2007 adaptive wave field synthesis for sound field reproduction: theory, experiments, and future...

8/11/2019 2007 Adaptive Wave Field Synthesis for Sound Field Reproduction: Theory, Experiments, and Future Perspectives

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Adaptive Wave Field Synthesis for Sound Field

Reproduction: Theory, Experiments, andFuture Perspectives*

PHILIPPE-AUBERT GAUTHIER, AES Student Member, AND ALAIN BERRY([email protected]) ([email protected])

Groupe dAcoustique, Universite de Sherbrooke, Sherbrooke, Quebec, Canada, J1K 2R1

Wave field synthesis (WFS) is a sound field reproduction technology that assumes that thereproduction environment is anechoic. A real reproduction space thus reduces the objectiveaccuracy of WFS. Adaptive wave field synthesis (AWFS) is defined as a combination of WFSand active compensation. With AWFS the reproduction errors are minimized along with adeparture penalty from the WFS solution. Analysis based on the singular value decompositionconnects WFS, active compensation, and Ambisonics. The decomposition allows the prac-tical implementation of AWFS based on independent radiation mode control. Results ofexperiments in different rooms support the theoretical propositions and show the efficiencyof AWFS for sound field reproduction.

0 INTRODUCTION

Sound field reproduction is one of the possible techno-logical approaches for spatial sound. It focuses on thesimulation of the physical stimulus of spatial hearing,which is the sound field in which an audience or a listeneris immersed in a natural hearing situation. Sound fieldsimulation, by opposition to perception simulation (level-difference stereophony, time-difference stereophony, bin-

aural audio technologies), which is based on illusion [1],mainly relies on the recreation of a physical acoustic quan-tity, such as acoustic pressure [2][5], intensity field [6],and direct or diffuse fields [7][9]. Sound field reproduc-tion for spatial audio relies on the fundamental hypothesisthat if the sound field is reproduced accurately, in objec-tive terms, the listener will be exposed to appropriate bin-aural and monaural cuesinteraural time differences, in-teraural intensity difference, and spectral cues caused by

external ear filtering as a function of the incident directionof the sound wave [10]. The reproduction of spatial cueswould then create a spatial impression corresponding tothe target that must be reproduced.

The best known sound field reproduction techniquesaddress the interior problem of sound field reproduction.The objective is then to reproduce or synthesize a givensound field inside a volume or a listening region sur-rounded by a reproduction source array. Typical tech-

niques are wave field synthesis (WFS) [2], [11] and Am-bisonics [12], [13], [5]. The WFS approach derives from asimple source formulation of the KirchhoffHelmholtz in-tegral and the Ambisonics approach derives from a mode-matching approach [14]. Theoretical connections betweenWFS and Ambisonics are already known [15]. Some ap-proaches for sound field reproduction are derived fromactive noise control methods and often include a cost func-tion for the minimization of reproduction errors [16][20].This paper presents the adaptive wave field synthesis(AWFS) method, which is a combination of WFS andactive noise control techniques.

*Presented at the 123rd Convention of the Audio EngineeringSociety, New York, 2007 October 58; revised 2007 November 26.

Editors Note:ThisJournalpaper is a fully reviewed submission, which was awarded the Student Technical Papers Award atthe 123rd Convention of the Audio Engineering Society in New York, 2007 October 58. The student, Philippe-AubertGauthier, presented the paper and was honored at the Convention. The Editor hopes this will encourage future student

submissions. The criteria for the award can be found at http://www.aes.org/events/124/authors.

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implies that only a part of the reproduction source array isactive for a given primary source. A spatial weightingwindow is used to reduce the WFS strength amplitudesprogressively. This is applied to the secondary sourcescloser to the end of the active part of the secondary sourcearray. Such spatial windowing limits the finite apertureeffects of the secondary source array. Here the spatialweighting window is a rectangular window with half-Hanning windows at its ends. The half-Hanning window

extends over 0.5 m [11].The stationary phase approximation [37] in the devel-

opment of the WFS operators also leads to the definitionof a reference line [11] on which the amplitude of thereproduction error should theoretically be zero in compari-son with points outside the reference line, again for thefree field. Indeed, the stationary phase approximation inWFS implies that the reproduced sound field would bereproduced perfectly only on a line in front of the second-ary source array. For WFS this line is chosen arbitrarily,and this corresponds to the WFS reference line. This lineis shown in Fig. 1. In this paper the secondary source arrayis placed on a circle, and the reference line is also definedas a circle, centered on the primary source position x0andpassing through the secondary source array center. Thechoice of a given reference line definition is not relevant tothe AWFS fundamental idea, but it remains important forthe WFS definition (for the reproducibility of numericaland experimental results) since the reference line partici-pates in the definition of the WFS operators of Eq. (1).

Practical WFS implementation implies discrete repro-duction sources on a finite line. The WFS reproducedsound field in free space is then

prep

x, =

l=1

L

QWFSxll,

ejkr

r (3)

with r|x xl(l) | .

1.2 Adaptive Wave Field Synthesis

AWFS is introduced as an optimal control approachwith the cost function

JAWFS= eHe+ QQWFS

HQQWFS (4)

which must be minimized, with being a real positivescalar. The superscript H denotes Hermitian transposition.Eq. (4) introduces the M-component reproduction errorcolumn vector e(xm

(m), ) p(virt)(xm(m), ) p(rep)(xm

(m),) p(virt)(xm

(m), ) G()Q(xl(l), ), where p(virt) is the

complex column vector of the target sound pressure fieldat the Msensor locations in xm

(m), and G() is an Mby Lmatrix of the plant complex response (from the Lrepro-duction source monopole amplitudes to the Macousticpressures at the error sensor array). The first term in Eq.(4) represents the summation of the quadratic reproductionerrors with respect to the target sound field, observed atthe error sensor locations. The first objective is then toreduce these reproduction errors caused possibly by roomresponse or system limitations. The second term in Eq. (4)

is weighted by the regularization parameter and repre-sents a quadratic departure penalty of the solution Q withrespect to the fixed WFS solution QWFS. The penalizationfor any departure from the WFS solution is motivated bysimple facts: the WFS direct sound field approaches thetarget sound field and the WFS solution accordingly pro-vides correct sound localization. More simply, AWFS im-plies a reproduction error minimization along with a favorfor the WFS solution. For active sound field reproductionusing few error sensors (as reported herein), the WFSsolution introduces supplementary spatial information,which would not otherwise be accessible using only re-production error minimization at a few sets of error sen-

sors. This is an advantage of AWFS.This formulation of the problem, using a classical in-

verse problem with Tikhonov regularization with a priori

Fig. 1. Definition of WFS operators. Virtual source is located in x0; reproduction source l is located in x l(l) (xl

(l), . . . , x l(l), . . . , xL

(l)).x(ref)point that belongs to reference line; xany field point, xm

(m)mth sensor position (x1(m), . . . , xm

(m), . . . , xM(m)).

