Design of a Beam-forming System in the Vehicle Cabin Wen-Kung Tseng

Transcription

1 ISSN: ISO 9:8 Certified Interntionl Journl of Engineering Science nd Innovtive Technology (IJESIT) Volume, Issue 6, Novemer 3 Design of Bem-forming System in the Vehicle Cin Wen-Kung Tseng Astrct This pper presents the design of em-forming system ( directionl udile sound system) in the vehicle cin, where pssengers t different positions in the vehicle cin cn listen to different music. A directionl udile sound cn e generted in vehicle cin y mplitude-modulting the ultrsound crrier with n udio signl, then trnsmitting it from n rry of ultrsonic trnsducers. A novel method hs een proposed in this pper to control the em width of the min loe nd the level of the side loe for the em pttern y using n optimiztion technique. The performnce of the udile sound em steering hs lso een investigted. Some preliminry experiment hs een crried out to vlidte the simultion results. The results show tht the optimiztion method proposed in the pper cn effectively control the em width of the min loe nd the level of the side loe for the udile sound in vehicle cin. The results lso show tht the em steering ngle of directionl udile sound cn e controlled y using the proposed method. Index Terms Directionl Audile Sound, Ultrsound Crrier, Ultrsonic Trnsducers, in Loe. I. INTRODUCTION Trditionl in-cr communiction systems, such s cell phones or rdios, generlly used trditionl loudspekers to rodcst. There re severl weknesses in such systems. For instnce, people in the cr cn ll her the sound. This mkes it impossile to mintin privcy. Besides, people feel othered nd thus the ride qulity would not e so plesnt. If crs re equipped with directionl udile sound systems, ech pssenger in the vehicle interior cn listen to the different music or informtion s shown in Fig.. Thus, people in the vehicle cin would not feel othered. An rry of ultrsonic trnsducers my e employed for generting the directionl udile sound through the self-demodultion of finite-mplitude sound ems []-[6]. The construction of producing directionl udile sound ems includes n ultrsonic trnsducer, driving mplifier for the rry, n A modultor, pure-tone oscilltor for the crrier frequency nd equlizer s shown in Fig.. An rry of ultrsonic trnsducers my e clled prmetric speker regrding the ppliction of the prmetric rry theory. The prmetric speker hs een used for decdes in underwter sonr pplictions for its highly directive response even t low frequencies [7]. The trnsducer rry in prmetric speker systems my comprise plurlity of piezoelectric trnsducers or polyvinylidene fluoride (PVDF) film trnsducers. For simplicity, we cn ssume tht the trnsducer is fed with two ultrsonic signls t closely frequencies f nd f s shown in Fig. 3. The resultnt coustic wves will e the wves with the frequencies of f, f, f ± f, nd higher order hrmonics, etc. Among these new components, the high-frequency terms f, f nd f f, etc. will e strongly ttenuted in ir nd decy rpidly with incresing rnge from the speker. The remining difference frequency f f is produced due to the reltively low sorption of this term in ir [6]. oreover, this low-frequency sound, the udile sound, inherits the sptil chrcteristics of the primry wves, nd its shrp directivity is the result of the coustic nonlinerity. The udile sound is the secondry wve generted from the primry wve y nonliner effect, which hs een reported for few decdes [7]. Since the first ttempt to estlish n udio spotlight system [8], the development of directionl prmetric speker hs ttrcted much ttention. ost of the works relted to directionl udile sound em focused on investigting the directivity of the sound em or the different trnsducer rrngement. There were only few works on the em width control in prmetric rry [6], [9]. Yng et l. proposed the weighted prmetric rry using Cheyshev window method for the trnsducer weightings to generte the directionl udile sound [6]. However in this pper n optimiztion method is used to clculte the optiml trnsducer weightings for controlling the em width of the min loe nd the level of the side loes for the directionl udile sound in vehicle. Also the em steering performnce hs een investigted in this work. Some preliminry experiment hs een crried out to vlidte the simultion results. The pper is orgnized s follows. First, the directivity of the udile sound em nd the formultion of the optimiztion method re derived. Second, simultion results of controlling the em width of the min loe nd the 7

