2004 sound reproduction using active control techniques: simulations in the frequency domain

8/11/2019 2004 Sound Reproduction Using Active Control Techniques: Simulations in the Frequency Domain

http://slidepdf.com/reader/full/2004-sound-reproduction-using-active-control-techniques-simulations-in-the 1/4

Sound Reproduction Using Active Control Techniques: Simulations in the

Frequency Domain

Philippe-Aubert Gauthier, Alain Berry

GAUS, Department of Mechanical Engineering

Universite de Sherbrooke, Sherbrooke

[email protected]

Wieslaw Woszczyk

CIRMMT, Faculty of Music

McGill University, Montreal

Abstract

This paper describes the simulations and results obtained

when applying active control to progressive sound field

reproduction over a ”large” area using multiple monopole

loudspeakers. The model is limited to the simulation of

the acoustical output of the prescribed loudspeaker array

in a simple room, and is based on achieving an optimal

control in the frequency domain. This rather simple ap-

proach is chosen for this first feasibility study concerning

a limited number of possible configurations of sensing

microphones and loudspeakers. Other issues of interest

concern the comparison with Wave Field Synthesis, the

control mechanisms and transducer configurations. As its

demonstrated, in-room reproduction of sound field using

active control can be achieved with a residual normalized

error below 2 percent while open-loop WFS gives morethan 100 percent of error in the same situation. Usage of

active control technique suggests the possibility to auto-

matically overcome the room’s natural dynamics.

1. Introduction

This paper investigates the possibilities for sound field re-

production using active control techniques. Major goals

of this work are feasibility studies with questions con-

cerning: 1) Effect of a reflective acoustic environment on

objective reproduction quality and 2) comparison of ac-

tive control technique with Wave Field Synthesis (WFS).This work is more connected to wave field simulation

than to perceptual simulation. Although the ultimate goal

of sound field reproduction is an audio application, we

have to be aware that perfect reproduction of sound field

does not necessarily leads to perfect auditory impression

of reproduction since multimodal sensory influences and

cognitive mechanisms are strongly influencing sound lo-

calization [1]. In spite of that, we assume that if not per-

fect, at least optimal sound field reproduction will achieve

desired auditory impression in reproduction if the audio

stimuli are not conflicting with visual indications or other

sensory experiences.

2. Recent advances in sound reproduction

Spatial sound reproduction has been a vivid research do-

main involving artists, engineers and scientists since the

beginning of the century and even sooner [2]. With the

relatively recent arrival of digital representation and mul-

tiple channel of audio, new possibilities of sound field

reproduction have been investigated. Commonly cited

examples are: Binaural techniques [1], ambisonic sound

[2], Wave Field Synthesis (WFS) [3], Stereo-Dipole [4]

and active equalization [4–6]. In a broad sense, most

of those techniques try to improve two aspects of the

consumer level reproduction technology, with variable

weighting and methods. 1) Achieve a large listening area

for a given audience. 2) Create an appropriate 3-D (or

2-D) auditory scene. Techniques mentioned above are

distinguished from simple multichannel loudspeaker sys-

tems where the mixing engineer is entirely responsibleof the channels’ content, like for the well-known 5.1 or

10.2 surround systems [2]. It should be noted that WFS

systems use synthesis operators (based on Kirchhoff-

Helmholtz theorem [3, 7]) to ”link” virtual monophonic

sources (radiating plane or spherical waves) to a given

loudspeaker array. WFS operates with an open-loop ar-

chitecture and implies fundamental assumptions: 1) Vir-

tual free-field space and 2) free-field reproduction space.

Room compensation is only considered, in specific appli-

cations [8], as a post-synthesis operation.

3. Review of the theoretical model

The reproduction system can be characterized by L sim-

ple monopole sources and M error sensors in a rectan-

gular room where we assume a uniformly distributed and

locally reactive acoustic admittance for the room’s sur-

faces. The current model is more effective for low fre-

quencies, where the monopole assumption may be more

firmly linked with closed-box loudspeaker cabinets. The

upper frequency limit is set to 400Hz for computation

efficiency. We still, however, cover a representative fre-

quency range (above and below the Schroeder frequency

[7]) for the given room where simple and harmonic wave

We4.D.1 III - 2149



reproductions are considered.