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solution (WFS) [40], is the principal originality of AWFS.Also note that the a priori solution could be of any othertype, such as Ambisonics or multichannel stereophony. Inthat case, although it could not be called AWFS, the re-maining theoretical developments would apply (QWFSbe-ing replaced by any solution Qpriori). This could be a sub-

ject of future research.JAWFSis a quadratic function ofQ.Although the repro-

duction system p(rep)(xm(m), ) G()Q(xl

(l), ) is under-

determined (assuming M< L, as for the remainder of thepaper) [41], the WFS departure penalty term, weighted by, ensures that there will be a unique minimum of Eq. (4).That is, the Hessian matrix ([GHG+I]) of the quadraticEq. (4) is positive definite, provided that > 0. The op-timum source vector minimizes the cost function of Eq. (4)[41],

QAWFS=GHG+ I1GHpvirt + QWFS. (5)

When , the solution reduces to the WFS operatorsQWFS; when 0, the solution is the optimal controlsolution, which minimizes the reproduction error in aleast-mean-square (LMS) sense. These two situations arethe limiting cases of AWFS [5].

1.2.1 Simple AWFS Examples in Free Field

Some preliminary examples of WFS and AWFS simu-lations in free field are now introduced for illustrativepurposes. They illustrate the very general behavior ofAWFS. AWFS as an active sound field reproduction andactive room compensation method will be discussed lateron the basis of experimental results.

The theoretical configuration, which also corresponds tothe experimental system, is shown in Fig. 2. The system

includes 24 secondary or reproduction sources grouped ina circular array and four error sensors for which the re-

production errors should be minimized according to theAWFS cost function of Eq. (4). This configuration is cho-sen to illustrate and study the AWFS behavior. For thepractical experiments, a linear array of eight monitoringsensors is used to evaluate the reproduced sound field. Forthe theoretical simulations and examples, a set of eightconcentric circular arrays, including a total of 96 monitor-ing sensors in the circular region circumscribed by theblack circular solid line shown in Fig. 2, is used.

Simulation results are reported in Figs. 3 and 4. Theresults are quantified by the performance criterion ELS,

ELS= e

Hxm

m, exmm,

pvirtH

xmm, pvirtxm

m, (6)

Fig. 2. AWFS system configuration including reproduction sources, virtual source, error sensors, monitoring sensors, and typical virtualsound field at 220 Hz. Solid black circular lineregion covered by 96 monitor sensors used for simulation only.

Fig. 3. Performance criterionELSevaluated at error sensors as afunction of frequency. WFS; AWFS using a singlegeneral penalization parameter 22.5 [Eq. (5)]; AWFS

based on independent radiation mode control (SVD, 1 22.5,2 3 0.75, 4 0.0125).

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which represents the mean normalized quadratic reproduc-tion errors at the error sensors. When ELSreaches 0, thereproduction error is null. When ELSis 1, the reproductionerror is as large as if the reproduced sound field wereperfect silence. This scalar criterion can also be evaluatedfor the 96 monitor sensors; xm

(m) is then replaced by themonitor sensor positions. The reproduction erroreis com-puted for the optimal AWFS solution QAWFS or for theWFS solution QWFS.

In Fig. 3 the performance criterion for sound field re-production ELSis shown for the error sensors. Since thisillustrative case is computed in the free-field situation,WFS already performs well (ELS K 1) since some of thehypotheses implied in the development of the WFS solu-tion are respected. However, the WFS solution provides anELS greater than for AWFS using a single penalizationparameter as in Eq. (5). (The penalization parameter wasset to 22.5.) This proves that the reproduction error iseffectively reduced by AWFS at the error sensor array.Typical WFS reproduction errors in the free field arecaused by the inherent WFS assumptions [11] and by thefinite size of the active reproduction source array in com-parison with the wavelength. Since the configuration usedfor these simulations is relatively small, this type of erroris dominant for the low frequencies. The third curve(heavy line) will be discussed in Section 1.2.2.

To illustrate the effect of AWFS outside the controlregion defined by the error sensor positions, Fig. 4 showsthe reproduction error minimization at the 96 monitor sen-sors. (See the region covered in Fig. 2.) Clearly, the re-production error minimization at the error sensors effec-tively reduces the WFS reproduction errors outside thiscontrol region. This illustrates the effectiveness of AWFSin compensating for reproduction errors in a region larger

than the control region covered by the error sensors. Thisissue is further developed in the following section. Thethird curve will be discussed in Section 1.2.2.

The corresponding real parts of reproduced sound fieldsat 220 Hz are shown in Figs. 5 and 6 for the target soundfield of Fig. 2. In these figures several results and infor-mations are included. The secondary source array is shownas a heavy circle. The reproduced sound field is shown asa gray surface. The wavefronts of the target sound pressurefield are shown as dashed contour lines for p(virt)(x,) 0. The contour lines of the local normalized performancecriterion ELS are also superimposed on the reproduced

sound fields.As shown in these figures, WFS effectively performs

sound field reproduction in the free field, but the repro-duction errors (visible through the local ELScontour lines)are smaller for the AWFS reproduced sound field. This

Fig. 4. Performance criterionELSevaluated at 96 monitor sensorsas a function of frequency. WFS; AWFS using a singlegeneral penalization parameter 22.5 [Eq. (5)]; AWFS basedon independent radiation mode control (SVD, 1 22.5,2 3 0.75, 4 0.0125).

Fig. 5. Real part of reproduced sound field at 220 Hz by WFS infree field.

Fig. 6. Real part of reproduced sound field at 220 Hz by AWFS,using a single penalization parameter, in free field.




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shown in Fig. 8, these multipole patterns are finite-difference approximations of pressure, perpendicular pres-sure gradients, and second-order mixed spatial derivativesat the error sensor array.

The harmonic sound fields produced by each of theseradiation modes are shown in Fig. 9. Clearly, the radiationmodes correspond to finite approximations of pressure,

pressure gradients, and second-order mixed spatial deriva-tives at the error sensor array, which is located at thecenter of the reproduction source array. It is then expectedthat the higher order radiation modes, which correspond tohigher order spatial derivatives, will play a significant rolein determining the size of the region where the reproduc-tion error would be reduced in comparison with WFS.

Taking the AWFS solution of Eq. (5) and using theSVD ofG, the AWFS solution can be expanded over the

source modes v i, QAWFS LiiQi vi,as follows:

Qi= i

i2 + i

pivirt +

i

i2 + i

viHQWFS i r M

viHQWFS

i 0, i r,

i L

0, i=0, i r,

i L(11)

where the independent contributions ofviin Q

AWFSwere

now individually regularized with i.AWFS thus proceedsto control and regularize each radiation mode indepen-dently. The AWFS solution of Eq. (4) implicitly assumedan identical regularization parameter for all source modes,i for all i .Note that Eq. (11) was slightly modifiedin comparison to Eq. (5) for the particular case i 0. Eq.(11) is forced to the pseudoinverse definition by the addi-tion of the third case. The AWFS solution [Eq. (11)] sug-gests that the underlying mechanism is independent radia-tion mode control. This mechanism can be used forpractical AWFS implementation.

Examples of AWFS based on independent radiation

mode control are included in Figs. 3 and 4, where theperformance criterion ELSis represented by dashed linesand was computed with different penalization parametersfor each of the radiation modes. Clearly the independentradiation mode control implementation yields a better per-formancethe size of the effective reproduction region isexpected to be larger.

Since the singular values i decrease with the modeorders i,the higher order radiation mode penalization pa-rameters iwere also reduced in amplitude. This is nec-essary since the effect of penalization for each of the ra-diation modes depends on the relative magnitude of thesquare of the singular value and the corresponding penal-

ization parameter [see Eq. (11)]. As the higher order ra-diation modes typically correspond to higher order spatialderivatives, it is important not to overpenalize these modesas they might enlarge the effective control region. (Thiswas the case for AWFS using a single penalization param-eter, which is fully equivalent to Eq. (11) using i .)This is supported by Fig. 10, which shows the reproducedsound field by AWFS based on independent radiationmode control. In this regard, future research on AWFSusing more error sensors in a compact sensor array wouldbe interesting since it is probable that the total number ofhigher order spatial derivatives included in the pressure

Fig. 9. (a)(d) Sound field radiated by first four source modes. (e)Sound field radiated by null space, representing sum of nullspace radiation modes. zero-pressure contours of soundpressure fields.