2 ISSN: ISO 9:8 Certified Interntionl Journl of Engineering Science nd Innovtive Technology (IJESIT) Volume, Issue 6, Novemer 3 level of side loes nd the em steering performnce re presented. Then, the preliminry experiment is performed. Finlly the conclusions re mde. Fig.. Directionl udile sound in the vehicle cin Source Signl Equlizer A odultor Power Amplifier Ultrsonic Trnsducer Crrier Signl Fig.. Construction of producing directionl udile sound ems 7

3 Ultrsonic Signls ISSN: ISO 9:8 Certified Interntionl Journl of Engineering Science nd Innovtive Technology (IJESIT) Volume, Issue 6, Novemer 3 Ultrsonic Trnsducer Resultnt coustic wves f f f Nonliner Interction in medium f f f f - f Higher order hrmonics Fig. 3. Nonliner interction process in ir II. FORULATION OF DESIGNING DIRECTIONAL AUDIBLE SOUND BEA In this section the formultion for designing directionl udile sound systems using n optimiztion technique is presented. The directionl udile sound cn e descried y the Khokhlov Zolotsky Kuznetsov (KZK) eqution which ccounts for the comined effects of nonlinerity, sorption due to viscosity nd het conduction, nd diffrction in finite-mplitude sound em s follows [6], []: p c z p 3 c 3 p 3 c 3 p () where p denotes the coustic pressure, z is the coordinte long the xis of the em propgtion direction, τ is the dely time, c is the speed of the smll signl sound, ρ is the mient density, δ is the sound diffusivity, β is the coefficient of nonlinerity, nd is the trnsverse Lplcin opertor. The solution to () cn e otined using the method of successive pproximtions. For simplicity the primry source with Cussin mplitude shding is ssumed. By using qusi-liner theory, the solution for the finite-mplitude sound em generted y the Gussin source cn e expressed s []: q z r/ pe r, z exp jz / z jz / z where p is the pek source pressure, is the sorption coefficient t primry frequency ω, z = /k is the Ryleigh distnce, nd is the effective source rdius. The directivity cn e esily otined s []: D ( k, xp[ ( k) tn ] (3) where k = ω/c is the wve numer nd θ is the ngle with respect to the xis of the em. Therefore, for i-frequency Gussin source, provided the sorption is neglected, the directivity of the difference frequency is given y the product of the directivity functions of the primry wves [], i.e.: D ( ) D ( )D ( ) () where D (θ) nd D (θ) re the directivity for frequency ω nd ω, respectively. Consider group of weighted primry sources, which re eqully spced with n interelement spcing of d s shown in Fig.. The directivity D (θ) of the weighted primry sources rry for frequency ω cn e written s: D ( ) D ( k, )H( k, ) (5) D ( k, is the perture directivity for frequency ω nd H( k, ) where ) e expressed s []: () is the rry response which cn 73

4 ISSN: ISO 9:8 Certified Interntionl Journl of Engineering Science nd Innovtive Technology (IJESIT) Volume, Issue 6, Novemer 3 jn ( ) H( k, ) hne (6) n where h n is the nth trnsducer weighting, nd n =,,,..., -. d / csin is the time dely due to the rry geometry. d / csin is the time dely due to the em steering ngle. Weightings h h Ultrsonic trnsducers d h Fig.. Uniform liner rry In our study the trnsducer weightings re vried with frequency. Therefore the rry response for frequency ω cn e expressed s: jn ( ) H( k, ) hn( (7) n Similrly, the directivity for primry frequency ω, D (θ), cn e written s: D ( ) D ( k, )H( k, ) (8) D ( k, is the perture directivity for frequency ω nd H( k, ) where ) e expressed s: H( k is the rry response which cn jn ( ), ) hne (9) n where h n is the nth trnsducer weighting, nd n =,,,..., -. If the weightings re vried with frequency, the fr-field rry response cn e expressed s: H( k jn ( ), ) hn( ) e () n Sustitution of (5) nd (8) into () yields D ( ) D ( k, )H( k, )D ( k, )H( k, ) D ( () where ) is em pttern for udile frequency, i.e. the difference frequency directivity. The em pttern for udile frequency cn lso e written y sustituting (3), (7) nd () into () s: 7

