SPATIAL EQUALISATION OF SOUND SYSTEMS IN CARS BY DIGITAL INVERSE FILTERING Angeo Faina (1), Emanuee Ugootti (2) (1) Dipatimento di Ingegneia Industiae, Univesità di Pama, Via dee Scienze - 43100 PARMA te. +39 521 905854 - fax +39 521 905705 E-MAIL: faina@pcfaina.eng.unip.it HTTP://pcfaina.eng.unip.it (2) ASK Automotive Industies, via Fatei Cevi n. 79, 42100 Reggio Emiia te. +39 0522 388311 - fax. 0522 388499 - E-MAIL: tec_ask@xmai.ittc.it 0 INTRODUCTION This pape descibes the theoy and an expeimenta appication of digita invese fiteing appied to the coection of the esponse of sound systems in ca compatments. The aim of this coection is not simpy to equaise the fequency esponse of the system: by a pope impementation of the invese fites, it is possibe to ceate a tansaua system, which makes it possibe to move the vitua position of the sound souces. So the istening conditions fo the dive ae made simia to those oiginay intended fo steeo epoduction, with the two souces at the same height of the eas and symmeticay ocated at +/- 30 fom the fonta diection. Futhemoe, it is possibe to ceate a vitua acoustics system, which substitutes the oigina sound fied inside the ca with a vey diffeent one, coming fom measuements taken in biiant concet has, o even fom numeica simuations of non-existing spaces. The possibiity of using digita signa pocessing units fo pefoming the equaisation of a sound system is widey diffused both fo audio-po appications and fo consume hi-fi home systems. Now some commecia units ae avaiabe aso fo ca-audio systems: but this paticua envionment caim fo diffeent soutions and pefomances, making the design of these units quite diffeent fom the othe appications. In fact in a ca compatment the sound fied is heaviy affected by the stange position of the sound souces, which is substantiay diffeent fom the optima steeo tiange. Futhemoe, the sma voume of the compatment, and the fact that some sufaces (the windows) ae highy efecting, poduces vey evident esonances and efections, which cause age ateations of the fequency esponse, and ae peceived subjectivey as a sma box effect. Fo these easons, a digita equaisation of a ca audio system is not intended simpy fo fattening the fequency esponse: aso time-domain effects ae incuded, fo e-aigning tempoay the sound coming fom souces ocated at diffeent distances fom the istenes. In some cases, the digita fite is used to pefom a vitua dispacement of the sound souces, giving to the istene the subjective impession of istening at a pai of vitua oudspeakes, popey paced in symmetica positions (Neson [1,2]). In the pesent wok a goba appoach to the pobem is undetaken, making use of the most ecent auaisation techniques. In this way, it is possibe to emove the unwanted sound fied chaacteistics, and substitute them with a competey new sound fied, possiby coming fom an appeciated concet ha, o fom a high-end audiophie istening oom. At the pesent stage, ony two-way systems ae consideed both fo the ca audio system and fo the idea oom system: this imits the vitua econstuction to ony one position in the ca. This fact can anyway be acceptabe, because it is we known that fo neay 80% of the time duing which the sound system is used, ony one peson is in the ca: the dive. The system is based on the measuement of the Head Reated Tansfe Functions (HRTF) of the dive in two conditions: seated inside the ca, and ocated in the idea space to be epoduced. In pincipe, both these HRTF measuements have to be obtained using the dive s head: but in this case ony dummyhead HRTFs wee avaiabe, fo the expeimenta measuements in theates and fo the numeica synthesis stating fom compute simuations of non-existent spaces. So aso inside the ca the same dummy head was used.