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mode basis would increase, as would the effective controlregion.

The AWFS realization based on independent radiationmode control (Fig. 10) implies a larger effective reproduc-tion region (characterized by a low local ELS) than AWFSbased on a single penalization parameter (Fig. 6). Thisstems from the ability to penalize the radiation modesindividually and from the contribution of the higher orderradiation modes.

1.2.3 AWFS, SVD, and Ambisonics

The SVD of the plant matrix as an analysis tool forAWFS introduces a link between WFS, AWFS, and Am-bisonics. Theoretical connections between WFS and Am-bisonics are already known on the basis of theoretical

orthogonal functions of the wave equation in cylindricalcoordinatescylindrical harmonics [15]. The SVD of theplant matrix for AWFS, however, introduces a new con-nection on the basis of orthogonal functions derived fromnumerical plant decoupling.

As the pressure modes (see Fig. 8) approach cylindricalharmonics, or Ambisonics components [5] at the errorsensor array, it is possible to understand that AWFS op-erates as a closed-loop implementation of Ambisonics,

with a penalty for the departure from the WFS solutionsince the pressure modes, which approach Ambisonicscomponents, are individually controlled on the basis ofleast-mean-square minimization, as for Ambisonics,which typically implies open-loop (that is, in a theoreticala priori step) minimization of the errors for these compo-nents. Accordingly these very specific shapes of the pres-sure modes at the sensor array allow for a conceptualconnection between Ambisonics and AWFS using theconfiguration presented. Further considerations and ex-amples are given [5].

1.3 Signal Processing for Adaptive WaveField Synthesis

For the sake of brevity, this section describes the im-plied signal processing for AWFS as defined in the pre-vious sections. Signal processing for AWFS is the topic ofa paper accepted for publication by the Journal of Acous-tical Society of America.

1.3.1 Modification of the Filtered-Reference LMSAlgorithm (FXLMS)

In a classical adaptive minimization of Eq. (4), a cen-tralized multichannel adaptive algorithm would be imple-mented using a feedforward architecture [44]. This is il-

lustrated in Fig. 11. A set ofz-transformed adaptive filtersw(z) are adapted to reduce the quadratic summation of theMreproduction errors eM(n), where nis the sample index.

Fig. 10. Real part of reproduced sound field at 220 Hz by AWFSbased on independent radiation mode control.

Fig. 11. AWFS using modified multichannel adaptive algorithm. Capitalized subscripts denote signal dimensions.




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The discrete filters w(z) are fed by a reference signal x(n)and produce the Lcommand signals yL(n) for the Lsec-ondary sources. HereG(z) is the only physical system. Allother operations are achieved in a discrete-time signal-processing domain. This includes G(z), which is an iden-tified approximation ofG(z). The target sound field defi-nition at the error sensors is obtained by passing thereference signal x(n) through the target pressure modelera(z). The WFS solution departure penalty [see Eq. (4)] is

automatically taken into account by the LMS adaptation,which is based on a gradient algorithm of the discrete-timerepresentation of the AWFS cost function of Eq. (4). Us-ing Merror sensors and Lreproduction sources, this willbe a multiple-inputmultiple-output (MIMO) L Msys-tem. The computational burden involved in the block dia-gram of Fig. 11 becomes prohibitive as L, M, and theadaptive filter order increase [44], [45]. Moreover, thismay slow down the gradient LMS algorithm convergenceasLandMincrease [45]. This type of algorithm implies ageneral convergence coefficient and a unique generalpenalization parameter [46] [see Eq. (5)].

1.3.2. Independent Radiation Mode ControlBased on Plant Singular Value Decomposition

As noted in Eq. (11), each source mode contributionQiinQAWFSis solely defined by the correspondingpi

(virt),i,i, and vi

H QWFS, which is the projection of the WFSoperatorQWFSon the ith source mode v i.It is possible toexploit this independence of the radiation modes for prac-tical implementation of AWFS.

This leads to another approach, illustrated as a blockdiagram in Fig. 12. G(z) is again the only physical system.With this diagram we seek to produce a set of M(withM L) independent SISO (single-input-single-output)

adaptive systemswi(z). This type of algorithm then impliesan independent convergence coefficient i and an inde-

pendent penalization parameter ifor each radiation mode.This is an advantage of AWFS based on independent ra-diation mode controlindependent fine-tuning of the con-vergence and penalization properties of each radiationmode. This is not the case with the modified multichannelFXLMS algorithm for AWFS. Here each independentadaptive system generates the signal sent to each sourcemode vifor i r M.This type of independent controlusing SVD was investigated by Bai and Elliott [45] for

loudspeaker-to-ear crosstalk cancellation, but without an apriori solution like QWFS. This independent radiationmode control of AWFS is also a modification of the prin-cipal-component LMS (PC-LMS) algorithm for activenoise control of tonal disturbance [46][48]. The PC-LMSis based on SVD, but for AWFS the SVD decoupling mustoperate over the entire frequency range of interest [5],[45].

This implementation requires the additional MIMO syn-thesis and MIMO analysis filters (s)G(z) and (a)G(z), re-spectively, which must be generated in a prior identifica-tion stage. In this case an identification of the frequencyresponse functions (FRFs)G

ml() between each secondary

source land each error sensor mmust be achieved. TheSVD of the corresponding transfer matrix for each fre-quency provides the source modes vi() and the corre-sponding pressure modesui(). The inverse Fourier trans-form ofvi()/i(), i r M,and ui() generates thez-transformed discrete-time impulse response (IR) matri-ces (s)G(z) and (a)G(z), respectively. The matrix (s)G(z)generates the inputs of the individual reproduction sourcesfrom the source mode inputs with a delay ofSVDsamples[45]. Note that division by i() implies plant whiteningalong uncoupling. (Plant whitening is optional; results pre-sented in this paper only include plant decoupling.) Con-

versely, the matrix (a)

G(z) is used to generate the pressuremode errors from the individual sensor errors, again with

Fig. 12. Block diagram of AWFS least-mean-square adaptive digital signal processing implementation based on independent radiationmode control. Subscripts denote signal dimensions.




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a delay ofSVDsamples [5], [45]. The second synthesisfilter matrix (s)G(z) is created from the null-space sourcemodes to produce the fixed part of the AWFS solution [seethe last two cases of Eq. (11)]. The delay block (Fig. 12)of 2SVD samples then represents the uncoupled plantmodel. This type of realization was more extensively de-scribed in [45] for loudspeaker-to-ear cross talk cancella-tion. Also, because of the WFS departure penalty in theAWFS definition, an additional set of fixed filters produce

the outputs for the i> r(and i L) WFS fixed sourcemode contributions qi, which belong to the null space.This introduction of an a priori solution is the principaldifference compared to the work of Bai and Elliott [45].

1.3.3 Synthesis and Analysis Filters: Radiation

Mode Reordering

The general procedure just described involves supple-mentary practical considerations before being usable forthe creation of the synthesis and analysis filtersit re-quires further operations.