5 ISSN: ISO 9:8 Certified Interntionl Journl of Engineering Science nd Innovtive Technology (IJESIT) Volume, Issue 6, Novemer 3 ( xp[ ( ) jn ( ) D k tn ] h ( exp[ ( k ) tn ] n n jn ( ) hn( n Sustituting k / c, f, d sin / c D ( ) exp[ (f, nd d / csin tn ] hn n ( f into eqution () yields jnf (sin sin ) d / c () exp[ ( jnf (sin sin ) d / c f tn ] hn( f (3) n Eqution (3) cn e used to determine the directivity of udile sound em. The min ojective of the optimiztion method proposed in the study is to control the em width of the min loe nd the side loes level of the difference frequency directivity in (3). The oservtion points re set from - to in the study. The formultion of the optimiztion pproch proposed in the work for designing directionl udile sound systems cn e expressed s: inimize D ( ) D ( ) Suject to D ( 3 ) D ( ) D ( 3 ) D ( ), is the ngle of the side loe, i.e. /, is the ngle of the side loe, i.e. /, 3 is the ngle of the min loe, i.e. / 3 /, is the desired em width, nd where () is the mplitude difference etween the min loe nd side loe. Sustitution of (3) into () yields inimize n exp[ (f h n ( f tn ] hn n ( f jnf (sin sin ) d / c exp[ (f tn ] sin ) d / c exp[ (f / ) tn ] ( ) c hn f e n jnf (sin jnf (sin sin ) d / c exp[ ( f Suject to exp[ (f n h n ( f (sin sin ) / tn jn f d c hn( f n tn 3] hn n ( f jnf (sin 3 sin ) d / c exp[ (f tn 3] 3 sin ) d / c exp[ (f / ) tn ] ( ) c hn f e n jnf (sin jnf (sin sin ) d / c 75

