Numerical simulation round robin of a coupled volume case:
Preliminary results
Antoine WEBER and Brian FG KATZ
Sorbonne Université, CNRS, Institut Jean le Rond d’Alembert, Lutheries - Acoustique - Musique, Paris, France,
antoine.weber@sorbonne-universite.fr & brian.katz@sorbonne-universite.fr

Abstract
The advantages and limitations of most numerical methods in room acoustics have to date been primarily evaluated in single-volume room conditions, placing emphasis on early reﬂection components and the early part of
the room acoustic impulse response. Few studies have examined the capabilities of simulations to model correctly the case of coupled volumes, where the late part of the impulse response is not a simple extension of theearly part and needs to be accurately represented. This work presents preliminary results of a round robin study
comparing numerical simulation results with coupled volume theory, using physical scale model measurements
to deﬁne general parameters. Numerical methods included geometrical acoustic solutions, with image source
method and ray/cone/path-tracing type approaches, and wave-based methods, comprising several FDTD implementations. A scale model was used to set the parameters of a statistical model to ensure a physically realistic
conﬁguration. Room model coordinates were speciﬁed. To avoid issues regarding variations in implementationof material and scattering behaviors across methods, the reverberation time of separate individual volumes wasprescribed in the uncoupled condition. Volumes were then coupled and the results analyzed. The comparison isof a rather simpliﬁed room acoustic model, assuming homogeneous boundary conditions.
Keywords: Room acoustics, Coupled volume system

1

INTRODUCTION

A system of coupled volumes consists of two or more spaces that are connected through an acoustically transparent opening. When a main room containing the source is coupled with a more reverberant auxiliary volume,the sound decay within the main volume can exhibit a non-exponential behavior. During the last decades, numerous new construction concert halls and other performing art spaces have had coupled volumes integrated intheir design. They offer various advantages like providing high perceived levels of clarity and reverberation at
the same time, two qualities that are usually contradictory in single volume spaces. In addition, coupled volumes are found in other situations, such as stage houses and stair wells. As such, an evaluation of the abilityof current numerical methods to model them sufﬁciently correct for a given purpose is of interest.
Three round robin type studies on room acoustical numerical simulations have been conducted between 1994
and 2002 [1, 2, 3, 4] which compared the results of different algorithms with measurements in single volume
spaces. The procedure followed was close to that encountered in acoustic planning in the ﬁeld of building designand construction. First the acoustic materials were either described, later the acoustic properties of the materials
were prescribed according to measurements or data tables for uniformity. These studies have highlighted sometrends between simulation tools, while also showing the importance of user variability and input data quality.
Comparing results obtained by novice or insufﬁciently-trained users, or using general data for speciﬁc materials
both lead to higher variances and poor matching to measured results.
In order to assess the capability of different room acoustic simulation tools to accurately predict the acoustics
of coupled volumes, the protocol employed in the present work aims to minimize the variance due to input
and user variables. For this ﬁrst comparison, a very simpliﬁed architecture is employed. Based on a physical scale model conﬁguration of a simple shoebox-type coupled volume system composed of two rooms (amain room and a single reverberation chamber) linked by a single large aperture, basic acoustic measurements6051

are carried out separately for the two volumes in isolation to determine the equivalent homogeneous acoustic
material properties. In order to avoid issues regarding variations in implementation of material deﬁnitions andscattering behaviors across different methods, participants were asked to ﬁt their boundary conditions in eachroom according to the measured reverberation times in the uncoupled conﬁguration. Identical geometrical data,
corresponding to the wall geometries of the scale model, transformed to 1:1 scale, and the uncoupled acoustic
parameters of the two volumes were provided. Participants were comprised principally of the developers of thetested software, so that error effects due to users was limited. To simplify the task of model calibration and as
a compromise between geometrical and wave-based methods, this study was limited to the 1 kHz-octave band.

2

MODELS AND METHODS

2.1 Coupled volume theory
A statistical-acoustics model of energy decay in a system of two coupled volumes [5, 6]. These models are
based on diffuse-ﬁeld theory assumptions, that reverberant energy within each volume decays exponentially, as
described by Sabine’s model, and rooms interact through the exchange of diffuse energy. These models lead tothe resolution of a system of ordinary differential equations. This system for N rooms can be written as:ViN
cSi j (Ei − E j )cAi Ei
dEi
=−
+ ∑
dt
4
4
j=1, j=i(1)where i = 1, ..., N, c is the speed of sound, Ei denotes the average energy density in the ith room, Vi is thevolume of the ith room, and Ai is the equivalent absorption of the ith room calculated according to Sabine’s
model as Si ᾱi , where Si and ᾱi are the total surface area and the averaged absorption coefﬁcient of the ith room,
respectively. The coupling area between room i and an adjacent room j is denoted Si j . The resulting system of
linear differential equations (Eq. 1) can be presented in matrix form and solved by ﬁnding the corresponding
eigenvalues and eigenvectors, determining the constant terms from initial conditions.
2.2 Scale model and measurements
To ensure the tested simpliﬁed conﬁguration represents a physically realisable system, a scale model was employed to obtain the basic parameters. Subsequent studies may rely on more detailed geometrical models with
the inclusion of speciﬁc material properties (absorption & scattering coefﬁcients determined via direct laboratory
measurements). Such details could affect local variations in the simulated ﬁeld across positions, as well as earlyreﬂection patterns and possible ﬂutter echoes when absorption and scattering are low and unevenly distributed.
The scale model is a very schematic coupled volume system representing the dimensions of a 1:20 scale concert
hall (Fig. 1). It is composed of two rooms: a large box with its walls covered with diffusive and lightly
absorptive materials and a smaller box with hard reﬂective materials to have a more reverberant cavity. They
represent a main room and a reverberation chamber of 17 000 m3 and 5400 m3 at full scale, respectively. The
two volumes are acoustically linked by a common wall which contains a single aperture whose surface areais ≈1 % of the total surface area of the main room’s walls. The side and rear walls are slightly tilted by anangle of 2° in each room to avoid ﬂutter echoes occurring between parallel surfaces in such simpliﬁed shoeboxshaped volumes. The main room is currently sparse, and the inhomogeneous material distribution is evident. A
schematic representation of the coupled room system and photo of the main room are shown in Fig. 1, also
indicating the prescribed source (2) and receiver (4) positions. Sources and receivers were considered to beomnidirectional for the purposes of this study. This model has been used in previous studies [7, 8, 9], though
the exact conﬁguration of the main room and its materials has been changed from those studies.
Measurements were conducted with a miniature dodecahedral loudspeaker (Dr-Three 3D-032) as a sound source
driven by an ampliﬁer (Samson Servo 120a) with several microphone receivers (DPA 4060). All were connected to an audio interface (RME Fireface 800) conﬁgured at a sample rate of 192 kHz and controlled via
MATLAB 2018b. The exponential swept-sine technique was used to obtain the room impulse responses. Fre-