Numerical SVD algorithms typically arrange the leftand right singular vectors in V() and U() according todecreasing singular values. Then, since the plant SVD iscomputed for each frequency independently, a radiationmode reordering algorithm is needed to smooth the fre-quency response functions of the uncoupling filters. Thissmoothing typically yields shorter impulse responses forthe corresponding filters in the time domain.

For the AWFS system the reordering algorithm simplyperforms a two-step smoothing by 1) rearranging the col-umns in V() and U() so that source modes varysmoothly as a function of frequency, and 2) verifying andcorrecting any sign changes in V() as the frequency in-creases. This proved to increase greatly the quality (com-

pactness in the time domain) of the synthesis and analysisfilters. (More details and examples will be given in thepaper on signal processing for AWFS.) Note that suchconsiderations for left and right singular vector reorderingwas not included in Bai and Elliotts original work onbroad-band plant decoupling [45].

2. ADAPTIVE WAVE FIELD SYNTHESIS:EXPERIMENTAL RESULTS

This section summarizes the experimental results ob-tained for AWFS in three different rooms: hemianechoicchamber, laboratory space, and reverberation chamberwith damping material. These rooms cover a wide range oftypical acoustical responses, from nearly free field tonearly diffuse field. A limited set of results are presented

here to validate the AWFS concept. The AWFS system isshown in Fig. 13 in the laboratory space. The loudspeakerand microphone setup corresponds to the configurationshown in Fig. 2.

2.1 Hemianechoic Chamber

Sound fields reproduced by WFS and AWFS in a hemi-anechoic chamber are presented to demonstrate the inter-est of AWFS in a very simple acoustical environment. TheWFS reproduced impulse responses (IRs) at the monitor-ing array are shown in Fig. 14. These reproduced soundfields were measured using swept sines as excitation sig-nals. Frequency response functions (FRFs) were first com-puted by averaging over 200 recordings in the frequencydomain. Inverse Fourier transforms of the resulting aver-

Fig. 13. Experimental AWFS setup in laboratory space.

Fig. 14. Reproduced (heavy gray lines) and virtual (thin black lines) impulse responses at monitoring sensor array (shown in Fig. 2)for WFS with system in hemianechoic chamber.




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age FRFs were used to obtain 256-coefficient impulse re-sponses. The bandwidth is limited to 600 Hz, which is justbelow the WFS aliasing frequency for this setup (634 Hzassuming at least two reproduction sources per smallestwavelength).

Clearly, the target sound field is approached by theWFS direct sound field. However, there are some discrep-ancies between this reproduced direct sound field and thetarget sound field, presumably caused by the loudspeaker

responses and the WFS approximations. After the directsound field impinges on the monitoring sensor array, thefloor reflection crosses this array. In this figure the latereflection corresponds to the low-frequency echo of thehemianechoic chamber, which is not anechoic below ap-proximately 100 Hz. All these differences are potentiallycompensated by AWFS.

Using the modified FXLMS algorithm and the indepen-dent radiation mode control algorithm for AWFS, the re-produced sound fields in the hemianechoic chamber areshown in Fig. 15 for the same virtual source position.Clearly, the two implementations of AWFS compensateboth for 1) the direct sound field coloration and 2) the

room response. This illustrates the interest of AWFS as anactive sound field reproduction method.

Although hardly visible on the figure, the AWFS algo-rithm based on independent radiation mode control per-forms better than the AWFS algorithm based on the modi-fication of the classical FXLMS algorithm. This is shownin Fig. 16, where the normalized energies of the reproduc-tion errors are computed for the reproduced sound fields ofFigs. 14 and 15 and for a supplementary virtual source

position. The normalized energies of the errors are com-puted from the differences between virtual and reproducedIRs shown in Figs. 15 and others, measured for differentvirtual source positions. The normalized energies are com-puted as the sums of the quadratic error signals (differ-ences between virtual IRs and reproduced IRs in the timedomain) over the length of the IRs normalized by the totalquadratic sum of the virtual IRs, divided by the number ofmonitoring microphones. The normalization is thusachieved by division by the mean virtual IR energies at themonitoring microphones.

According to the results shown in Fig. 16, the AWFSalgorithms reduce on average the reproduction errors ascompared to WFS by controlling the reproduction error atthe four error sensors (two of which are monitoring sen-sors number 4 and 5). As suggested earlier in this paper,AWFS based on independent radiation mode control ef-fectively provides a larger reproduction region since thehigher order modes are included in the controller in thatcase. Note that the size of the effective control region isalso blurred by the fact that this type of representationincludes all the frequencies at once. AWFS modified byFXLMS provides a significant reproduction error reduc-tion at the two central monitoring microphones, but thereproduction errors are not so small for the other monitor-

ing microphones. AWFS performs better than WFS for allthe virtual source positions reported; active room compen-sation by AWFS is effective and proven. The convergencecoefficients and i,the penalization parameters and i,

Fig. 15. Reproduced (heavy gray lines) and virtual (thin blacklines) impulse responses at monitoring sensor array (shown inFig. 2) for AWFS with system in hemianechoic chamber. (a)FXLMS algorithm with 20. (b) Independent radiation modecontrol.

Fig. 16. Normalized energies of error signals at each monitoringmicrophone for two virtual source positions in hemianechoicchamber. Position #1x0 [0, 4, 0], position #2x0 [ 4, 0,0]. WFS errors; errors of AWFS by FXLMS; errors ofAWFS by independent radiation mode control.




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and the number of control coefficients are summarized inTable 1 for all the results reported, including those for thelaboratory space and the reverberation chamber.

2.2 Laboratory Space andReverberation Chamber

Since AWFS is proposed as an active room compensa-tion method for sound field reproduction, several ex-amples of room compensation in more hostile environ-

ments are summarized. To validate some theoreticalpropositions, Fig. 17 presents the pressure modes at theerror sensor array at 220 Hz in the reverberant chamber.These are the pressure modes ui, as was done for thetheoretical case shown in Fig. 8. Although they differ fromthose obtained in the theoretical case, the pressure modeseffectively yield finite approximations of pressure, pres-sure gradients, and second-order mixed spatial derivativesof pressure at the error sensor array. This proves experi-mentally that AWFS applied to the specific loudspeakerand sensor layout presented herein can be understood as aclosed-loop implementation of Ambisonics since the pres-sure modes approach the typical low-order Ambisonicscomponents (further details are given in [5]).

IRs reproduced by WFS in laboratory space are shownin Fig. 18. As for the WFS experiment in the hemi-anechoic chamber, the reproduced direct sound field ap-proaches the target sound field. The late part of the IRscontains, as expected for the room shown in Fig. 13, farmore energy than that obtained in the hemianechoic space.This increases the discrepancy between WFS and the tar-get sound field and can potentially be compensated byAWFS.

Reproduced sound fields by AWFS illustrated in Fig. 19show that this discrepancy can be reduced drastically. A

long part of the tail of the reproduced IRs caused by theroom response is compensated. The reproduced soundfields by AWFS show less effect of the room than WFS,and even the reproduced direct sound field approachesmore precisely the target direct sound field.

As shown earlier for the reproduced sound field inhemianechoic space (Fig. 16), Fig. 20 shows the normal-ized energies of the reproduction errors at the eight moni-toring sensors (see Fig. 2) for two virtual source positions,one of which was used to produce the sound field shownin Figs. 18 and 19.