6 exp[ n ISSN: ISO 9:8 Certified Interntionl Journl of Engineering Science nd Innovtive Technology (IJESIT) Volume, Issue 6, Novemer 3 jn f (sin sin ) d / c ( f tn ] hn( f n exp[ (f h n ( f tn 3] hn n ( f jnf (sin 3 sin ) d / c exp[ (f tn 3] 3 sin ) d / c exp[ (f / ) tn ] ( ) c hn f e n jnf (sin jnf (sin sin ) d / c jn f (sin sin ) d / c exp[ ( f tn ] hn( f, (5) n The optiml vlues of h n (f ) nd h n (f ) cn e clculted using the function fmincon( ) in ATLAB. By sustituting the optiml vlues of h n (f ) nd h n (f ) into (3) the directivity of udile sound em, D ( ), cn e otined. III. SIULATION RESULTS In this section the simulted directivity of the udile sound em creted y using the optimiztion method s shown in (5) is presented, nd then compred to those otined y using Cheyshev weighting method [6]. In this study, the numer of weighting functions in the directionl udile sound system is 8 for frequencies f nd f s shown in Fig. 5. Therefore there re 6 weighting functions, i.e.. The crrier frequency of the ultrsonic h ( f ),h ( f ),...,h ( f ) h ( f ),h ( f ),...,h ( f ) 7 trnsducer rry is set s khz, i.e. f = khz. The demodulted signl is t the frequency from.5 khz to 6 khz with 5 Hz intervl. A totl of = 8 ultrsonic trnsducer rry is used with inter-element spcing d = 9.7 mm. The effective source rdius is set t = 3.85 mm nd the speed of sound c is 3 ms -. The weighting functions, h n (f ) nd h n (f ), re clculted for difference frequency s em width for, nd 6 using the proposed method. Figs. 6, 7 nd 8 show the difference frequency s directivity with, nd 7, i.e. without em steering, for 6 respectively. Figs. 6(), 7() nd 8() re the difference frequency s directivity using Cheyshev weighting method [6], nd Figs. 6(), 7() nd 8() re the difference frequency s directivity using the optimiztion method proposed in the pper. From the figures it cn e seen tht the mplitude in the side loe using the proposed method is lower thn tht using the Cheyshev weighting method. This is ecuse the optimiztion method tried to find the optiml weighting functions which minimize the sum of the squred mplitude of the side loe nd suject to the mplitude difference etween the min loe nd the side loe. Therefore the optimiztion method proposed in this pper performs etter thn the Cheyshev weighting method. As cn e seen from the figures the em width cn lso e controlled using the optimiztion method. This is ecuse the difference frequency s directivity is the product of two primry frequency s directivities, nd its em width lwys tkes on the nrrowest em width of the two primry wves. It cn oviously e seen tht constnt em width is chieved for ll frequencies using the proposed method. The highest side loe mplitude of difference frequency sound y using the optimiztion method nd Cheyshev weighting method is summrized in Tle. The highest side loe mplitude with the proposed method gets ttenuted more compred to the method with Cheyshev weighting. This is since the sum of the squred mplitude of the side loe region is minimized through ll the frequencies. Therefore the lower side loe mplitude is otined using the propose method. From the Figs. 6, 7, 8 nd Tle we cn oserve tht etter directivity of the udile sound em is creted using the optimiztion method proposed in the pper thn tht using the Cheyshev weighting method. In this study the performnce of the difference frequency s directivity for with nd em steering hs lso een investigted. Figs. 9 nd show the difference 76

7 ISSN: ISO 9:8 Certified Interntionl Journl of Engineering Science nd Innovtive Technology (IJESIT) Volume, Issue 6, Novemer 3 frequency s directivity for with nd em steering respectively. As cn e seen from the figures the difference frequency cn e steered ccurtely nd the em width is lmost constnt through ll frequencies. Also the mplitude difference etween the min loe nd side loe is out 8dB. Therefore the difference frequency s steering ngle cn e controlled y using the proposed method. In the next section some preliminry experiments will e crried out to vlidte the simultion results. f f Weightings h (f ) h (f ) h (f ) h (f ) h (f ) h (f ) h 3 (f ) h 3 (f ) h (f ) h (f ) h 5 (f ) h 5 (f ) h 6 (f ) h 6 (f ) h 7 (f ) h 7 (f ) Trnsducers Fig. 5. The directionl udile sound system with 8 weighting functions for frequencies f nd f. () 77

8 ISSN: ISO 9:8 Certified Interntionl Journl of Engineering Science nd Innovtive Technology (IJESIT) Volume, Issue 6, Novemer 3 Fig. 6. Difference frequency s directivity for (). () Cheyshev weighting method. () Optimiztion method. () 78

9 ISSN: ISO 9:8 Certified Interntionl Journl of Engineering Science nd Innovtive Technology (IJESIT) Volume, Issue 6, Novemer 3 Fig. 7. Difference frequency s directivity for (). () Cheyshev weighting method. () Optimiztion method. () 79

10 ISSN: ISO 9:8 Certified Interntionl Journl of Engineering Science nd Innovtive Technology (IJESIT) Volume, Issue 6, Novemer 3 () Fig. 8. Difference frequency s directivity for 6. () Cheyshev weighting method. () Optimiztion method. Tle The highest side loe level Cheyshev method Optimiztion method Bem width = -5 db - db Bem width = -5 db - db Bem width = 6-75 db - db 8

11 ISSN: ISO 9:8 Certified Interntionl Journl of Engineering Science nd Innovtive Technology (IJESIT) Volume, Issue 6, Novemer 3 Fig. 9. Difference frequency s directivity for with em steering. Fig.. Difference frequency s directivity for with em steering 8