Afte this, the constuction of the digita fites is possibe by means of a new pocessing pocedue, which takes into account aso the coss-tak effect, to ensue that at each ea of the dive ony the signa oiginay eceived by the coespondent dummy-head s ea in the vitua space is peceived. The pape pesents the detais of the theoy needed fo the ceation of the digita fites. Then an appication exampe foows, in which the constuction of the digita fite is made in a test ca equipped with 4 diffeent sound systems. 1 THEORY Fig. 1 shows the paths of the sound fom oudspeakes to eas in a theate (o in a good istening oom), and the same paths inside the ca compatment. It is cea how in the second case the paths ae unsymmetica, being pesent an unavoidabe diffeent deay aong them. Fist binaua measuements of the idea impuse esponses ae pefomed in an high quaity istening envionment, which can be a concet ha o an esoteic hi-fi system. In a simia way, the unwanted impuse esponses ae measued inside the ca, making use of the same dummy head aeady used in the idea envionment, o simpy of the head of the paticua istene, equipped with a weaabe binaua micophone set (Sennheise MKE 2002). x h h x y y g g h g x h z z x g Fig. 1 Idea istening conditions in a theate (eft) and effective istening conditions inside a ca (ight) CD paye x convove f f w x f f w Fig. 2 Bock diagam of the convove Then, though the fomuation descibed in this chapte, the pope invese fites ae numeicay computed, and stoed in the memoy of a ea-time convove, shown in fig. 2. At this point it is possibe to
pocess (in ea time) any kind of souce signas, coming fo exampe fom a CD paye o fom a adio eceive, fiteing them in such a way that they aive at the istene s eas with the same chaacteistics as if they wee payed in the idea istening envionment, instead of in the ca. Obviousy the whoe pocess woks ony if each pat of the system is pefecty inea, because the theoy of inea systems is equied fo pefoming impuse-esponse based pocessing. Thus this digita equaise cannot coect non-inea distotions, caused fo exampe by the attempt to exceed the powe handing imits of the system. If the oigina signas, coming fom the CD paye, ae denoted as x and x, when they ae payed in the idea istening envionment, chaacteised by the fou impuse esponses denoted h, h, h and h, the idea istening signas y and y ae eceived at the istene s eas: y y = x = x + x Instead, if the same oigina signa is payed inside the ca, chaacteised by the fou impuse esponses denoted f, f, f and f,, the peceived signas ae: z = x + x + x (2) z = x + x Now we intoduce the digita equaise, foowing the scheme shown in fig. 2, which aso contains 4 impuse esponses, denoted f, f, f and f. It pocesses the signa coming fom the CD paye, and sends to the oudspeakes modified signas, denoted w and w, which ae given by: w = x f + x f (3) w = x f + x f The goa of the digita equaise is to make so that, fiteing the signa coming fom the CD paye befoe sending them to the ca s oudspeakes, at the istene s eas the idea istening signas y and y ae peceived; this means that it shoud be: y y = w = w + w Substituting in equations (4) the expession of y and y, coming fom eqn. (1), and those of w and w, coming fom eqn. (3), the foowing is found: x x + x + x = = + w ( x f + x f ) + ( x f + x f ) ( x f + x f ) + ( x f + x f ) Fo these equaities to be aways tue, it is needed that fo any vaue of the input signas x and x, on the eft and ight tem the factos mutipied (o, bette, convoved) with them ae the same. So it must be: h h h h = f = f = f = f + f + f + f + f (1) (4) (5) (6)
Afte a few, easy mathematica passages, this inea system is soved, and we find the expessions fo the wanted fites: f = f = f = f = InvDen ( g g ) InvDen ( g g ) InvDen ( g g ) InvDen ( g g ) InvDen = InvFite( g g ) In which the tems within backets of the fist fou expessions ae simpy computed, being the sum of two convoutions: the pobem is in computing the invese of the denominato (InvDen), ceating an invese fite fo the expession given by the fifth expession. The ceation of the invese fite fo a mixed-phase impuse esponse is not an easy task, athough it was addessed by many authos, and paticuay by Moujopouos [3]. A softwae modue which impements the Moujopuoos east-squaes appoximate invesion