According to the results shown in Fig. 20, the AWFSalgorithms reduce on average the reproduction errorswhen compared to WFS by controlling the reproductionerror at the four error sensors. As for the hemianechoicspace, AWFS based on independent radiation mode con-trol effectively provides a larger reproduction region incomparison with AWFS based on the modification of theFXLMS algorithm. AWFS performs better than WFS forall the virtual source positions reported. Active room com-

pensation by AWFS is effective even in a more hostileacoustic environment than the hemianechoic chamber.

Further WFS and AWFS experiments were carried outin a reverberation chamber. Several sheets of dampingmaterial were placed on the floor and in the corners of theroom to reduce the reverberation time. Otherwise the ma-

jor source of acoustical absorption was the system opera-tor, and this typically caused excessively long system IRs.The addition of these absorbent panels reduced the lengthand level of the room reverberation, although these re-mained above the reverberation length and level obtainedin the laboratory space.

Results are summarized in Fig. 21, which shows thenormalized energies of the reproduction error at the moni-toring sensors for four different virtual source positions.

Fig. 17. Measured pressure modes at 220 Hz in reverberantchamber. sensor position; positive real part; negative realpart; + positive imaginary part; negative imaginary part. Sym-bol diameter illustrates magnitude of corresponding value. equivalent computed free-field directivity.

Table 1. Number of coefficients (for AWFS filters and reproduced sound field), convergence coefficients, and penalizationparameters for different rooms and algorithms.

Rooms and Algorithms Coefficients or i or i

Hemianechoic, modified FXLMS 256 0.00001 20Hemianechoic, independent radiation mode control 256 0.0001 0.0004 2 0.2

0.0004 0.002 0.2 0.1Laboratory, modified FXLMS 512 0.000002 30Laboratory, independent radiation mode control 512 0.0000075 0.00003 2 0.2

0.00003 0.00015 0.2 0.1Reverberant, modified FXLMS 1024 0.0000005 50Reverberant, independent radiation mode control 1024 0.0000125 0.00005 4 0.4

0.00005 0.00025 0.4 0.04




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Clearly, the normalized energies of the reproduction errorsfor WFS are greater than those obtained for the hemi-anechoic chamber and the laboratory space. Once again,AWFS effectively reduces the reproduction errors. AWFSperforms better than WFS for progressive sound field re-production (spherical wave from the virtual source in thehorizontal plane). This proves that AWFS can effectivelyreduce the effect of the room response on reproducedsound fields by WFS even in a hostile environment. More-

over, the AWFS algorithm based on independent radiationmode control performs better than AWFS based on themodified FXLMS algorithm. This concludes the experi-mental validation of the AWFS concept for active soundfield reproduction in rooms.

2.2.1 Effect of the Higher OrderRadiation Modes

In Section 1.2.2 it was claimed that the higher orderradiation modes are of relevance in increasing the effec-tive control region. This was verified experimentally in thelaboratory space. For the dedicated AWFS experiment theWFS operators were forced to zero, Q

WFS0, and the

independent radiation mode controllers were sequentiallyadded in the solution. The WFS solution is forced to zeroto illustrate the effects of the individual radiation modesone to four. The test was made for harmonic sound fieldreproduction by AWFS at 400 Hz.

The results of these experiments are shown in Fig. 22,where the normalized criterion ELS E[e(n)

T e(n)/p(virt)T

(n)p(virt)(n)] at the monitor sensors is represented. E[] rep-resents mathematical expectation.

Clearly, when AWFS based on independent radiationmode control includes only one radiation mode, the resultscorrespond to AWFS by FXLMS. When the number of

higher order modes included in AWFS based on independentradiation mode control increases, the size of the effectivereproduction region increases from a quarter wavelength(one radiation mode) to half a wavelength (four radiationmodes). This supports the previous observations regardingthe importance of the higher order radiation modes to en-large the effective active sound field reproduction region.

3. SOUND FIELD REPRODUCTION FOR SOUNDENVIRONMENT REPRODUCTION

Independent of the chosen spatial sound technology,one of the very promising applications for spatial sound,

Fig. 18. Reproduced (heavy gray lines) and virtual (thin black lines) impulse responses at monitoring sensor array (shown in Fig. 2)for WFS with system in laboratory space.

Fig. 19. Reproduced (heavy gray lines) and virtual (thin blacklines) impulse responses at monitoring sensor array (shown inFig. 2) for AWFS with system in laboratory space. (a) FXLMSalgorithm with 20. (b) Independent radiation mode control.




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including sound field reproduction, is sound environmentreproduction for psychoacoustics or acoustics experi-ments. Sound field reproduction systems or spatial sound

technologies are interesting because they simplify the ex-perimental process and they do not imply in situ subjectivemeasurements. They also simplify the process of ABcomparative listening, and they allow virtual interactiveuse of the system. Sound environment reproduction is usedin the automotive sector for the prediction of sound invirtual automobiles. Examples are using multichannelacoustic simulation and binaural transfer path analysis[49], [50]. Similar work has been conducted in the aero-

space sector to create virtual environments for aircraftcommunity noise [51], [52], as well as for aircraft cabinnoise [53] and cockpits [54], and to evaluate the soundquality of aircraft interior noise using modeling tools [55].Other recent examples of sound field reproduction forsound environment reproduction within the aerospace con-text are given in [34], [35], one of which is concerned withsound reproduction in a helicopter mock-up.

Most of this work has been using auralization and bin-aural reproduction techniques to reproduce acousticstimuli at ear locations [56], [57]. However, these tech-niques are limited to small reproduction zones, the listen-ers ears. This limits the application of these techniques inmock-up situations where it is expected that the auditornavigates in a visual installation. Research on interactivesound field reproduction of aircraft cabin and cockpitnoise proves to be an interesting future research avenue forthe spatial audio community as it includes very specificproblems and constraints, which can lead to significantnew knowledge and technologies. One of the great chal-lenges is to provide and define an integrated solution thatincludes sound field characterization (both subjectivelyand objectively), mock-up characterization, hierarchicalclassification of the sound field elements, and a combina-tion plus an adaptation of several known spatial sound

technologies to fit the sound field element classification(that is, select or create appropriate techniques for differ-ent types of field components such as modal response,diffuse field, localized sources, direct sound fields, aero-

Fig. 20. Normalized energies of error signals at each monitoringmicrophone for two virtual source positions in laboratory space.Position #1x0 [0, 4, 0]; position #2x0 [ 4, 0, 0].

WFS errors; errors of AWFS by FXLMS; errors of AWFSby independent radiation mode control.

Fig. 21. Normalized energies of error signals at each monitoringmicrophone for four virtual source positions in reverberantchamber. Position #1x0 [0, 4, 0]; position #2x0 [ 4, 0,0]; position #3x0 [0, 1.5, 0]; position #4x0 [ 1.19,0.91, 0]. WFS errors; errors of AWFS by FXLMS; errors of AWFS by independent radiation mode control.

Fig. 22. Normalized ELScriterion at monitoring sensors usingharmonic algorithms at 400 Hz after convergence in laboratoryspace using AWFS with QWFS 0. Wave length and somecorresponding fractions are included.




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acoustic noise sources, and stationary versus transientsounds). Moreover, this constitutes an interdisciplinarychallenge, gathering acousticians, psychoacousticians, en-gineers, and vehicle users. As an example, the projectmight include an ecological validation of the proposedreproduction system [58] to validate the proposed soundenvironment reproduction process.