12 ISSN: ISO 9:8 Certified Interntionl Journl of Engineering Science nd Innovtive Technology (IJESIT) Volume, Issue 6, Novemer 3 IV. PRELIINARY EXPERIENTS In this experiment we investigte the performnce of the directionl udile sound systems in the vehicle cin with weighted trnsducer rry using n optimiztion method. The configurtion of the directionl udile sound experimentl system is plced in front of the right front set in the vehicle cin s shown in Fig.. The experimentl setup of the directionl udile sound system s shown in Fig. includes n ultrsonic trnsducer rry comprising eight trnsducers s shown in Fig. 3, high-frequency microphone (type PCB 377C), mplifiers, filters, function genertor, nd n FFT nlyzer for signl cquisition. The high-frequency microphone ws set-up to rotte t rdius of cm from the center of the trnsducer rry on turntle. The rotting microphone ws swept round n rc from - to reltive to the trnsducer rry s shown in Fig.. It should e noted tht stndrd udio microphones re not suitle for these mesurements, s their own nonlinerities cn crete demodultion t the microphone element itself, cusing incorrect mesurements. One nd-pss filter ws connected etween the function genertor nd the 8 independent mplifiers. The other nd-pss filter ws connected etween the FFT nlyzer nd the mplifier. The signl mesured y the microphone, which ws pssed through nd-pss filter nd then smpled t frequency of 6 khz, ws recorded t increments. The smpled signls were cquired into n FFT nlyzer. A function genertor ws used to generte the signls from to 6 khz in 5 Hz intervls. The directivity of khz for ech trnsducer ws mesured first nd then the directivities of.5 khz 6 khz for ech trnsducer were mesured. The directivity dt mesured ove were tken to clculte the optiml weighting functions, h n (f ) nd h n (f ), for difference frequency s em width,, using the proposed method s shown in (5). The optiml weighting functions clculted were implemented in digitl signl processor (DSP) ord s shown in Fig.. Within the DSP, the udio signl ws converted into digitl signl y n nlogue-to-digitl converter (ADC), modulted y crrier frequency, weighted y weighting functions, nd converted ck to nlogue y the digitl-to-nlogue converter (DAC). The signls were finlly sent to the driver circuit, which provides high current to drive the high cpcitive ultrsonic trnsducers. Fig. 5 shows the difference frequency s directivity normlized to the mximum level for through the experiment. It cn e seen tht constnt em width is chieved for ll frequencies nd the mplitude difference etween the min loe nd side loe is out 7dB. From Fig. 5 we cn oserve tht the result in the experiment is similr to tht in the simultion s shown in Fig. 6(). Therefore the optimiztion method proposed in the pper cn etter control the em width. Also good directivity cn e chieved using the proposed method. - The directionl udile sound experimentl system icrophone Fig.. Configurtion of the directionl udile sound system in vehicle cin 8

13 ISSN: ISO 9:8 Certified Interntionl Journl of Engineering Science nd Innovtive Technology (IJESIT) Volume, Issue 6, Novemer 3 icrophone - Amplifier Ultrsonic trnsducer rry Bnd-pss filter 8 independent mplifiers Power supply Bnd-pss filter FFT nlyzer Function Genertor Fig.. The directionl udile sound experimentl setup with the microphone t different positions reltive to the ultrsonic trnsducer rry, i.e., - to degrees. Fig. 3. An ultrsonic trnsducer rry comprising eight trnsducers 83

14 ISSN: ISO 9:8 Certified Interntionl Journl of Engineering Science nd Innovtive Technology (IJESIT) Volume, Issue 6, Novemer 3 DAC Driver Ultrsonic trnsducers - Audio signl ADC odultion, weighting nd filtering DAC Driver DAC 7 Driver Amplifier DSP ord FFT nlyzer Bnd pss filter Fig.. Hrdwre configurtion of the directionl udile sound system Fig. 5. Difference frequency s directivity normlized to the mximum level for through the experiment. 8