In a room, the reproduced pressure is related to

monopoles’ source strength by a Green’s function expan-

sion over the room’s damped modes (see Morse and In-

gard [9] who suggest the used first-order approximation

assuming uniformly distributed low specific acoustic ad-

mittance ratio over room’s walls). The following simu-

lations are performed using such model including 6137room’s modes in the Green’s function. This has shown

the total acoustical potential energy convergence below

400Hz. Once the reproduced pressure is determined in

the room’s volume, one can apply optimal control formu-

lation which gives an Hermitian quadratic function of the

source strength [7]. This function is defined as J M =eH e + γ q H q , where q is the complex source strength col-

umn vector, γ the regularization parameter and e the error

vector at the error sensors, namely pressure sensors. H superscript denotes the Hermitian transpose. The error

vector is defined by e(x(m)) = p(

im)(x(

m)) − Z(

m) q,,

where p(im) is the target field evaluated at the total M sensors’ positions , Z(m) a transfer impedance matrix and

q , the reproduction source strength. Using Tikhonov reg-

ularization, we include some frequency independent reg-

ularization in the inverse problem [10] using γ which is

fixed at 50 since it seems to provide, following numer-

ical experiments, a good compromise between optimal

source strength minimization and error reduction. When

M > L, J M shows a unique minimum defined by the

optimal source strength complex vector

q opt = Z(m)H Z(m) + γ I

−1

Z(m)H p(im)(x(m)), (1)

where I is the identity matrix. We now define the

residual normalized quadratic error E LS which is sim-

ply the minimized cost function (excluding regulariza-

tion) divided by the cost function evaluated with q = 0and finally the l source’s acoustical power output Πl =

(1/2)Re

p(x(l)

l )H q l

.

For WFS simulation, general non-focusing synthe-

sis operators are used with straight reference line across

room’s center [3]. Some adjustments have been applied

to match the time dependence convention and monopole

source strength definition.

4. Simulation results

The system configuration is depicted in Fig. 1. The

simulation system includes 50 sources and 81 sensors

which cover a 1m2 area. Room’s dimensions have been

defined in accordance with the Audio Engineering So-

ciety and German Surround Sound Forum’s recommen-

dation for the optimum size of multichannel monitor

rooms [2, 11]. For the given volume, 139m3 (precisely

7.5 × 6.4 × 2.8956; sources and sensors height: 1.2m),

a nominal reverberation time of 0.28s is suggested [2].

Using the Eyring-Norris reverberation model for diffuse

Figure 1: Configuration (square: sources, asterisk: sen-

sors) and real part of the target wave field at 220Hz.

field [12], we find an associated absorption coefficient

which is transformed to an equivalent specific conduc-

tance ratio [12]. In this case, we set the surface-specific

conductance ratio, β , to 0.0651, which is frequency inde-pendent and uniform on room’s surfaces.

We first evaluate the reflective environment’s effect

on optimal reproduction at the sensor array position in

comparison with WFS. Fig. 2 introduces the compar-

ison, for such a configuration, between optimal control

and WFS. E LS for optimal control in room is clearly be-

low 0.02. Reduction of the error over the considered fre-

quency range is also evident. By comparison, WFS pro-

duces an E LS higher than one for the same frequency

range in the simulated room. Recalling that an E LS value of one corresponds to an error as important as per-

fect silence in the reproduction space, we may expect

serious difference between target wave field and repro-

duced wave field by WFS. (Note that for this configu-

ration of sources, WFS aliasing frequency is just below

400Hz [3].) This idea is presented in Fig. 1 to 7 where

real and imaginary parts of the pressure have been in-

troduced. The optimal control system seems to properly

recreate the wave front at the position of sensor-array in

the room. Moreover, Fig. 8 to 10 clearly show power ab-

sorption as a beneficial operating mechanism responsible

for providing optimal reproduction.

Another configuration is introduced in Fig. 11 for

free-field condition. This interesting setup may be con-

ceptually linked with WFS since the adjustment of pres-sure and pressure gradient produces a convenient repro-

duced wave field inside the surrounding sensor array, as

we can expect from Kirchhoff-Helmhotlz theorem. Fu-

ture work should be devoted to this type of sensor arrays.

5. Discussion

Loudspeakers can be relatively inexpensive allowing

their liberal use in multiple-loudspeaker arrays. On the

other hand, a microphone array (sensor-array), such as

the one introduced in Fig. 1 and 11, gives no practical

III - 2150



100 200 300 40010

−3

10−2

10−1

100

101

L S

20 100 200 300 4000

2

4

6x 10

−4

| q o p

t |

Freq. [Hz]

← E

L S

= 0 . 5

Dashed lines : WFS

Figure 2: E LS (on left) and | q opt| =

q H optq opt (on right)

for spherical wave reproduction (see Fig. 1). Solid lines:

Optimal control. Dashed lines: WFS.

