2007 Objective Evaluation of Room Effects on Wave Field Synthesis

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ACTA ACUSTICA UNITED WITH ACUSTICAVol. 93 (2007) 824 836

Objective Evaluation of Room Effects on Wave

Field Synthesis

Philippe-Aubert Gauthier, Alain Berry

Groupe dAcoustique de lUniversit de Sherbrooke, Universit de Sherbrooke, 2500 boul. de lUniversit, Sher-

brooke, Qubec, Canada, J1K 2R1. [email protected]

Summary

This technical paper reports the objective evaluation of sound field reproduction using wave field synthesis (WFS)

in a listening room. WFS is an open-loop technology for spatial audio and it assumes a free field as the repro-

duction space. The main objective of this experiment was to understand how much, and how, WFS performance

is reduced in-room situation in comparison with free-field situation. These undesirable eff

ects are characterizedby the coloration of the frequency response functions (FRFs) and the presence of echoes and reverberation in

the reproduced impulse responses of the WFS system. This paper only addresses the objective performance (fre-

quency response functions and wavefront shape; not the perceptual appreciation) of sound field reproduction. On

that matter, this technical paper thus validates and complements other objective evaluations previously published

and performed with various WFS systems in different listening rooms. A comparative review of spatial aliasing

frequency definitions is also discussed in the context of sound field reproduction.

PACS no. 43.38.Md, 43.60.Tj, 43.38.Ar

1. Introduction

Sound field reproduction has applications in multiple do-

mains. The most commonly known is spatial audio where

one is interested by the artificial reproduction of the natu-

ral spatial character of hearing. In this context, sound field

reproduction corresponds to a physical approach which

can be divided in two subclasses: interior and exterior

problems of sound field reproduction. The wave field syn-

thesis (WFS) system considered in this applied paper em-

phasizes on the interior problem, i.e. reproducing a sound

field over an extended region surrounded by acoustical

sources. The exterior problem is defined by sound field

reproduction around acoustical sources. For more details

on this functional classification or spatial audio, see refer-

ences [1, 2, 3].

Sound field reproduction also finds applications in ac-

tive control of noise (canceling a sound field is equivalent

to reproducing it with a sign difference), panel transmis-

sion loss measurements [4] (low-frequency diffuse field

reproduction in reverberant chambers), electroacoustical

device measurements [5] (diffuse sound field reproduction

in anechoic spaces), experimental acoustics and psychoa-coustics [2, 6] and potentially more.

Wave field synthesis (WFS) is a specific method of

sound field reproduction which has been introduced for

audio applications [7, 8, 9, 10, 11, 12, 13]. One of the

Received 16 February 2006, revised 15 November 2006,

accepted 13 June 2007.

WFS assumptions is that the reproduction space is ane-

choic [11]. In a practical utilization of WFS, the listening

room, or the reproduction space, is not anechoic and there-

fore reduces, in objective terms, the quality of the repro-

duced sound field [2, 14, 15, 16, 17].

This paper reports the measurements of various sound

fields reproduced by a WFS system in a studio. This in-

cludes frequency responses, room effects, direct wave-

fronts and global room effects. The main objective was to

understand how, and by which dominating effects, WFS

reproduced sound fields differ from the virtual sound fields

which have to be reproduced. This technical paper thus

validates and complements other WFS evaluations previ-

ously published [14, 15, 16, 18] and performed with differ-

ent WFS systems in various listening rooms. The results

presented herein can thus serve as a basis for compari-

son and to enlarge the available examples of in-situ WFS

objective evaluation. As originally pointed by Boone and

Verheijen [17], objective measurements (like multi-trace

impulse responses used in this paper) for the evaluation

of reproduced sound field allow for later comparison be-

tween different setups and published experimental reports.

The work reported in this technical paper is motivated by apreliminary study on sound field reproduction using adap-

tive control and WFS [2, 19, 20] to compensate for the

undesirable room effects on WFS.

A similar evaluation of WFS systems has been reported

by Kutschbach [18] but his work focused on the definition

of a measurement method for the verification of spatial

sound systems. His method was proposed to circumvent

two potential drawbacks: (1) the less precise sound field

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Gauthier, Berry: Room effects on wave field synthesis ACTA ACUSTICA UNITED WITH ACUSTICAVol. 93 (2007)

evaluation based on wave field extrapolation techniques

(from a linear or circular array of microphones) and (2)

the time-consuming process of measurement over an en-

tire 2D microphone grid (which can include over than one

hundred measurement points) in the reproduction space.

Kutschbach performed measurements over an entire 2D

grid using 24 moving microphones using a 2-axis linearstepper motor system which created powerful analysis and

visualization tools. In this paper, a more conventional and

simpler method was used by utilizing a fixed linear micro-

phone array without field extrapolation [17].

This work differs from other published WFS evaluations

regarding the WFS system, the listening room and the re-

search intentions. In 1997, Start [14] focused on the objec-

tive and subjective evaluations of WFS systems for sound

enhancement (or sound reinforcement) in concert halls.