has been aeady deveoped by one of the authos (Faina [4]), and can be used fo this task. But in some cases, bette esuts ae obtained if a simpe zeo-phase (o equivaent minimum phase) invesion is done, foowing the we-known appoach of Neey and Aen [5]; anothe softwae modue is avaiabe fo this task (Faina [4]). In this second way a simpe fequency domain equaisation is pefomed, and the apass component (which caies the evebeation) is eft unequaised, the compete fites f poduced ae moe stabe, and no audibe atefact is intoduced. Both these modues, aong with the fast convoution modue, wi be biefy descibed in the next chapte If the evebeation, contained in the desied impuse esponses h, is geate than the evebeation of the ca compatment, as it happens when the fist is, fo exampe, a concet ha, then thee is no need fo emoving the ca evebeation, which is anyway masked unde the oom's evebeation. Being the denominato the same fo the 4 fites, the incompete invesion of it does not affect the spatia peception of the sound fied, and thus the vitua dispacement of the sound souces is achieved anyway. If instead the idea istening oom is amost anechoic, as in the case of the audiophie steeo system, not emoving the ca evebeation is usuay unacceptabe, and causes a subjective peception significanty diffeent fom the idea one, paticuay fo apid tansients o when the music suddeny stops. 2 SOFTWARE FOR DIGITAL SIGNAL PROCESSING In ecent yeas a ot of appications wee deveoped making use of speciaised hadwae, such as DSP units o data acquisition boads equipped with DSPs. The pogamming of such units is usuay sow and compex, and the sound quaity is patiay educed by the fact that in most cases fixed-point math is used. Athough ow-cost DSP back boxes ae sti an economic soution fo seies poduction, fo eseach puposes the moden appoach is to use powefu, genea pupose pesona computes, which povide a favouabe atio between cost and deveopment time. In fact it is easy to ceate sma computing codes, which pefom the equied mathematica manipuation on the audio signas, and to un them fom within sound editing pogams, aeady equipped with a ot of standad fiteing and pocessing capabiities. In this case, the shaewae pogam CooEdit (by D.Johnston) was used as a stating point: it is a wavefom edito, which can be easiy expanded by witing itte additiona subpogams, in the fom of custom DLLs (Dynamic Linked Libaies). These ae automaticay inseted in the main pogam menus, giving a smooth integation as if they wee pat of the oigina pogam. Ten of these softwae modues wee deveoped, coveing many tasks encounteed in the digita equaisation of sound systems. In paticua, the 5 modues eevant fo the goas of this eseach ae: (7)
- geneation of the excitation signa (Maximum Length Sequence) and deconvoution of the system s impuse esponse fom the signa samped at the output of it; - ceation of an invese fite of a given impuse esponse, both with the Moujopouos compete invesion and with the Neey and Aen minimum-phase invesion; - ea-time convoution of abitay ong (mono o steeo) signas with up to fou impuse esponses, poducing a steeo output which is a fiteed vesion of the input signa, passed though the FIR fites epesented by the impuse esponses. Fig. 3 shows the use s inteface of the convoution modue, which cosey esembes the computationa scheme shown in fig. 2. The capabiities of these softwae toos substantiay exceed those of hadwae-based measue instuments and fiteing units: in fact thee is no imit in the ode of the MLS signa, making it possibe to measue incediby ong impuse esponses, and aso the subsequent pocessing of them have no imit about thei ength, apat of the memoy avaiabe on the compute. Futhemoe, the computations ae aways made with foating-point math, and ony at the end the fina esuts ae conveted to 16-bits integes, though a e-scaing pocess which maximises the dynamic ange just pio of the D/A convesion. Fig. 3 Use s inteface of the ea-time convove modue. Aso the ea-time pefomances of the convove ae moe than adequate: a Pentium Po unning at 200 MHz can convove a mono input signa (samped at 44.1 khz) with a mono IR of moe than 800,000 points, and with a steeo (o binaua) IR of moe than 200,000 points/channe. A ow-cost, potabe PC was used fo this eseach, equipped with a