays. As shown n Fg., the aay of fou mcophones s dvded nto ovelappng sub-aays of thee mcophones. The coss-spectal matx R can be ecomputed by aveagng the coss-spectal matces of each sub-aay. 1 f b Rpp = ( R + R ), () 4 = 1 whee R s the aveaged coss spectal matx (3 f b by 3) and R and R ae the fowad and conjugate bacwad coss spectal matces computed fom the -th sub-aay. The fowad and conjugate bacwad coss spectal matx can be calculated as R E f f, (1) f = [ ], = 1, b = E = R ( [ b b ]), 1,, () whee f [ 1 1] T = + and b [ 1 1] T = +, and the ma * denotes the conjugate opeato. By eplacng the coss-spectal matx R wth R n Eq. (19), the sngula condton caused by the coheence between the two sgnals can be emoved whle educng the aay sze by thee [8]. To estmate the angle of ncdence, the egenvalue decomposton of R s consdeed. 3 Rpp = λqvq v q, (3) l= 1 whee λ l s the l-th egenvalue and v l s the egenvecto coespondng to t. As the matx R s composed of two sgnals wth the level of coheence educed by spatal smoothng, the fst and second egenvalues coespond to the sgnal-plus-nose subspace and the thd egenvalue s elated to the nose subspace. Theefoe, the thd egenvalue s λ = σ. (4) 3 n Fom elatonshp between the egenvalue and the egenvecto, the next equaton can be deployed. ( σ n ) 3 = R I v. (5) By substtutng Eq. (19) nto Eq. (5), followng equaton can be obtaned as [ ] ss [ ] 3 = g g R g g v. (6) Eq. (6) mples that each beam steeng vecto g o g s othogonal to the egenvecto assocated wth the nose subspace, as the sgnal coelaton matx R ss s non-sngula and the beam steeng matx [ g g ] has a full an [13]. Thus, Eq. (6) can be wtten as [ ] 3 = g g v. (7) Fnally, the MUSIC powe s gven by 1 P =, (8) g v MUSIC t 3 whee g t s the dectonal vecto coespondng to decton θ t. As the MUSIC powe has pea values that esult fom the othogonal popety when the tal vecto g t s exactly paallel to the ncdent and the eflected beam steeng vectos g and g, the angles of ncdence and eflecton ae estmated by detemnng the pea values of the MUSIC esults. Gven that the MUSIC algothm s hghly senstve to the pecson of the expemental setup, each mcophone must be put on ts pecse pont. 3. Measuement of the nomal acoustc mpedance and dscusson 3.1 Relatve phase calbaton Fg.. Decomposton of the lne aay nto two ovelappng sub-aays. In the poposed method, the measued nomal acoustc mpedance may be senstve to the phase dffeence between each mcophone as the dectonal vectos ae dependent on the phase dffeence,

6 174 J. C. Sun et al. / Jounal of Mechancal Scence and Technology 3 (9) 169~178 as shown n Eq. (1) o (3). Patculaly, at low fequences, although the absolute phase eo of the tansfe functons between each mcophone s small, the elatve phase eo nceases, as the wave length s much longe than the space between the mcophones. To obtan meanngful data at lowe fequences, t s essental to calbate the elatve phase eo between each mcophone. We employed the tube method to calbate the phase eo at low fequency, as shown n Fg. 3. Mcophones used to measue the nomal acoustc mpedance wee aanged at the end of the tube. To pevent the geneaton of a mode n the tube, the end of the tube was closed by usng absopton mateal. At the othe sde, one speae was set to adate the pessue sgnal unde the plane wave condton. If the measued tansfe functon fom the fst to the cal (m+1)-th mcophone s m, the calbated tansfe functon can be calculated by the next equaton, functon between the fst and second mcophones wth and wthout de-nosng by the Symlet wavelet and at a decomposton level of fve. As shown n ths fgue, the tansfe functon wth de-nosng s slghtly smoothe than the ognal values. Addtonally, t s eadly appaent that the phase values at low fequences below 1 z wee vey close to zeo, as mentoned n secton 3.1. Next, fom these two sets of tansfe functons, eflecton coeffcents and absopton coeffcents wee calculated by usng the adaptve =, (9) mea cal m m m mea whee m s the measued tansfe functon fom the fst to the (m+1)-th mcophone n a fee feld. 3. Measuement of the nomal acoustc mpedance and dscusson Shown n Fg. 4 s the expemental setup fo the measuements of the nomal acoustc mpedance at nomal ncdence n a sem-anechoc oom. The test mateal of glass wool of 1 cm thcness was placed on the concete floo. Its sze was 1m by 1m. One speae was set at a heght of m n a vetcal decton elatve to the floo n ode to satsfy the plane wave condton. The aay conssted of B&K Type 4935 mcophones, and the dstance fom the suface of the test mateal to the fst mcophone was.4 cm. The space between each mcophone was.7 cm. The data acquston equpment and softwae wee LMS SCADAS III and CADA-X, espectvely. The tansfe functons between each mcophone wee obtaned by aveagng 15 tals when the FFT sze and fequency esoluton wee 819 and 8 z, espectvely. The effect of de-nosng wth the wavelet shnage technque was consdeed n the fst expement. The lne aay conssted of thee mcophones, and the tansfe functons between the fst and the addtonal mcophones wee measued and calbated, as povded n secton 3.1. Fg. 5 shows the aveage tansfe Fg. 3. Expemental setup of the elatve phase calbaton. Fg. 4. Expemental setup of the measuement of the nomal acoustc mpedance at nomal ncdence.