The tested systems were typically front-oriented (linear

or convexly bent arrays) and placed on a stage. In agree-ment with the sound reinforcement intention, the physical

evaluation was based on the comparison between repro-

duced sound field and the measured virtual sound field ob-

tained when a real acoustic source was placed at the vir-

tual source position, on stage. These reported experiments

showed that WFS is able to reproduce the virtual source

direct sound field in a large space such as concert halls

and in an anechoic chamber. Boone and Verheijen [17] re-

ported objective WFS evaluation methods for a rectangular

WFS system surrounding the listening region. The multi-

trace impulse responses showed that the virtual source di-rect sound field is effectively reproduced by WFS. In 2003,

Klehs and Sporer [15] published solely subjective evalu-

ations of a modified WFS system in a living room. The

modifications were evoked for practical reasons. First, the

loudspeaker array did not encircle the listening region en-

tirely since large gaps were needed for two doors and the

loudspeaker were in proximity of the walls. Also, since

the number of channels was limited, the independent loud-

speaker spacing was different on the front (0.17 m spac-

ing) compared to the back and to the sides (0.17 m, but

two adjacent speakers reproduced the same signal). The

experiments took place in a small room with a floor surface

of approximately 25.4 m2. Various parameters were tested

and evaluated by the researchers, including the special and

a practical configuration, loudspeaker spacing, etc. From

these subjective evaluations, it was shown that WFS can

tolerate some practical compromises without considerable

sound quality degradation. Similar experiments were later

conducted in a movie theater [16] where the listening room

was larger (with a floor surface of approximately 96 m2)

and the tested WFS system was made of a frontal linear

loudspeaker array (roughly 6.6 m wide with a loudspeaker

spacing of 0.17 m). In agreement with previous evalua-

tions [15], it was shown that WFS can tolerate practical ap-

proximations without significant sound quality reductions.

In this objective evaluation of room effect on WFS, the

WFS system completely encircles the listening area with

a uniform loudspeaker spacing and the listening room,

which is a small studio, has a floor surface of roughly

31.5 m2. This setup is comparable to the living room used

in Klehs subjective evaluations [15]. The objective eval-

uation presented herein complements the existing WFS

evaluations. As it will be shown, WFS effectively repro-

duces the direct sound field of the virtual source, but the

room effects causes serious colorations and alteration on

the reproduced wave field. Several subjective experimentswith this WFS system in the same listening room were

reported by Usher et al. [21]. The experiments discussed

in this technical paper thus complete Ushers experiments

with an objective perspective.

Room effect, as evaluated in this paper, is an impor-

tant issue for the practical development and the future

of WFS: it contributes to the understanding that listen-

ing rooms have noticeable effects on objective physical

parameters and on subjective perception (sound quality,

sound localization, etc.) for audio commercial WFS ap-

plications. It is then possible to determine whether ornot WFS needs specifically acoustically designed listen-

ing rooms. In recent research activities on WFS, room

effect is also relevant in relation to room compensation

[2, 20, 22, 23, 24, 25, 26, 27, 28]. The usefulness of ac-

tive room compensation in comparison with passive de-

sign methods of WFS listening rooms is currently being

debated, and is still unresolved.

A general review of WFS is presented in section 2, the

experimental setup and procedure are described in sections

3 and 4 while the results are reported in section 5. A dis-

cussion summarizes the important observations on WFS

physical performance in room and adresses potential mod-

ifications of WFS to improve sound field reproduction.

2. Wave Field Synthesis (WFS)

WFS has been introduced by Berkhout in the late 80s

[7, 8, 9, 10, 11, 12]. The underlying theory comes from

the Huygens construction principle which states that a

given wave field, produced by a primary source, at a given

time, can be reconstructed, at a later time, by replac-ing a given wavefront by a continuous set of secondary

sources on the initial wavefront. The general WFS concept

is depicted in Figure 1. This reconstruction idea is math-

ematically expressed and generalized by the Kirchhoff-

Helmholtz integral from which the basics of WFS are de-

rived [7, 8, 9, 10, 11, 12]. Practically speaking, WFS uses

this integral formulation along with simplifications to de-

fine inputs (as a function of both reproduction sources cor-

responding to secondary sources, and virtual source, cor-

responding to primary source, positions) to a loudspeaker

array. The virtual wave field is defined by virtual sources(spherical waves, plane waves, etc.) in a free-field virtual

space (see Figure 4). In its common form, WFS is an open-

loop system which is theoretically valid for a free-field re-

production space. Such an assumption is not applicable

to common listening environments such as studios, the-

aters or living rooms including a real audio system. Real

applications typically include reproduction errors caused

by the system limitations (coloration, finite size, etc.) [29]

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ACTA ACUSTICA UNITED WITH ACUSTICA Gauthier, Berry: Room effects on wave field synthesisVol. 93 (2007)

Figure 1. Symbol definition for the derivation of the WFS opera-

tors. The virtual source is located at xo. The reproduction sourcel is located at xl. x

(ref) describes points which belong to the

reference line. x describes any field or measurement point. L

is the reproduction source line, the virtual source is on the left

of the source line and the reproduction space is on the right of

the source line. All sources and sensors are located on the x1x2plane.

and by the reproduction room [24]. However, from sub-

jective and perceptive arguments, this free-field simplifica-

tion can be partly justified [30]. This paper focuses on the

physical measurements of the reproduced sound field in areal reproduction space using a real system. As noted ear-

lier, objective (physically valid) reproduction and evalua-

tion are still fundamentally important to understand how to

increase the physical WFS reproduction quality in rooms

[2, 20].