Our future research in sound field reproduction will bededicated to sound environment reproduction in vehicle

mock-ups. This goal, which differs somewhat from theobjectives and ideas presented in this paper on AWFS, isdiscussed briefly in this section.

To highlight the differences, consider, as an example,the extreme experimental AWFS case where active soundfield reproduction was tested in the reverberation chamber.In that situation the objective was to reproduce locally,inside the reproduction source array, a progressive soundfield, like in an anechoic chamber. In that situation thedifficulty arises from the acoustical response differencesbetween the virtual space and the reproduction space.Transforming a part of a reverberant chamber into an an-echoic space using active sound field reproduction is aconsiderable challenge. Although such an experiment wasachieved to evaluate the performance limitations of AWFSin hostile acoustic situations, it is not practically interest-ing. Indeed, a reverberation chamber does not correspondto any common multichannel listening room for spatialsound.

Typically, classical WFS systems are installed in nor-mal listening rooms with an acoustical response more at-tenuated than in the reverberation chamber. This type ofreproduction spaces for spatial sound implies a specific setof technical problems for the chosen technology. The sys-tem must adapt to various a priori unknown reproduction

spaces with more or less reverberant responses and variousdifferences between rooms (as the listening rooms are ex-pected to be well designed for multichannel listening).That being said, for spatial sound application (music re-production, virtual reality display) the method must begeneral enough to tolerate various environments and differ-ent loudspeaker and microphone arrays without a problem.

On that very specific point, sound field reproduction invehicle mock-ups that imitate faithfully the visual aspectsof the original vehicles implies a reduced acoustical dif-ference between the virtual space and the reproductionspace. If the mock-up is a convenient visual and spatialrepresentation of the real vehicle (including geometry, ma-

terials, furniture), it is expected that the acoustical re-sponse of the mock-ups enclosed volume will be nearlysimilar to that of the real vehicle. This poses a very spe-cific set of problems, constraints, and simplifications incomparison with the general aim of progressive soundfield reproduction in rooms as reported herein. In the caseof sound field reproduction in mock-ups, the method canbe very case-specific since it strongly depends on the situ-ation, and the system is only designed for a given vehicle.

Accordingly, it is possible to imagine that a fine andcase-specific sound field component hierarchical classifi-cation according to physical and perceptive sound field

characteristics can be applied to that problem to select themost efficient methods and needed precision or fidelity foreach of the retained sound field or sound environmentcomponents. This is the topic of our future research inspatial sound reproduction for sound environment repro-duction in vehicle mock-ups. We then expect to elaboratea comprehensive and general method for sound field char-acterization and reproduction in mock-ups from our expe-rience with a given vehicle.

Within that context, AWFS might be used to compen-sate for the discrepancies between the real vehicle re-sponse and the mock-up response and for the electroacous-tical system response. Moreover, further, yet very simple,modifications of the AWFS definition can enhance its con-tribution within such a research project. It is possible togeneralize the cost function of Eq. (4) using any a priorisolution. This might be a subject of further research.

4 CONCLUSION

In this paper WFS was first reviewed from a generaldescription. One of the important aspects that was recalledfor WFS is the reproduction error introduced by the roomresponse, which was also illustrated by measurements inthree different spaceshemianechoic chamber, laboratoryspace, and reverberant chamber.

To compensate for reproduction errors caused by thelistening room response, AWFS was introduced as a re-production error minimization combined with a penaltyfor any departure from the WFS solution. This is the majororiginality of AWFS. Note that AWFS is not limited to theconfiguration used in this paper. Testing the cost functionof Eq. (4) for different loudspeaker and error sensor setupscould be the topic of further research on AWFS. Usage of

the WFS solution as a favored solution in AWFS is simplymotivated by the fact that WFS, although potentially suf-fering from room coloration, provides relatively accuratesound localization over 360 degrees for a large listeningregion delimited by a reproduction source array. It wasshown that AWFS can then reduce the reproduction errorswithout being very different from the WFS solution, de-pending on the penalization parameters ( or ifor AWFSbased on independent radiation mode control). Analysis ofAWFS using SVD showed the underlying mechanism ofAWFSindependent radiation mode control. It also in-troduced a unified vision of WFS, Ambisonics, AWFS,and control using plant SVD.

Two algorithms for AWFS were then introducedmodified FXLMS and independent radiation mode controlon the basis of plant decoupling using SVD. One of theadvantages of AWFS based on independent radiationmode control is the ability to fine-tune the convergenceproperties of each radiation mode controller and its con-tribution in the total solution. As the higher order radiationmodes imply higher order spatial derivatives at the errorsensor array, this causes an enlargement of the effectivereproduction region where the reproduction error is re-duced. Further research on AWFS could be dedicated tothe development of more efficient adaptive algorithms.




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Experimental investigations of both WFS and AWFS inseveral rooms showed how AWFS can effectively reduceboth the room response and the electroacoustical systemcoloration. This demonstrates the effectiveness of AWFSto compensate for room responses, the original objectivebehind this project. Moreover it was shown that improvedsound field synthesis in a reverberant environment ispossible.

Experimental comparison between the two algorithms

supports the fact that AWFS based on independent radia-tion mode control enlarges the effective control region byallowing the contribution of the higher order radiationmodes to be more present in the resulting solution. Furtherresearch on the practical implementation and algorithms ofAWFS based on independent radiation mode control (in-cluding plant SVD) could be interesting. More details onAWFS can be found in the first authors thesis [59].

5 ACKNOWLEDGMENT

This work was supported by NSERC (Natural Sciencesand Engineering Research Council of Canada), NATEQ(Fond Quebecois de la Recherche sur la Nature et lesTechnologies), VRQ (Valorisation Recherche Quebec),and the Universite de Sherbrooke. This research has beenconducted in collaboration with CIRMMT (Centre for In-terdisciplinary Research in Music, Media, and Technol-ogy, McGill University). The authors acknowledge thecontribution of Emmanuel Corratge who contributed to theconstruction of the harmonic AWFS system and to theharmonic experiments.

6 REFERENCES

[1] W. B. Snow, Basic Principles of StereophonicSound, J. SMPTE,vol. 61, pp. 567589 (1953).[2] A. J. Berkhout, D. de Vries, and P. Vogel, Acoustic

Control by Wave Field Synthesis, J. Acoust. Soc. Am.,vol. 93, pp. 27642778 (1993).

[3] A. J. Berkhout, M. M. Boone, and D. de Vries,Generation of Sound Fields Using Wave Field Synthe-sisAn Overview, in Proc. Active 95(1995).

[4] P. A. Gauthier, A. Berry, and W. Woszczyk,Sound-Field Reproduction In-Room Using Optimal Con-trol Techniques: Simulations in the Frequency Domain,J. Acoust. Soc. Am.,vol. 117, pp. 662678 (2005).

[5] P. A. Gauthier and A. Berry, Adaptive Wave Field

Synthesis with Independent Radiation Mode Control forActive Sound Field Reproduction: Theory, J. Acoust.Soc. Am.,vol. 119, pp. 27212737 (2006).

[6] J. W. Choi and Y. H. Kim, Manipulation of SoundIntensity within a Selected Region Using MultipleSources, J. Acoust. Soc. Am.,vol. 116, pp. 843852 (2004).

[7] I. Veit and H. Sander, Production of Spatially Lim-ited Diffuse Sound Field in an Anechoic Room, J. Au-dio Eng. Soc.,vol. 35, pp. 138143 (1987 Mar.).