Pentium 166 pocesso and 32 Mbytes of RAM: a Sound Baste 32 audio boad was inseted into it, and used both fo the peiminay impuse esponse measuements and fo paying back the pocessed signas duing the istening tests. Fo the impuse esponse measuements inside cas, an MLS sequence of ode 15, at a samping ate of 44.1 khz was geneated. As in this case the absoute deay and gain of each IR, eative to the othes, is impotant, the measuement was made connecting though a switch just one of the two micophones to the PC ight channe input, whie the eft channe input was diecty wied to the signa output. In this way, each measued steeo IR contains aways the same eectic oopback signa on the eft channe, with maximum ampitude and constant deay, and on the ight channe the measued IR, with pope deay and
eative ampitude. Afte stipping away the eft channe infomation, the 4 measued IRs wee packed into two steeo (binaua) IRs, and saved in.wav fomat. The ceation of the numeatos of eq. 7 was staightfowad, making use of the softwae convove, and saving the esuts in 2 new steeo fies. Aso the cacuation of the denominato was made the same way. The ceation of the invese of the denominato is a deicate point, as aeady expained in the pevious chapte: both the minimum phase and the compete invesion wee attempted. In the fist case, a 512- point invese fite was ceated, with a fequency smoothing of 0.05 octaves and an Hanning time window. In the second case, a 2048-points invese fite was buit, with a deay of 1024 points. Afte the computation of the invese of the denominato, it was appied by convoution to the peviousy measued numeatos, obtaining the equied digita equaising fites f. These fites wee then empoyed again by means of the softwae convove unning (in ea time) on the PC (Faina [4]), athough the pactica impementation fo in-ca instaation wi be based on a ow-cost DSP unit. 3 EXPERIMENTS Fist of a, the idea impuse esponses of two diffeent istening envionments wee measued: a famous theate and an hi-fi istening oom. The fist was the Teato La Scaa in Mian, Itay, and the second the test oom of ASK Industies, in Reggio Emiia, Itay. Fig. 4 epots the binaua esponse measued at a Scaa in the midde of the stas, whie the oudspeake was paced on the eft of the stage (fom the istene s point-of-view). The esponse with the oudspeake on the othe side was obtained simpy by intechanging the eft and ight impuse esponses, because the istening conditions ae assumed to be pefecty symmetic. Fig. 4 Binaua Impuse Response measued in the Teato La Scaa in Mian, Itay The measuements in the ASK test oom wee pefomed empoying the pai of high-quaity, sef-buit oudspeakes aeady fitted in it and the Sennheise dummy head.
Fig. 5 shows both the binaua impuse esponses obtained by the two oudspeakes. In this case the oudspeake esponse is consideed pat of the idea istening system, and thus it was not emoved fom the measued IRs. Fig. 5 Binaua Impuse Responses of the ASK test oom A test ca, equipped with 4 diffeent, switchabe sound systems, was used fo the istening tests. They wee numbeed fom 1 to 4, foowing a anking ode based on the quaity of the components: this means that the system #1 is the bette one, and the system #4 is the one with the smaest, ow quaity oudspeakes.fo each sound system, a set of 4 impuse esponses was measued: fig. 6 epots the two binaua IRs fo the system #1. Fig. 6 Binaua Impuse Responses of the test ca sound system #1
At this point, the invese fites wee computed fo the 4 sound systems and the two idea istening envionments, poducing a set of 8 diffeent cases. As an exampe, fig. 7 shows the invese fites which, appied to the sound system #1, tansfom it in the ASK test oom: these fites wee computed with the Neey and Aen equivaent minimum phase invesion of the denominato: this way shote fites ae obtained, which coecty equaise the fequency esponse of the sound system, but which eave the natua evebeation of the ca compatment uncoected. Obviousy, aso the invese fites fo eceating the theate sound fied wee obtained with the same appoximation, and the same was epeated aso fo the othe 3 sound systems instaed on the test ca. Fig. 7 Invese Fites fo equaisation of the sound system #1, eceating the ASK test oom. 4 SUBJECTIVE TESTS The anaysis of the pefomances of the