7 J. C. Sun et al. / Jounal of Mechancal Scence and Technology 3 (9) 169~ (a) (b) Fg. 5. Compason of the tansfe functon wth and wthout de-nosng. (a) and (b) ae the magntude and phase of the tansfe functon between the fst and second mcophones , tansfe functon wthout de-nosng; , tansfe functon wth de-nosng. (a) (b) Fg. 6. Compason of the measued esults by the beamfomng method wth and wthout de-nosng. (a) Reflecton coeffcent, (b) Absopton coeffcent.,, esults wth de-nosng;, +, esults wthout de-nosng. nullng method. It s shown n Fg. 6 that the esults wth de-nosng wee less spead compaed to those wthout de-nosng. Patculaly, the effect of denosng was sgnfcant concenng the esults of the absopton coeffcents as shown n Fg. 6 (b). These esults show that de-nosng wth wavelet shnage can be a good means of ovecomng the nosy condton. To vefy the values obtaned by the poposed method, the nomal acoustc mpedance and eflected coeffcent wee also measued wth a B&K twomcophone mpedance measuement tube (Type 46). As shown n Fg. 7, the values obtaned by the beamfomng method wth wavelet de-nosng ae n good ageement wth the data fom the mpedance tube n the fequency ange 4 to 64 z. At low fequences below 4 z, the esults by the poposed method ae vey dffeent fom those obtaned usng mpedance tube method. One eason fo ths eo s that the dstance between each mcophone was vey shot n compason wth the wavelengths of the low fequences. oweve, the eo cannot be educed by nceasng the space between each mcophone, as the plane wave condton wll not be satsfed when t s dstant fom the suface due to the fnte sample sze

8 176 J. C. Sun et al. / Jounal of Mechancal Scence and Technology 3 (9) 169~178 1 Reflecton Coeffcent Fequency (z) Nomal Specfc Acoustc mpedance Fequency (z) (a) (b) Fg. 7. Compason of the measued esults wth the mpedance tube and the beamfomng methods. (a) Reflecton coeffcent, (b) Nomal acoustc mpedance , mpedance tube method (eal pat); , mpedance tube method (magnay pat);, beamfomng method (eal pat);, beamfomng method (magnay pat). 1 1 MUSIC Powe Angle (degee) Fg. 8. Expemental setup of the measuement of the nomal acoustc mpedance at oblque ncdence. The nomal acoustc mpedance was then measued fo the oblque ncdence case. Befoe computng the nomal acoustc mpedance, the ncdent and eflected angles wee estmated by the MUSIC algothm. As shown n Fg. and Fg. 8, fou mcophones (B&K Type 4935) wee set on a vetcal lne aganst the suface of the test mateal. The dstance between each mcophone was.7 cm. One speae was located m fom the aay. These expements wee conducted at a vey hgh fequency of 6 z, as the space between each mcophone was vey close and because the esoluton of the MUSIC esults s geneally fne at hghe fequences, although the ncdent and eflected angles ae ndependent of the fequency. Fg. 9 shows the esults of the MUSIC method wth Fg. 9. Compason of the MUSIC powes wth and wthout spatal smoothng at 6 z. By detemnng the pea value at the left sde n ths fgue, an ncdent angle of appoxmately 58 o could be estmated , MUSIC powe wth spatal smoothng; , MUSIC powe wthout spatal smoothng. and wthout spatal smoothng. As shown n these esults, the ncdent angle could be clealy estmated usng MUSIC wth spatal smoothng, wheeas the esult wthout spatal smoothng faled to detect the angles. The nomal acoustc mpedance fo the ncdent angle estmated by MUSIC was calculated by beamfomng method wth wavelet de-nosng. Although fou mcophones wee set to measue the pessue sgnal, thee mcophones located close to the suface of the test mateal wee used to calculate the nomal acoustc mpedance. To vefy the esults measued by the beamfomng method, theoetcal values wee obtaned by the tansfe matx method [14] usng the popetes n Table 1.