[8] J. Merimaa and V. Pulkki, Spatial Impulse Re-sponse Rendering I: Analysis and Synthesis, J. AudioEng. Soc.,vol. 53, pp. 11151127 (2005 Dec.).

[9] V. Pulkki and J. Merimaa, Spatial Impulse Re-sponse Rendering II: Reproduction of Diffuse Sound andListening Tests, J. Audio Eng. Soc., vol. 54, pp. 320(2006 Jan./Feb.).

[10] C. I. Cheng and G. H. Wakefield, Introduction toHead-Related Transfer Functions (HRTFs): Representa-tions of HRTFs in Time, Frequency, and Space, pre-sented at the 107th Convention of the Audio EngineeringSociety, J. Audio Eng. Soc. (Abstracts), vol. 47, p. 100

(1999 Nov.), preprint 5026.[11] E. N. G. Verheijen, Sound Reproduction by Wave

Field Synthesis, Ph.D. thesis, Delft University of Tech-nology, Delft, The Netherlands (1997).

[12] M. A. Gerzon, Ambisonics in MultichannelBroadcasting and Video, J. Audio Eng. Soc.,vol. 33, pp.859871 (1985 Nov.).

[13] D. G. Malham and A. Myatt, 3-D Sound Spatial-ization Using Ambisonic Techniques, Computer MusicJ.,vol. 19, pp. 5870 (1995).

[14] M. A. Poletti, Three-Dimensional SurroundSound Systems Based on Spherical Harmonics, J. AudioEng. Soc.,vol. 53, pp. 10041025 (2005 Nov.).

[15] R. Nicol and M. Emerit, 3D-Sound Reproductionover an ExtensiveListening Area: A Hybrid MethodDerivedfrom Holophony and Ambisonic, in Proc. AES 16th Int.Conf.(Rovaniemi, Finland, 1999 April 1012), pp. 436453.

[16] S. J. Elliott and P. A. Nelson, Multiple-PointEqualization in Room Using Adaptive Digital Filters, J.Audio Eng. Soc.,vol. 37, pp. 899907 (1989 Nov.).

[17] S. Ise, A Principle of Sound Field Control Basedon the KirchhoffHelmholtz Integral Equation and theTheory of Inverse System, Acta Acustica,vol. 85, pp.7587 (1999).

[18] J. Garas, Adaptive 3D Sound Systems, Tech-

nische Universiteit Eindhoven, Eindhoven, The Nether-lands (1999).[19] M. Bouchard and S. Quednau, Multichannel Re-

cursive-Least-Squares Algorithms and Fast-Transversal-Filter Algorithms for Active Noise Control and SoundReproduction Systems, IEEE Trans. Speech Audio Pro-cess.,vol. 8, pp. 606618 (2000).

[20] A. O. Santillan, Spatially Extended Sound Equal-ization in Rectangular Rooms, J. Acoust. Soc. Am.,vol.110, pp. 19891997 (2001).

[21] E. Corteel, On the Use of Irregularly SpacedLoudspeaker Arrays for Wave Field Synthesis, PotentialImpact on Spatial Aliasing Frequency, in Proc. 9th Int.

Conf. on Digital Audio Effects (DAFX)(2006).[22] S. Spors and R. Rabenstein, Spatial Aliasing Ar-

tifacts Produced by Linear and Circular Loudspeaker Ar-rays Used for Wave Field Synthesis, presented at the120th Convention of the Audio Engineering Society, J.Audio Eng. Soc. (Abstracts),vol. 54, p. 689 (2006 July/Aug.), convention paper 6711.

[23] B. Klehs and T. Sporer, Wave Field Synthesis inthe Real World: Part 1In the Living Room, presented atthe 114th Convention of the Audio Engineering Society,J.Audio Eng. Soc. (Abstracts),vol. 51, p. 408 (2003 May),convention paper 5727.




17/18

[24] T. Sporer and B. Klehs, Wave Field Synthesis inthe Real World: Part 2In the Movie Theater, presentedat the 116th Convention of the Audio Engineering Society,J. Audio Eng. Soc. (Abstracts),vol. 52, p. 796 (2004 July/Aug.), convention paper 6055.

[25] E. Corteel, Equalization in an Extended Area Us-ing Multichannel Inversion and Wave Field Synthesis,J.Audio Eng. Soc.,vol. 54, pp. 11401161 (2006 Dec.).

[26] S. Spors, A. Kuntz, and R. Rabenstein, An Ap-

proach to Listening Room Compensation with Wave FieldSynthesis, presented at the AES 24th International Con-ference, Banff, Canada (2003).

[27] S. Spors, M. Renk, and R. Rabenstein, LimitingEffects of Active Room Compensation Using Wave FieldSynthesis, presented at the 118th Convention of the Au-dio Engineering Society, J. Audio Eng. Soc. (Abstracts),vol. 53, p. 681 (2005 July/Aug.), convention paper 6400.

[28] T. Betlehem and T. S. Abhayapala, Theory andDesign of Sound Field Reproduction in ReverberantRooms, J. Acoust. Soc. Am.,vol. 117, pp. 21002111(2005).

[29] L. Fuster, J. J. Lopez, A. Gonzalez, and P. D. Zuc-carello, Room Compensation Using Multichannel InverseFilters for Wavefield Synthesis Systems, presented at the118th Convention of the Audio Engineering Society, J.Audio Eng. Soc. (Abstracts),vol. 53, p. 686 (2005 July/Aug.), convention paper 6401.

[30] D. de Vries, A. J. Reijnen, and M. A. Schonewille,The Wave-Field Synthesis Concept Applied to Genera-tion of Reflections and Reverberation, presented at the96th Convention of the Audio Engineering Society,J. Au-dio Eng. Soc. (Abstracts), vol. 42, p. 396 (1994 May),preprint 3813.

[31] D. de Vries, E. W. Start, and V. G. Valstar, The

Wave-Field Synthesis Concept Applied to Sound Rein-forcement: Restrictions and Solutions, presented at the96th Convention of the Audio Engineering Society,J. Au-dio Eng. Soc. (Abstracts), vol. 42, p. 396 (1994 May),preprint 3812.

[32] H. Buchner, S. Spors, and W. Kellermann, Full-Duplex Systems for Sound Field Recording and Auraliza-tion Based on Wave Field Synthesis, presented at the116th Convention of the Audio Engineering Society, J.Audio Eng. Soc. (Abstracts),vol. 52, p. 812 (2004 July/Aug.), convention paper 6120.

[33] T. Bravo and S. J. Elliott, Variability of Low Fre-quency Sound Transmission Measurements, J. Acoust.

Soc. Am.,vol. 115, pp. 29862997 (2004).[34] N. Epain, E. Friot, and G. Rabau, Indoor Sonic

Boom Reproduction Using ANC, in Proc. Active 2004(2004).

[35] M. Keller, A. Roure, and F. Marrot, AcousticField Reproduction for Psychoacoustic Experiments: Ap-plication to Aircraft Interior Noise, Proc. Active 2006(2006).

[36] E. W. Stewart, D. de Vries, and A. J. Berkhout,Wave Field Synthesis Operators for Bent Line Arrays ina 3D Space,Acustica/Acta Acustica,vol. 85, pp. 883892(1999).

[37] E. G. Williams, Fourier AcousticsSound Radia-tion and Nearfield Acoustical Holography (AcademicPress, London, 1999).