Figure 3: Imaginary part of the target field at 220Hz.

advantages to an audience and its presence may be even

questionable in comparison with multiple channel open-

loop systems such as WFS. Strong benefits of the sen-

sor array and active control are related to closed-loop and

adaptive architectures for automated room spatial equal-

ization, as we have seen. From an active control perspec-

tive, the systems which include a huge quantity of chan-

nels may become a computational burden. On the other

hand, depending on controller architecture and adapta-

tion scheme, reduction in adaptive computation time can

be achieved. We still use the physical model for inves-

tigation purposes, because it can give good indications

about the possibilities for creating a simple wave front in

a given horizontal region. From the practical aspects of

audio systems and sound control, it is more than evident

that a reduced quantity of sensors should be considered

in subsequent simulations (Fig. 11 can be seen as such

solution). Any reduction in sensor load would provide a

practically more viable solution.

6. Conclusions

In view of the presented here simulations, it may be con-

cluded that active control techniques can be applied to

sound field reproduction with promising results achieved

in rooms. This technique seems to provide more accu-

rate sound field reproduction than a standard open-loop

WFS system operating in a room. Even if the model

used here is oversimplifying the real situations, reveal-

ing conclusions can be derived from these simulations.

Further work should be devoted to simulations with vari-

ous practical arrays, larger listening areas, free-field situ-

ations and control mechanisms.

7. Acknowledgments

This work has been supported by NSERC, NATEQ, VRQ

and Universite de Sherbrooke.

8. References

[1] Blauert, J., Spatial Hearing: The Psychophysics of

Human Sound Localization, MIT Press, Cambridge,

1999.

[2] Rumsey, F., Spatial Audio, Focal Press, Oxford,

2001.

[3] Verheijen, E.N.G., Sound Reproduction by Wave

Field Synthesis, Ph.D. thesis, Delft University of

Technology, Delft, 1997.

[4] Nelson, P.A., ”Active Control for Virtual Acous-

tics”, Proc. of Active 2002, 2002, p. 67-89.

[5] Kirkeby, O. and Nelson, P.A., ”Reproduction of

Plane Wave Sound Fields”, J. Acoust. Soc. Amer.,

Vol. 94, No. 5, 1993, p. 2992-3000.

[6] Garas, J., Adaptive 3D Sound Systems, Technische

Universiteit Eindhoven, Eindhoven, 1999.

[7] Nelson, P.A. and Elliott, S.J., Active Control of

Sound , Academic Press, London, 1992.

[8] Spors, S., Kuntz, A. and Rabenstein, R., ”An

Approach to Listening Room Compensation with

Wave Field Synthesis”, Proc. of the AES 24th In-

ternational Conference, 2003, p. 70-82.

[9] Morse, P.M. and Ingard, K.U., Theoretical Acous-

tics, McGraw-Hill, New York, 1968.

[10] Nelson, P.A., ”A Review of Some Inverse Problems

in Acoustics”, International Journal of Acoustics

and Vibration, Vol. 6, No. 3, 2001, p. 118-134.

[11] AES Technical Council, AESTD1001.0.01-05,

Multichannel surround sound systems and opera-

tions, AES, New York, 2001.

[12] Kinsler, L.E., Frey, A.R., Coppens, A.B. and

Sanders, J.V., Fundamentals of Acoustics, John Wi-

ley and Sons, New York, 2000.

III - 2151



Figure 4: Real part of the reproduced wave field using

optimal control at 220Hz.

Figure 5: Imaginary part of the reproduced wave field

using optimal control at 220Hz.

Figure 6: Real part of the reproduced wave field at

220Hz using WFS.

Figure 7: Imaginary part of the reproduced wave field at

220Hz using WFS.

2.5

5

7.5

0

2.5

5

0

5

10

x 10−7

x1 [m]

x2 [m]

P o w e r

o u t p u t

[ W

]

Positive

Negative

Figure 8: Power output for optimal control while repro-

ducing a spherical wave at 220Hz.

2.55

7.5

0

2

4

6

0

0.5

1

x 10−6

P o

w e r

o u t p u t

[ W

]

Figure 9: Power output while reproducing a spherical

wave at 220Hz , with WFS. Diamond markers denote

sources that are turned off.

2.5

5

7.5

0

2.5

5

0

2

4

x 10−7

x1 [m]x

2 [m]

P o w e r

o u

t p u t

[ W

]

Positive

Negative

Figure 10: Power output for optimal control while repro-

ducing a spherical wave at 70.5Hz.

Figure 11: Real part of a reproduced wave field at 220Hzin free field with optimal control (target wave field defined

by a spherical source in (-1,2.8,1.2)).

III - 2152

2004 sound reproduction using active control techniques: simulations in the frequency domain

Documents