digita equaise was based excusivey on diect subjective tests, obtained with subjects seating inside the test ca, istening at vaious sound sampes. These wee obtained by digitay tansfeing some music sampes fom commecia CDs to the had disk of the PC. Each sound sampe, having a ength of 90 s, was patiay fiteed though the digita equaise, making use of the ea-time softwae convove aeady descibed in Faina [4]; in moe detai, haf of the sampe was fiteed (sometimes the fist haf, sometimes the second), whie the othe pat was eft unfiteed. The change between the two pats was vey evident fo any kind of music sampes. Each subject had then simpy to expess his pefeence fo the fist o the second pat of each sampe, without knowing which of the two was fiteed. The foowing tabe summaises the esuts of the pefeence test fo the 4 sound systems and the two vitua spaces :
Sound System Vitua Space Pefeence pecentage fo the signas N. Fiteed Unfiteed Uncetain 1 La Scaa theate 74 % 16 % 10% 2 La Scaa theate 65 % 20 % 15% 3 La Scaa theate 54 % 22 % 24 % 4 La Scaa theate 33 % 45 % 22 % 1 Hi-Fi oom 35 % 60 % 5 % 2 Hi-Fi oom 28 % 65 % 7 % 3 Hi-Fi oom 18 % 68 % 14 % 4 Hi-Fi oom 0 % 85 % 15 % It is cea how the digita equaise was pefeed ony in the fist thee cases, with the theate as vitua space and with the bette oudspeakes. As the quaity of the sound system deceases, the digita equaise ooses pefeence, and with the itte, bad oudspeakes of the system #4 the unfiteed signas ae aways pefeed, even with the theate as vitua space. This fact was easiy expained: the pooest sound system has a quite uneven fequency esponse, and the invese fite ties to compensate these deficiencies with stong peaks in its equaising esponse. This causes a vey itte ovea gain, and the signa comes out at a vey ow eve, as the fiteed signa s magnitude is aways scaed to fit within the 16-bit constaint of the D/A convete. The subsequent heavy ampification pushes the system ove its ineaity system. It was concuded that the nove technique can be appied ony to good quaity systems, which aeady have an amost fat fequency esponse, and which can be diven by stong signas without causing distotion. Futhemoe, it is cea how the hi-fi istening oom was not appeciated at a. In genea, it esuted cea that the choice of the vitua space is citica: the imited numbe of spaces empoyed in this fist step of the eseach does not aow fo an anaysis of the optima one, but suey this aspect wi be expoed in the next futue. The subjects wee asked to descibe biefy the easons fo each pefeence choice: it tuned out that the theate gives a good effect of enveoping, whie the hi-fi steeo system makes the sound to come ony fom the font (and in some cases fom a vitua position even highe than the istene s eas), with a imited width of the sound scene, and gobay a poo steeo effect. No one compained about too much evebeation with the theate, but this is pobaby due to the paticua acoustics of La Scaa, which is quite dy compaed to its voume, athough the spatia impession is wide. The esuts with the hi-fi steeo system ae supising: it is a common beieve that the idea istening conditions ae obtained when the sound souces ae paced in font of the istene, at +/- 30 fom the centa diection, in an anechoic envionment. Amost any sound puist ties to achieve these conditions in his istening oom! On the othe hand, acoustics eseach about concet has pointed out the impotance of being enveoped by the sound (Ando [6]). This fact expains the geat inteest about movie-ike suound systems, and the eviva of the Ambisonics technoogy, which seemed dead ony 5 yeas ago. The subjective esuts obtained hee confim the impotance of the suound effect, which is natuay pesent in most ca sound systems (due to the oudspeake pacement), and is competey emoved by the digita equaisation with the hi-fi istening oom idea esponses. Anothe fact must be kept in mind: as the istenes wee seating inside a ca, they wee mentay pepaed to isten at a ca sound system. Heaing the sound coming fom emote phantom souces in font of them seems unnatua, and the mind eject an auditive expeience inconsistent with the infomation coming fom the othe senses. In this espect, aso the theate sounded a bit unnatua, because some istenes said that the sound seemed age than expected.