[38] A. Asano and D. C. Swanson, Sound Equalizationin Enclosures Using Modal Reconstruction, J. Acoust.Soc. Am.,vol. 98, pp. 20622069 (2002).

[39] A. D. Pierce, Acoustics: An Introduction to ItsPhysical Principles and Applications(Acoustical Societyof America, Woodbury, NY, 1991).

[40] C. Hansen, Rank-Deficient and Discrete Ill-PosedProblems(SIAM, Philadelphia, PA, 1998).

[41] P. A. Nelson and S. J. Elliott, Active Control ofSound(Academic Press, London, 1992).

[42] G. H. Golub and C. F. van Loan, Matrix Compu-tations(Johns Hopkins University Press, Baltimore, MD,1996).

[43] P. Lancaster and M. Tismenetsky, The Theory ofMatrices(Academic Press, Orlando, FL, 1985).

[44] S. Elliott, Signal Processing for Active Control(Academic Press, London, 2001).

[45] M. R. Bai and S. J. Elliott, Preconditioning Mul-tichannel Adaptive Filtering Algorithms Using EVD- andSVD-Based Signal Prewhitening and System Decou-pling,J. Sound Vib.,vol. 270, pp. 639655 (2004).

[46] S. J. Elliott, Optimal Controllers and AdaptiveControllers for Multichannel Feedforward Control of Sto-chastic Disturbances, IEEE Trans. Signal Process.,vol.48, pp. 10531060 (2000).

[47] R. H. Cabell and C. R. Fuller, A Principal Com-ponent Algorithm for Feedforward Active Noise and Vi-bration Control, J. Sound Vib.,vol. 227, pp. 159181(1999).

[48] R. H. Cabell, D. Palumbo, and J. Vipperman, APrincipal Component Feedforward Algorithm for Active

Noise Control: Flight Test Results, IEEE Trans. Contr.Sys. Technol.,vol. 9, pp. 7683 (2001).

[49] J. Perisse, F. Magand, M. Henry, S. Chouteau, andN. Leclerc, SD-Lab: An Interactive Sound Design Simu-lator for Vehicle Interior Noise, Acta Acustica,vol. 89,suppl., p. S90 (2003).

[50] K. Genuit and W. R. Bray, Prediction of Soundand Vibration in a Virtual Automobile,J. Sound Vib.,vol.36, no. 7, pp. 1219 (2002).

[51] J. Chevret, R. Maier, J. M. Nogues, J. Perisse, andC. Thirard, Towards Virtual Sound for Aircraft Simula-tion,Acoust. Bull.,vol. 31, no 1, pp. 2527 (2006).

[52] S. A. Rizzi and B. M. Sullivan, Synthesis of Vir-

tual Environments for Aircraft Community Noise Im-pact Studies, in Collection of Technical Papers11thAIAA/CEAS Aeroacoustics Conf.,vol. 4, pp. 22912306(2005).

[53] R. Weber, I. Baumann, N. Freese, R. Kruse, and V.Mellert, Psychoacoustic Analysis of Sound in the Cabinof Passenger Aircrafts, Acta Acustica,vol. 89, suppl., p.S10 (2003).

[54] Y. He, A. Djordjevich, and L. Fuyuan, SoundRendering and Its Application in Virtual Cockpit, inProc. Int. Conf. on Signal Processing,vol. 2, pp. 14121415 (1998).




18/18

[55] A. Vecchio, T. Polito, K. Janssens, and H. van derAuwearaer, Real-Time Sound Quality Evaluation of Air-craft Interior Noise, Acta Acustica,vol. 89, suppl., p. S5(2003).

[56] M. Kleiner, B. I. Dalenback, and P. Svensson, Au-ralizationAn Overview,J. Audio Eng. Soc.,vol. 41, pp.861875 (1993 Nov.).

[57] L. Savioja, J. Huopaniemi, T. Lokki, and R.Vaanenen, Creating Interactive Virtual Acoustic Envi-

ronments,J. Audio Eng. Soc.,vol. 47, pp. 675705 (1999Sept.).

[58] C. Guastavino, B. F. G. Katz, J. D. Polack, D. J.Levitin, and D. Dubois, Ecological Validity of Sound-scape Reproduction, Acta Acustica/Acustica,vol. 91, pp.333341 (2005).

[59] P. A. Gauthier, Synthese adaptative de champssonores, Ph.D. thesis, Universite de Sherbrooke, Sher-brooke, Quebec, Canada (2007).

THE AUTHORS

P.-A. Gauthier A. Berry

Phillipe-Aubert Gauthier was born in 1976. From theage of 14, for nearly 8 years, he played electric bass guitarwhile learning jazz, improvisation, slapping, tapping, andso on. He received a B.Ing. degree in mechanical engi-neering from Universite Laval, Quebec City, Canada, in2000 and an M.Sc. degree in 2003. In 2007 he received aPh.D. degree from Sherbrooke University, Quebec,Canada. His thesis was dedicated to adaptive wave fieldsynthesis. In 2006 he received the Leonard de Vinci medalfrom the Engineering Faculty of Sherbrooke University.He is interested in spatial sound, multichannel sound re-production, audio signal processing, room acoustics, loud-speaker and microphone arrays, spatial hearing, psycho-acoustics, and active control. At present he is involved asa postdoctoral student in an industrial research project(GAUS, CIRMMT) dedicated to sound environmentreproduction.

Dr. Gauthier is also an active sound artist mostly in-volved in electroacoustic music, electronic music, genera-tive music, sound installation, performance, and writing.Several of his artistic projects were collaborations withTanya St-Pierre. He received a grant from SherbrookeCity in 2006 for the realization of a sound installation forthe Pure-Data Convention 2007 in Montreal, Canada. His

artistic production has been presented in Canada, theUnited States, and Europe, including at the Fine-Art Mu-seum of Sherbrooke and at the Spark Festival (WeismanArt Museum, Minneapolis). Since the beginning of hisgraduate studies in sound and vibration, his artistic and

scientific activities have been linked through a multidis-ciplinary approach.

Alain Berry graduated in aerospace engineering fromENSICA, France, in 1985. He received M.Sc. and Ph.D.degrees in acoustics from the Universite de Sherbrooke,Que., Canada, in 1988 and 1991, respectively. After a post-doctoral fellowship at INSA-Lyon, France, he was appointedprofessor in the Department of Mechanical Engineering,Universite de Sherbrooke, in 1992. He carries out his re-search within GAUS (Groupe dAcoustique de lUniversitede Sherbrooke), a research group focused on engineeringacoustics and vibrations. His research interests include struc-tural acoustics, active noise and vibration control, vibrationand acoustic transducers, and source localization techniques.

Dr. Berry is the author of over 50 peer-reviewed pub-lications in scientific journals. In recent years he has beeninvolved in a number of multi-institutional research projectson acoustic comfort issues, mainly in the automotive andaerospace sectors. Since 2007 he has been holding a seniorindustrial chair in aviation acoustics in collaboration withBombardier Aerospace, Pratt & Whitney Canada, and BellHelicopters. He is an associate member of CIRMMT

(Centre for Interdisciplinary Research in Music Media andTechnology) centered at McGill University in Montreal.Since 2002 he has been collaborating with CIRMMT re-searchers on sound field reproduction techniques and thedevelopment of novel loudspeaker concepts.


2007 adaptive wave field synthesis for sound field reproduction: theory, experiments, and future...

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