2.1. Derivation of the WFS operators

A more detailed and technical description will be intro-

duced for the WFS definition seen in Figure 1. The pri-

mary source is located at xo, the secondary source (acting

like a monopole) lis at xl while the measurement micro-phones are located at x. The virtual wave field is defined

as a primary monopole pressure field in the frequency do-

main:p(x, ) =A()ejk|xxo|/|x xo| where[rad/s] isthe radial frequency,A() [P a m] is the monopole ampli-

tude andk [rad/m] is the wave number [31]. Note that the

time convention is ejt for the complex variables. TheWFS operators, expressed in terms of secondary source

monopole amplitudes, are then defined as follows [11]

QW F S(xl, ) =

A()jjk2

cos (1)

ejkro

ro

r(ref)/(r(ref) + ro)l,

where [rad] is the angle between the primary source

and the normal to the reproduction line at the secondary

source position xl, ro = |xo xl| is the distance [m]between the primary source (in xo) and the secondary

source (in xl) and r(ref) = |x(ref) xl| is the distance

[m] between the secondary source and the reference line

along the linero. In equation (1), l [m] is the secondary

source (loudspeaker) separation (l =|xlxl+1|). Equa-tion (1) expresses the WFS monopole source amplitude

QW F S(xl, ) to reproduce p(x, ) as defined earlier. In

this paper, capital letters are typically used for monopole

source amplitude (A and Q). For a given primary sourceposition, equation (1) gives the monopole amplitudes for

all the secondary sources. However, not all the secondary

source needs to be active. In other words the secondary

sourcel is active (QW F S(xl, )=0) if||< 90 degrees.The reproduced sound pressure in space is denoted

p(rep) (x, ). For a total ofL secondary sources in free field,

one finds that

p(rep) (x, ) =

Ll=1

QW F S(xl, )ejkr /r, (2)

where ejkr

/r represents the acoustical radiation of a sec-ondary source andr is the distance between the secondary

source xl and the field point xso thatr =|x xl|. As onemight expect, the sound radiation of secondary sources

will in reality be affected by factors such as loudspeaker

response, as well as directivity and room response. These

effects are the focus of this paper.

Note that the interest is in the reproduced impulse re-

sponses (IR) and frequency response functions (FRF)

from the primary source to the measurement points:

h(x, ) =p(rep)

(x, )/A().

The theoretical reproduced IRs and FRFs units are then

[Pa/Pam] [1/m]. Theoretically reproduced FRFs andIRs in free field were compared to measured FRFs and IRs

in room to separate the room effect from classical WFS

approximations.

2.2. Reference line

As shown in Figure 1, a reference line is needed for the

definition of the WFS operators in equation (1). The refer-

ence line corresponds to the positions where the reproduc-tion error is zero (for theoretical free-field situation), i.e.

where there is no magnitude and phase errors in the repro-

duced sound field. Outside the reference line, magnitude

errors exist but phase errors are still zero. Several proposi-

tions for the choice of the reference line have been made

[11]: linear, circular or optimal [32]. Typically, the refer-

ence line passes through the secondary source array center.

The secondary source array center is defined by the axis

origin (see Figures 1 and 4). The linear reference line is

perpendicular to the line between the primary source and

the secondary source array center. An example of linearreference line is shown in Figure 4. For the WFS simula-

tions used as a basis for comparison, a linear reference line

was assumed.

2.3. Spatial sampling and spatial aliasing

Spatial sampling of a continuous source distribution, as

introduced in equation (1), by a set of discrete secondary

sources can create spatial aliasing if the spatial sampling

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Figure 2. Simulation of plane wave reproduction by WFS in free

field at 900 Hz (left) and 1100 Hz (right). The secondary sources

are marked with white dots. The listening region is delineated by

the secondary source array and the white lines. The reproduced

sound fields are divided in two portions: sound fields from the

horizontal portion of the secondary source array [shown in (a)and (d)] and sound fields from the oblique portion of the sec-

ondary source array [shown in (b) and (e)]. The complete sound

field reproductions are shown in (c) [superposition of (a) and (b)]

and (f) [superposition of (d) and (e)].

tion with the corresponding angles, display different SA

frequencies consistent with the linear array theory of SA.

In Figure 2, the sound pressure amplitudes are arbitrarily

selected for illustration purposes.

For this array, with a secondary sources separation of17.5 cm, the first and severe aliasing criterion givesf#1SA =

945.7 Hz assuming a sound speed of 331 m/s. As shown on

the left side of Figure 2 for 900 Hz, none of the two parts

of the array create SA so that the resulting wave field (Fig-

ure 2c) is effectively a plane wavefront along negative x1and negativex2. In this case, WFS is physically effective.

At 1.1 kHz, SA starts to appear for the horizontal portion

of the array, as shown in Figure 2d. Note that the oblique

portion of the array (Figure 2e) does not create SA. This

is in perfect agreement with Spors [33] prediction of SA

frequency, where the SA frequency of the oblique part ofthe array (with =0) isf#3SA =1891.4 Hz. Typically, SA

artefacts appear as one or more additional beams of plane

wavefronts with a propagation direction different from the

virtual one. As shown in this figure, and as noted by Spors

[33], the width of the supplementary beams depends on

the aperture of the linear secondary source array. This also

dictates if the supplementary beams will reach the listeners

depending on their positions.