5 CONCLUSION Fom the esuts of the subjective istening tests, which wee commented at the end of the pevious chapte, it can be concuded that the fist esuts of this eseach ae encouaging. It must be noted aso that the new scheme fo computing the fite paametes is simpe and staightfowad, and it does not equie advanced mathematica anaysis, as it happens instead fo the one pesented by Neson [1,2]. Thus the new equaise can be easiy impemented without the need of compex cicuits o esoteic DSP agoithms. The pobem of inveting a mixed-phase impuse esponse has been soved with two diffeent techniques, but fom the esuts it came out that in this paticua case the patia invesion of the equivaent minimum phase component gives bette esuts than the compete east-squaes invesion. The choice of the idea envionment, which has to be simuated inside the ca, has eveaed to be citica: on one hand the sound fied has to seem natua fo a ca compatment, whie on the othe hand the possibiity to give the impession of being in a age, evebeant space is usuay appeciated by the istenes. Pobaby in the fina commecia unit, a set of vaious sonic envionments wi be avaiabe, so that each istene can choose the sound fied moe suited to his tastes and to the musica piece being payed. Aso atificia spaces can be simuated, making use of fo exampe of oom acoustics compute pogams equipped with auaization extensions (Faina, [7]). Anyway, fo the success of the method, it is impotant that eithe expeimenta o computed impuse esponses ae incuding the HRTFs of the same dummy head used fo the peiminay measuements inside the ca. It must be emaked that the new equaisation technique is based on the ineaity assumption: it cannot coect any kind of distotion, and futhemoe the sound system needs to be aeady of good quaity, fo avoiding the isk of being diven out of his dynamic ange by the equaised signas. The extension of the equaisation technique to muti-channes systems is staightfowad: it is quite easy to simuate moe than two vitua oudspeakes, and this way an hoizonta 5-speakes suound system can be emuated, o even an 8-speakes Ambisonics fu-3d system. On the othe hand, the use of moe than two epoduction channes inside the ca makes it possibe in pincipe to obtain the vitua acoustics effect fo moe than one occupant. The eseach wi posecute aong these ines, with the goa of making it avaiabe a ow-cost DSP unit, to be mounted in any kind of cas, afte a pope in-situ pogamming of the FIR fites, based on MLS binaua measuements of the impuse esponses on each ca. Fo hi-end music oves, even a pesonaised setup wi be avaiabe, empoying thei own head both duing the measuement of thei pefeed idea sound spaces, and fo the ca compatment chaacteisation. 6 REFERENCES [1] P.A. Neson, F. Oduna-Bustamante et a., Mutichanne signa pocessing techniques in the epoduction of sound, JAES vo. 44, n. 11, 1996 Novembe, pp. 973-989. [2] P.A. Neson, F. Oduna-Bustamante et a., Expeiments on a system fo the synthesis of vitua souces, JAES vo. 44, n. 11, 1996 Novembe, pp. 990-1009. [3] J.N. Moujopouos, Digita Equaization of Room Acoustics, JAES vo. 42, n. 11, 1994 Novembe, pp. 884-900. [4] A. Faina, F. Righini, Softwae impementation of an MLS anayze, with toos fo convoution, auaization and invese fiteing, Pe-pints of the 103 d AES Convention, New Yok, 26-29 Septembe 1997. [5] S.T. Neey, J.B. Aen, Invetibiity of a oom impuse esponse, J.A.S.A., vo.66, pp.165-169 (1979). [6] Y. Ando, Concet Ha Acoustics, Spinge-Veag, Bein 1985. [7] A. Faina, Auaization softwae fo the evauation of a pyamid tacing code: esuts of subjective istening tests, ICA95 (Intenationa Conf. on Acoustics), Tondheim (Noway) 26-30 June 1995.