15 ISSN: ISO 9:8 Certified Interntionl Journl of Engineering Science nd Innovtive Technology (IJESIT) Volume, Issue 6, Novemer 3 V. CONCLUSION In this pper n optimiztion method hs een proposed for designing directionl udile sound system in the vehicle cin. A uniform liner rry composed of eight ultrsonic trnsducers with different weighting functions ws used for generting the udile sound em. The optiml weighting functions were clculted using the optimiztion method. The theoreticl derivtion of the proposed method hs een descried nd some simultion results hve lso een presented in the pper. A preliminry experiment hs een crried out to vlidte the simultion results. The performnce of the em width control using the proposed method hs een evluted. It cn e seen tht the proposed method could effectively control the em width of the min loe nd the level of the side loes for the udile sound em. The directionl udile sound em could lso e steered using the proposed method. It is verified y the simultion nd experiment results tht the lower side loes level could e otined y using the proposed method. Therefore the proposed method could etter control the em width nd good directivity could lso e chieved. ACKNOWLEDGEENT The study ws supported y the Ntionl Science Council of Tiwn, the Repulic of Chin, under project numer NSC---E-8-. REFERENCES [] H.O. Berkty, Possile exploittion of nonliner coustics in underwter trnsmitting pplictions, Journl of Sound nd Virtion, vol. (), pp. 35-6, 965. [] in Chen, Limei Xu, Dgui Hung, Ying Wng nd Xuesheng Li, Experimentl verifiction of squre rooting lgorithm for prmetric loudspeker with PVDF film trnsducer, Interntionl Journl of Innovtive Computing, Informtion nd Control, vol., Numer 8, pp , August 8. [3] F.J. Pompei, The use of irorne ultrsonic for generting udile sound ems, Journl of Audio Engineering Society, vol. 7(9), pp , 999. [] P.F. Joseph, The use of irorne ultrsonic for generting udile sound ems, Journl of Audio Engineering Society, vol. 7(9), pp , 999. [5] D.I. Hvelock nd A.J. Brmmer, Directionl loudspekers using sound ems, Journl of Audio Engineering Society, vol. 8(), pp ,. [6] J. Yng, K.S. Tn, W.S. Gn, nd J. Tin, odeling of finite-mplitude sound ems: second order fields generted y prmetric loudspeker, IEEE Trnsctions on ultrsonics, ferroelectrics, nd frequency control, vol. 5(), pp. 6-68, 5. [7] P.J. Westervelt, Prmetric coustic rry, Journl of Acousticl Society of Americ, vol. 35(), pp , 963. [8]. Yoneym nd J. Fujimoto, The udio spotlight: An ppliction of nonliner interction of sound wves to new type of loudspeker design, Journl of Acousticl Society of Americ, vol. 73(5), pp , 993. [9] W.S. Gn, J. Yng, K.S. Tn, nd.h. Er, A digitl emsteerer for difference frequency in prmetric rry, IEEE trnsctions on udio, speech, nd lnguge processing, vol. (3), pp. 8-5, 6. [].F. Hmilton nd D.T. Blckstock, Nonliner Acoustics, Acdemic press, Sn Diego, 998. [] D.H. Johnson nd D.E. Dudgeon, Arry signl processing, Prentice-Hll, NJ, 993. AUTHOR BIOGRAPHY Wen-Kung Tseng received the B.Eng. in mechnicl engineering from the Ntionl Tipei University of Technology, Tipei, Tiwn, nd.sc. nd Ph.D. degrees in coustics from the University of Southmpton, U.K., in 998 nd, respectively. He joined the Nnki University of Technology, Tiwn, in y s n Assistnt Professor. He ws promoted to n Associte Professor in 7. He joined the Ntionl Chnghu University of Eduction, Tiwn, in August 7 s n Associte Professor. He ws promoted to Professor in 3. His reserch interests include ctive noise control, nonliner coustics, signl processing, optimiztion techniques, nd DSP pplictions. 85