Figure 3. Simulation of plane wave reproduction by WFS in

free field at 1300 Hz (left) and 2400 Hz (right). The secondary

sources are marked with white dots. The listening region is delin-

eated by the secondary source array and the white lines. The re-

produced sound fields are divided in two parts: sound fields from

the horizontal portion of the secondary source array [shown in(a) and (d)] and sound fields from the oblique portion of the sec-

ondary source array [shown in (b) and (e)]. The complete sound

field reproductions are shown in (c) [superposition of (a) and (b)]

and (f) [superposition of (d) and (e)].

Two other examples are given in Figure 3 for 1.3kHz

and 2.4 kHz. At 1.3 kHz, only the horizontal portion of the

array creates SA. In comparison with the 1.1 kHz case, the

additional aliased beam introduces more energy in the lis-

tening region, as predicted by the SA analysis of Spors

[33]. WFS is then physically less effective since SA arte-

facts now contaminate the listening region. Note that the

oblique portion of the array does not create SA, as pre-

dicted by the valuef#3SA = 1891.4 Hz. The last example is

shown in Figure 3d to 3f for 2.4 kHz which is above all

the predicted SA frequencies except the second criterion

which predicts f#2SA = with = 0 [34, 35]. Clearlythe two parts of the array create SA artefacts which ap-

pear as two additional undesirable beams of plane wave-

fronts for each portion of the array. This invalidates the

second criterion for the SA frequency but supports thethird one [33]. According to these free-field simulation ex-

amples, SA starts to occur between f#1SA = c/(2l) and

f#3SA =c/(l (1 + | sin()|) with =0.At the beginning of this section, a second perspective

for the consideration of SA frequency criterion was de-

scribed [36] and is based on the listening positions. Al-

though the presented examples were not discussed in re-

lation to the listening position, it is worth noting that the

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examples show how, depending on the chosen perspective,

the SA phenomenon is interpreted: existence of additional

aliased beams of plane wavefronts or existence of addi-

tional aliased components (created by the SA beams) at

the listening positions.

In the case of WFS in a room, the relation between the

path direction of the additional aliased beams and the lis-tening positions are less clear than for the reported free-

field simulations [33]. Indeed, some aliased beams can

reach the listening region by reflection or diffraction from

surfaces and objects without any direct propagation. Ac-

cordingly, the SA frequency criterion which is used for the

following objective evaluation sticks to the most severe:

f#1SA =c/(2l) below which, strictly no SA artefacts exist

for any primary source position, and above which some SA

artefacts might exist depending on the virtual sound field

in relation to the secondary source array geometry. This

criterion,f#1SA = c/(2l), can be described as the mini-

mal possible SA frequency for a given secondary source

array for any primary source type or position. Moreover,

any existing SA artefact would pollute the objective eval-

uation of room effects on WFS at the microphone array

since it would include room effects on WFS, which is the

main concern of this evaluation, and room effect on SA,

which is not addressed in this paper. Also, as any WFS

system (except with some modifications like spatially fil-

tered WFS [34]) might be used by various users to create a

plethora of different virtual sound fields, it is indeed risky

to state that the SA frequency criterion could be higherthan f#1SA = c/(2l). For all of these reasons, it was de-

cided that it is best to adhere to the worst case scenario

for the definition of the SA frequency criterion. Note that

this definition corresponds to the classical spatial sampling

theorem from array theory [37].

3. Experimental setup

The experiments were performed with a WFS system

built by Fraunhofers Institute for Digital Media Technol-ogy [38]. The system included 88 two-ways loudspeakers

mounted on 11 flat units of 8 loudspeakers each. The loud-

speakers and microphones configuration are shown in Fig-

ure 4 and a photograph of the system is shown in Figure 5.

The secondary source array approximately forms a circle

in the horizontal plane (at a height of 1.22 m above the

floor) with a radius of about 2.2 m. The secondary source

array center is defined by the x1x2 origin in Figure 4.

The WFS system [11, 38] is based on: (1) A reference

line defined by a line passing through the center of the

secondary source array and perpendicular to a line fromthe primary source to the center of the secondary source

array (see Figure 4 for an example) and (2) a spatial win-

dow (half-Hanning) to progressively reduce the secondary

source amplitudes from the active secondary sources to

the non-active secondary sources [11]. The reproduction

room is located in the Redpath Hall (McGill University,

Montral, Canada) basement. The room is schematically

shown in Figure 6. Room partitions are made of 1.27 cm

Figure 4. The 88 loudspeakers of the WFS system (shown as

black squares) and the 8 microphones used in sound field mea-

surements (shown as circles). O: The 6 different primary source

positions in the experiments, (a) to (c) being those described in

this paper. The reference line is shown as a dash-dot line for the

primary source (b).

Figure 5. Photograph of the WFS experiments including the front

loudspeaker array (four visible 8-loudspeaker units), the com-puter interface and the microphone array.

(1/2 inch) plaster on brick walls and acoustical curtains

cover the whole surface of the walls (see Figures 5 and 6).

There is a suspended ceiling above which there is approxi-

mately 30 cm of compressed mineral wool-like material

for sound and thermal isolation while the concrete floor is

covered by a thin commercial carpet. The room dimen-

sions are 5.2 m6.05 m2 m (the 2 m height is the dis-

tance between the floor and the suspended ceiling), andcan be considered as a medium-sized listening room. The

background sound pressure level was estimated to be 47

[dB ref 2 105] and the typical sound reproduction levelwas estimated to be 78 [dB ref 2 105] between 100 and1000 Hz. The main noise sources were outdoor vehicles

and water pipes above the room.