9 J. C. Sun et al. / Jounal of Mechancal Scence and Technology 3 (9) 169~ Table 1. Popetes of the test mateal. Reflecton Coeffcent Thcness (mm) 1 3 Bul Modulus ( g / m ) Flow esstvty ( MKS Rayls / m ) 481 Stuctue Facto ( - ) 1.5 Poosty ( - ).88 Vscous chaactestc length ( µ m ) Themal chaactestc length ( µ m ) Angle (degee) (a) (b) Fg. 1. Compason of the measued esults wth theoetcal and beamfomng methods fo the oblque ncdence at 1 z. (a) Reflecton coeffcent, (b) Nomal acoustc mpedance , theoetcal values (eal pat); , theoetcal values (magnay pat);, beamfomng method (eal pat);, beamfomng method (magnay pat). These popetes, wth the excepton of the thcness, wee also estmated by a numecal method and nomal absopton coeffcent [13]. Fgue 1 shows a compason of the theoetcal values and expemental esults at 1 z. In these fgues, the esults obtaned by the poposed method ae n good ageement wth the theoetcal values. 4. Concluson The nomal acoustc mpedances at nomal and oblque ncdence wee measued by a new beamfomng method n a fee feld. The accuacy of the measued nomal acoustc mpedance could be mpoved by usng a tansfe functon vecto whch had the whte Gaussan nose educed by the wavelet shnage. A speae and mcophone aay wee located at pecse dectons o postons by estmatng the ncdent and eflected angles fom MUSIC wth spatal smoothng. The poposed method was vefed though compasons wth the mpedance tube data and theoetcal values. Patculaly, fo the nomal ncdence case, the values obtaned by the poposed method wee n good ageement wth the values obtaned usng the mpedance tube n a ange of 4 to 64 z. Refeences [1] ASTM E15 Standad test method fo mpedance and absopton of acoustcal mateals usng a tube, two mcophones and a dgtal fequency analyss system, ASTM, E15-EBGL (1998). [] J. F. Allad and B. Seben, Measuements of acoustc mpedance n a fee feld wth two mcophones and a spectum analyze, J. Acoust. Soc. Am. 77 (4) (1985) [3] Y. Champoux, J. Ncolas and J. F. Allad, Measuement of acoustc mpedance n a fee feld at low fequences, Jounal of Sound and Vbaton, 15 () (1988) [4] M. Tamua, Spatal Foue tansfom method of measung eflecton coeffcents at oblque ncdence. I: Theoy and numecal examples, J. Acoust. Soc. Am. 88 (5) (1985) [5] M. Tamua, J. F. Allad and D. Lafage, Spatal Foue-tansfom method fo measung eflecton coeffcents at oblque ncdence. II: Expemental esults, J. Acoust. Soc. Am. 97(4) (1995) [6] R. Lanoye, G.. Veme, and W. Laus, Measung

10 178 J. C. Sun et al. / Jounal of Mechancal Scence and Technology 3 (9) 169~178 the fee feld acoustc mpedance and absopton coeffcent of sound absobng mateals wth a combned patcle velocty-pessue senso, J. Acoust. Soc. Am. 119 (5) (6) [7] Y. J. Kang and E. S. wang, Beamfomng-based Patal Feld Decomposton n NA, Jounal of Sound and Vbaton, 314 (8) [8] T. -J. Shan, M. Wax and T. Kalath, On spatal smoothng fo decton-of-aval estmaton of coheent sgnals, IEEE Tansactons on Acoustcs, Speech and Sgnal Pocessng, ASSP-33 No. 4 (1985) [9] M. R. Ba and J. Lee, Industal nose souce dentfcaton by usng an acoustc beamfomng, system Tansactons of ASME, 1 (1998) [1] Y. -Y. Shh, J. -C. Chen and R. -S. Lu, Development of wavelet de-nosng technque fo PET mages, Computezed Medcal Imagng and Gaphcs, 9 (5) [11] Y. Y. Km and J.-C., ong Fequency esponse functon estmaton va a obust wavelet de-nosng method, Jounal of Sound and Vbaton, 44(4) (1) [1] A. Bahtazad, A. Palazoglu and J. Romagnol, Pocess tend analyss usng wavelet-based denosng, Contol Engneeng Pactce 8 () [13] Y. J. Km, Y. J. Kang and J. S. Km, Paametes estmaton and pefomance pedcton of acoustcal mateals, ICSV 1 Poceedngs (5). [14] Y. J. Kang, Studes of Sound Absopton by and Tansmsson though Layes of Elastc Nose Contol Foams: Fnte Element Modelng and Effects of Ansotopy, Ph.D. dssetaton, School of Mechancal Engneeng, Pudue Unvesty (1994). [15] J. C. Lbet J. and T. S. Rappapot, Smat antennas fo weless communcatons: IS-95 and Thd Geneaton CDMA Applcatons, Pentce all, Uppe Saddle Rve, (1999) [16] D.. Johnson and D. E. Dudgeon, Aay sgnal pocessng: concepts and technques, Pentce-all, Englewood Clffs, NJ (1993). Jongcheon Sun eceved hs B.S. degee n Mechancal Engneeng fom Koea Unvesty, Koea, n. e s cuently n the Unfed Maste's and Docto's couse at the School of Mechancal and Aeospace Engneeng at Seoul Natonal Unvesty, Koea. s eseach aeas ae acoustc hologaphy and beamfomng.