Each 8-loudspeakers unit included ADAT optical input,

digital-analog converters and power amplifiers while the

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Figure 6. Room geometry and relative WFS system position.

rendering system included four computers. The WFS sys-

tem also included a subwoofer channel for sound repro-

duction below the panel cut-on frequency. For these ex-

periments, the subwoofers were turned offand the analog

subwoofer channel (which is an unfiltered version of the

virtual source wave file) was used as the reference input

for FRFs and IRs identification. Since the loudspeakers

were separated by 17.5 cm, the WFS spatial aliasing fre-

quency was found to be 945.7 Hz assuming a sound speed

of 331 m/s and at least two reproduction (or secondary)

sources per wavelength to avoid spatial aliasing [11] (see

section 2.3). Therefore, the reference signal, also used to

feed the virtual source, was limited to 01 kHz (3 dBcut-off point of a 12-order Butterworth filter). This fre-

quency limitation simply stems from the fact that we are

exclusively concerned with the effective WFS (below the

WFS spatial aliasing frequency) reproduction quality and

not with the entire audio-bandwidth quality.

Sound pressure was measured using a linear micro-

phone array (shown in Figures 4 and 5). The array in-

cluded 8 TMS microphones (model 130M01 with 130P10

preamplifiers) separated by 17.5 cm. For the sound field

reproduction measurements, the linear array was placed

in the center of the loudspeaker array at the same el-

evation, i.e. 121.92 cm (48 inches), as the reproduction

sources (Figure 4). ICP conditioners (two 4-channels PCB

442B104) were used to store the microphones signals on a

DAT recorder (SONY PC216A) from which the data was

later exported and analysed. The microphones were cali-brated for amplitude using a 1 kHz sound level calibrator.

4. Experimental and analysis procedure

The experimental setup and post-processing analysis pro-

cedure are both schematically shown in Figure 7. The

reference signal, also used to feed the primary source,

Figure 7. Schematic representation of the experimental setup and

the impulse response extraction.

was uncorrelated white noise low-pass filtered at 1 kHz to

avoid SA.

The microphone outputs and reference signal were

stored with a DAT recorder (a SONY PC216A, with a vari-

able sampling rate, set to sample data at 6 kHz and with

an anti-aliasing filter correspondingly adjusted to 2.5 kHz)

for later post-processing.

Before impulse response identification in the post-pro-

ssing operation, the measured pressures and the reference

signal were high-pass filtered above 100 Hz. This high-

pass filtering was used to remove uncorrelated measure-

ment noise (mainly coming from exterior vehicle traffi

c)due to the fact that the two-ways loudspeakers were not

effective at lower audible frequencies. Impulse responses,

between the reference signal and the measured pressures,

were then identified using an adaptive LMS algorithm

[39, 40]. The adaptive modeling proceeded on for approxi-

mately 6 minutes of data (2, 160, 000 samples). Validation

tests were performed and proved the validity of the result-

ing identifications: these tests showed that the identifica-

tions can predict a set of modeled pressures that matches

the measured pressures of the real system when using a

measured reference signal sequence, which has not beenutilized in the adaptive identification process [41]. The

adaptive LMS algorithm was used as an iterative identi-

fication method since this type of identification algorithm

is already included for on-line identification in the adap-

tive wave field synthesis (AWFS) system [19]. Along with

other standard identification methods such as maximum-

length-sequence (MLS) or sweep sines, adaptive identifi-

cation can typically converge towards very similar results

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obtained from the two others mentioned. This is a mat-

ter of convergence time, adaptation coefficient, MLS se-

quence length, number of averages, etc.

Once the adaptive identification had converged, the re-

sulting impulse responses were low-pass filtered below

1 kHz. Thus, the frequency range of the system response

become strictly limited to a 1001000 Hz bandwidth. Thefrequency response functions were obtained by Fourier

transformation from the identified impulse responses.

Since the identified system input is the analog refer-

ence signal [V] and the identified system outputs are sound

pressure [Pa], the impulse responses and frequency re-

sponses are expressed as sound pressure per volt [Pa/V].

All the following experimental results are based on the

aforementioned analysis procedure.

5. Experimental results

The experiments were performed for six primary source

positions. However, only three are presented here. These

positions (a), (b) and (c), shown in Figure 4, and were cho-

sen to create different incidence angles on the secondary

source and microphone arrays, and to vary the number of

active secondary sources (more active secondary sources

correspond to position c). The experiments focused on

frontal positions of the primary sources as this corresponds

to the most typical positions for primary sources.

The results are presented in two sections: the first is ded-icated to reproduced FRFs showing frequency coloration

by the room, the second shows the reproduced IRs to illus-

trate the room effects in terms of reflections and wavefront

passages at the microphone array. As it will be shown, both

coloration and reflections explain most of the discrepan-

cies between theoretical and experimental reproduced IRs

and FRFs by WFS.

5.1. Measured WFS frequency response functions

This section presents the FRFs between the reference sig-

nal and the microphones for three primary source posi-

tions (three different virtual wave fields). The objective is

to evaluate the room effects on the FRFs in comparison

with theoretical FRFs obtained from free-field simulations

of WFS using the same configuration.

The first reproduced sound field is generated by a point

primary source located at x1 = 0 m, x2 = 4 m (position

(a) in Figure 4). Both the measurement [Pa/V] and the

simulation [1/m] gains are transformed in dB ref 1 gains.

The simulation gains are obtained with WFS simulations

(see reference [2] and section 2) in free field and fromthe division of the output sound pressures by the primary

monopole amplitude. As shown in Figure 8, the eight FRFs

measured by the microphone array display similar types

of responses. The various fluctuations and dips that appear

above approximately 250 Hz are due to comb-filtering ef-

fects, destructive standing-wave interferences and possi-

bly finite aperture artefacts (diffraction waves) produced

by the corners of the reproduction source array [11, 35].

Figure 8. Measured (thick line) and simulated (dashed line) WFS

FRFs gains [dB ref 1] for the primary source (a). Sensors #1 and

#8 are respectively the leftmost and rightmost sensors in Fig-

ure 4.

The corresponding FRFs dips are more significant in the

frequency range above 250 Hz where the sound pressure

FRFs show a reduced spatial correlation, i.e. the FRFs

vary for each sensor. A reduced spatial correlation char-

acterizes a more diffuse field response and highlights the

destructive interference effect, which varies strongly as a

function of position. Below 250 Hz, the response seems to

be controlled by spatially correlated modal response. This

is mostly visible around 150 Hz where one possibly ob-serves a strong room mode (or a group of modes, some-

times called a room formant [42]) resonant response. The

possible existence of damped standing waves (in the low

frequency limits) and comb-filter response (corresponding

to reflection and diffraction by objects and walls in the

higher frequency limits) suggests the need for WFS im-

provements in room situation (as already pointed by sev-

eral authors [2, 20, 28]). To support such observations,

Figure 8 also shows the comparison of the measured FRFs

with theoretical FRFs obtained from the free-field WFS

simulations in the frequency domain for the same con-figuration. Since the measured and simulated FRFs units

are different, the free-field simulation FRFs have been ad-

justed to fit the measured data on average. Clearly, the

measured FRFs colorations are stronger than those of the

free-field simulations, which are hardly visible on this fig-

ure. The free-field simulation colorations arise from vari-

ous effects including: finite aperture array (only a part of

the reproduction source array is active) and corner effects

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Figure 9. Gains [dB ref 1] of the measured (thick line) and sim-

ulated (dashed line) WFS FRFs for the primary source (b). Sen-

sors #1 and #8 are respectively the leftmost and rightmost sensors

in Figure 4.

[11, 35] (caused by piecewise linear secondary source ar-

rays). To illustrate this difference and the soft coloration

of the free-field FRFs, it is possible to evaluate the mean

(over the eight microphone positions) of the standard de-

viation of the FRFs gains between 100 and 1000 Hz for

both the experimental and theoretical cases. For the exper-

imental FRFs, the mean standard deviation is 5.7576 dB

(a variance of 33.1495) while for the theoretical free-field

the mean standard evaluation is low as 0.3365 dB (a vari-

ance of 0.1132). This shows that the free-field FRFs devi-

ation from the ideal flat FRFs is small in comparison with

the room effect: room effects dominate the reproduction

errors. On that matter, one can see that any variation in

the WFS operators definition (approximations, position

of the reference line [32], spatial window [35], etc) would

not cause such large deviations as seen in the experimental

data.

Other experiments were conducted with five different

primary source positions. Two of these measurements areshown in Figures 9 and 10 for the primary source positions

(b) and (c) in Figure 4. Most of the comments presented

for the primary source position (a) apply for these two

other cases. Note that the difference in the primary source

distances between (b) and (c) (see Figure 4) does not af-

fect the measured FRFs gains on average. This is simply

because the distance-dependent amplitude has not been

considered in these experiments (i.e. the loudness does not

Figure 10. Gains [dB ref 1] of the measured (thick line) and sim-

ulated (dashed line) WFS FRFs for the primary source (c). Sen-

sors #1 and #8 are respectively the leftmost and rightmost sensors

in Figure 4.

change with the distance of the primary source). The free-

field WFS simulations include the distance-dependent am-

plitude, but have again been adjusted to fit the measured

data on average. By comparing the FRFs for various pri-

mary source positions (Figures 8 to 10, primary monopole

source in positions (a), (b) and (c), respectively), one can

conclude that WFS FRFs departure from idealized ones is

mainly due to the electroacoustical system including the

loudspeakers, the furniture and the room response, and

much less to the primary source position or WFS specific

approximations.

This is supported by the fact that even if the FRFs

change with the primary source position, there is no clear

relation between the FRFs global trends and the primary

source position as it is for free-field WFS simulations. That

is, in free-field simulated situations, the WFS FRFs depar-

ture from the ideal primary source FRFs solely depends on

(1) frequency, (2) the primary source position in relation

with the secondary source array position and (3) the size ofthe secondary source array. Some other effects like finite

loudspeaker array aperture and diffraction from the cor-

ners of the secondary source array [11] can easily be lim-

ited using WFS modifications such as spatial windowing.

Spatial windowing was used for both WFS simulations

and experiments. In all case, as shown by these three fig-

ures, most of these free-field colorations were dominated

by the prominent room response.

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Figure 11. Measured [Pa/V] (thick line) and simulated [1/m]

(dashed line) IRs for the primary source (a). Sensors #1 and #8

are respectively the leftmost and rightmost sensors in Figure 4.

Time of arrivals and amplitudes of the virtual field are marked by

circles and they are connected by thick dotted line.

Again, by looking at the mean (along the microphone

positions) of the individual FRFs standard deviations (be-

tween 100 and 1000 Hz), it is possible to highlight the

insignificancy of the free-field colorations in comparison

with the drastic room effect. For case (b), the experimen-

tal FRFs mean standard deviation is 5.3968 dB (variance

of 29.1259) while for the free-field case, the FRFs mean

standard deviation is 0.3484 dB (variance of 0.1214). For

case (c), the experimental FRFs mean standard deviation

is 5.5827 dB (variance of 31.1669) while for the corre-

sponding free-field case, the FRFs mean standard devia-

tion is 0.3502 dB (variance of 0.1227).

5.2. Measured WFS impulse responses

In this section, the multitrace IRs (impulse responses) will

be used to represent the directions of arrival and wavefront

curvatures of the reproduced sound field that includes dis-

tinct sound reflections.Multitrace IRs are measured and analysed to evaluate

the geometry of the reproduced wavefronts. In this exper-iment, the objective was to evaluate the room effect on

wavefront reconstruction by WFS. The IRs were obtained

from adaptive identification using the LMS algorithm with

a band-limited noise input reference as well as the micro-

phone outputs described in section 4.The IRs are detailed in Figures 11 to 13 for the primary

source at positions (a), (b) and (c) respectively (see Fig-

ure 4 for the primary source positions). The arrival time


(dashed line) IRs for the primary source (b). Sensors #1 and #8




and amplitude of the primary wavefronts are also shown

in these figures. This has once more been adjusted (global

amplitude and time delay) to fit the measured data on av-

erage so that relative comparisons of amplitudes and de-

lays are possible. The free-field WFS simulations are also

shown on these three figures in order to highlight the room

effects. The simulated WFS IRs were obtained by inverse

Discrete-Time Fourier Transform (DTFT) of the simulated

FRFs. Clearly, WFS produces a direct field (the first wave-front that impinges the sensor array) which matches both

the free-field WFS simulated reproduced field and the su-

perimposed passage of the virtual field. Here, this relation-

ship is noted in terms of relative delays and amplitudes

along the microphone array. It can thus be concluded that

direct field reproduction by WFS is effective in rooms.

However, after the direct field has reached the sensor ar-

ray, the reflections on room walls are clearly visible, which

causes an important mismatch between the virtual wave

field (or the free-field WFS simulations) and the WFS re-

produced sound field in a room.Comparison of Figures 11 and 12 shows that the direc-

tion of the incident wave on the microphone array due to

the primary source angular position is properly achieved

by WFS. In Figure 11, all initial wavefronts arrive almost

simultaneously, corresponding to a normal incidence as

suggested by the relative positions of the primary source

(a) and the microphone array in Figure 4. By comparing

Figures 12 and 13, one can also observe that the change of

833


11/13



(dashed line) IRs for the primary source (c). Sensors #1 and #8




Figure 14. Measured IRs for the primary sources (a), (b) and (c).

Color scale on top; virtual positions (a), (b) and (c) in the middle;

time zoom for the virtual positions (b) and (c) in the bottom.

the virtual source distance (4 m to 12 m) is effectively re-

produced by a wavefront curvature which is larger in Fig-

ure 13 than in Figure 12. (This will be further explained

by Figure 14.)

In all the IR illustrations, one can see that the arrival

of the first wavefront is preceded by growing (as time

increases) oscillations at 1 kHz. This is a signal process-

ing artefact which stems from the rectangular window fil-

tering (low-pass at 1 kHz) of the IRs, in the frequency

domain, which creates a time-domain symmetrical band-

limited impulse (a sinc function with decaying oscillations

on both sides of the main impulse).

Figure 14 summarizes the results of Figures 11 to 13

in the time domain. The band-limited measured IRs areplotted as a function of time and spatial position of the

microphone array for the three primary source positions.

The color scale contrast has been increased to enhance the

lower values of the IRs. The color scale [Pa/V] is shown at

the top of the figure. The bottom portion of the figure is a

time zoom around the arrival of the first wavefront of the

IRs for primary positions (b) and (c). On this figure, the

arrivals of the virtual wave field are also shown as dashed

lines for comparison purposes. This graphical representa-

tion, when compared with Figures 11 to 13, better illus-

trates the geometry of the reflected wavefronts. The roomeffects include strong reflections (with wavefront curva-

tures similar to the virtual wave field) and late di ffused

reverberation. The discrete early reflection shapes, in rela-

tion to the virtual wave field, are also visible for the repro-

duced sound fields shown in Figure 14.

According to these figures, WFS does not accomplish

objective (in physical terms) sound field reproduction of

the virtual wave field, except for the direct field, which

approximately corresponds to the geometry of the virtual

wave field created by the primary source.

6. Discussion

A physical interpretation of the experiments can be sum-

marized as follows. In terms of physical measurements,

the performance of WFS is affected by the presence of

the reproduction room which strongly colors FRFs and

introduces reflections and reverberation in the IRs. Since

the virtual wave field is generated by a primary monopole

source in a virtual free field, the ideal FRFs have a flat

frequency dependence and the corresponding IRs are sim-

ple band-limited impulses with a geometrical spreading inspace. The measurements clearly highlight the discrepan-

cies between this virtual field and the reproduced FRFs

and IRs. On the other hand, the geometry of the direct

field approaches the free-field simulated WFS reproduc-

tion, which is itself similar to the virtual wave field defi-

nition. This includes wavefront curvature. The differences

between the free-field simulations and experiments high-

light potential technical improvements of WFS on a phys-

ical basis.

These results are in accordance with the WFS defini-

tion which relies on free-field assumption for the repro-duction space. According to the results presented in this

paper, correction of WFS response in room is needed to

increase the objective performance of sound field repro-

duction with WFS. Since the WFS derivation from the

Kirchhoff-Helmholtz integral would be too difficult for

practical reproduction spaces (this would require an ac-

curate room model, leading to a very case-specific ap-

proach which would be unadaptable to adapt to varia-

834


12/13


tions of the room characteristics in time), active com-

pensation using error sensors in the reproduction space

and adaptive signal processing is a promising research

area. This is the subject of current and recent researches

[2, 20, 22, 23, 24, 27, 43, 44, 45, 46, 47].

Although most of the previous sections described WFS

in terms of physically measurable quantities, the audioapplications of WFS address the human hearing system.

Therefore, a brief discussion relating to spatial hearing

perception and the measurements shown in this paper is

needed. This discussion mostly relates to the precedence

effect [30]. According to the precedence effect, human

sound localization in presence of a set of coherent wave-

fronts (in our case: the direct reproduced field and the re-

flected and reverberated fields) uses the direction of ar-

rival of the first wavefront - as long as the time separation

of the first wavefront and the other coherent wavefronts is

less than the echo threshold time - to determine the local-ization of the auditory event. This suggests that most of

the reflected wavefronts in these experiments should not

influence sound localization provided by the first wave-

front (the direct field which satisfactorily corresponds to

the virtual wavefront curvature) since the major WFS re-

flections (see Figure 14) appear before the echo threshold,

which is between 30 and 40msfor the two-channel stereo-

phonic configuration described by Blauert [30]. If this is

the case, most of the perceivable WFS objective perfor-

mance degradations caused by the room effect should be

the frequency-dependent colorations of the FRFs causedby the rooms response and spatial localization should be

less influenced. This should be verified by further exper-

imentation and suggests the need for frequency equaliza-

tion of WFS in rooms, specifically at low frequency. On

this matter, one should note that the limited 1001000 Hzbandwidth somehow limits the extent of the subjective ef-

fects interpretation.

7. Conclusion

In this technical paper, experiments on WFS sound fieldreproduction in rooms have been described as an objec-

tive evaluation of WFS performance in rooms. The results

have shown that WFS objective performance - described

with measured FRFs and IRs - is significantly reduced in

comparison with free-field WFS simulations and virtual

wave field created by a primary source. These differences,

entirely caused by the loudspeaker and room responses,

suggest the need for room compensation along with WFS

to increase the objective performance of the system. This

topic is the subject of current research using closed-loop

control and digital signal processing borrowed from ac-tive noise control techniques [2, 20, 22, 23, 24, 27, 43,

44, 45, 46, 47]. The work presented in this technical paper

was a preliminary step towards what the researchers have

proposed as adaptive wave field synthesis (AWFS) for

reproduction systems and room compensation with WFS

and active noise control (for more details, see reference

[20]). AWFS offers the possibility to control the amount of

room compensation. Current research activities on AWFS

have been devoted to signal processing and experimental

evaluations of AWFS versus WFS reproduced sound fields

in different reproduction rooms, hemi-anechoic chamber,

laboratory space and reverberant chamber. The results are

promising since AWFS effectively compensates the repro-

duction errors. This should be reported in upcoming re-

search papers. The results presented herein directly or in-directly motivates further works on system limitations or

reproduction room compensation [24, 36]. The results also

revive the debate between room compensation or specific

room design for WFS. Aside from room compensation

based on dedicated signal processing and modification of

the classical WFS algorithms, one can imagine a reproduc-

tion room with considerable amounts of sound absorbing

material, that would induce reproduction errors to be dom-

inated by system limitations. This is an interesting simple

approach since typical WFS system are, and will be, used

in dedicated rooms. In such cases, direct sound field equal-ization for WFS [29] would be an efficient method to re-

duce the remaining WFS reproduction errors. The afore-

mentioned ideas are open issues for future development of

WFS.

Acknowledgements

This work has been supported by NSERC (Natural Sci-

ences and Engineering Research Council of Canada),

FQRNT (Fond Qubecois de la Recherche sur la Nature et

les Technologies), VRQ (Valorisation Recherche Qubec)

and Universit de Sherbrooke. The authors wish to ac-

knowledge the Institute for Digital Media Technology at

Fraunhofer in Ilmenau (Germany) for their technical sup-

port and for the lending of the WFS system to McGill Uni-

versity. This work has been conducted within CIRMMT

(Centre for Interdisciplinary Research in Music Media and

Technology, McGill University). The first author wishes to

acknowledge John Usher from McGill University (CIR-

MMT) for his help and availability regarding the use of

the WFS system. The first author wishes to acknowledge

Hugo Fourier for English language correction.

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Documents

2007 Objective Evaluation of Room Effects on Wave Field Synthesis