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0
Energy decay curve
Slopes
Bending point

Reverberation chamber
Main room

S1

R2

R3

R4

Level (dB)

R1
S2

-20

-40 BP

L

-60

BP t

0

1

DT

DT 1

-80

2

2

3

4

5

6

Time (s)Figure 1. (left) Schematic view of the coupled volume model. (center) Photo of the main room of the scalemodel. (right) Deﬁnition of acoustical parameters adapted to double-slope energy decay curves.
quencies spanned 200 Hz to 60 kHz, covering the octave band of interest centered on 1 kHz at full scale.
2.3 Analysis and quantiﬁcation
Several quantiﬁers and methods have been proposed to described non-exponential decays [10]. The quantiﬁcation method used in this study to analyze decay curves derived from Schroeder’s backwards integration method,
obtained in the measurements and in the simulations, is called the Marching Line [7]. It is based on a directcomparison between the decay curve and linear regressions. It provides the number of slopes with equivalent
decay rates, and the time & level of bending points between two consecutive slopes. To describe such a decay
curve with two slopes, the employed parameters are the equivalent reverberation times DT1 and DT2 of the ﬁrst
and second slope, respectively, and the coordinates of the bending point in time BPt and level BPL (see Fig. 1).
2.4 Entries
Solicitations for participants in this study was done via requests over email to a number of persons involved in
the research, development, or use of room acoustics simulations. They were provided with all the geometrical
data needed for the construction of the 3D model, as well as the instructions concerning the calibration procedure based on the uncoupled acoustic parameters. In total, there were 11 different entries using 10 different
numerical methods with 3 wave-based methods, and 7 geometrical acoustic implementations. A short descriptionof the programs used, mostly provided by participants, and their parameters are presented in arbitrary order.
I-Simpa: Version 1.3.4 is an open-source graphical user interface developed to host three-dimensional numericalcodes for the modeling of sound propagation in complex geometrical domains. The calculation code used was
SPPS (from French “Simulation de la Propagation de Particules Sonores"), version 2.2.1, based on a particletracing method [11]. The radius of the receivers was set to 10 cm, 50 million particles were used for eachsource and were collected using time slots of 20 ms.1
Wave-based: Two academic participants used CE-FDTD methods with different schemes. One used an implementation of the 3D standard rectilinear scheme, known as standard leapfrog scheme (SLF) [12] while theother used the interpolated wideband (IWB) scheme [13]. The SLF scheme used a c =344 m s−1 , fs =18 933 Hz,
a spatial grid of 31.5 mm and Δt =52.82 μs. The IWB scheme used c =340 m s−1 , spatial grid of 8.5 mm,
and Δt =23.75 μs. The room surface boundaries were assigned to be locally reacting and the impedance isfrequency-independent in both implementations. A third entry used a software developed at the University of
Edinburgh based on the hybrid FDTD/FVTD method described in [14].
RAMSETE: Version 3.02 uses a Pyramid Tracing algorithm capable of solving the sound propagation problems
in large enclosures or outdoors [15]. The method employed was pyramid tracing with surface scattering andedge diffraction up to the second order. Discrete paths were saved up to fourth order. The number of pyramidal
1 The resulting data were echograms, not impulse responses. In consequence, no 1 kHz-octave band ﬁlter was applied.

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beams launched by each source was 32 768 and the energetic impulse responses were computed with a resolutionof 1 ms.
CATT-Acoustic: TUCT v2.0e:1.01 algorithm 1 [16] was used. Ray split-up between diffuse and specular reﬂections are performed randomly with a probability determined by the scattering coefﬁcient (max split-order= 0).
Calibration of the main room used 716 486 rays, the reverberation chamber 638 082 rays, for each source. The
coupled conﬁguration used 2 000 000 rays with auto-edge scattering applied on the aperture edge planes.
ODEON: Simulations were performed using ODEON Combined version 15.13 [17]. The calculation model ishybrid, using image source method plus radiosity for early reﬂections and ray tracing plus radiosity for late
reﬂections. Reﬂections of ﬁrst and second order were treated as early reﬂections. A total of 16 000 rays wereused for late reﬂections for each source. Ray tracing was made using the method of reﬂection based scattering.
RAVEN: The Room Acoustics for Virtual ENvironnements software, developed at RTWH Aachen University[18, 19], uses a hybrid algorithm that combines Image Source Method for the direct sound and early reﬂections
with ray-tracing for the late reverberation, with ray tracing calculating an energy decay histogram based on
specular reﬂections of order ≥ 3, diffuse reﬂections for order ≥ 1, and diffuse energy based on the diffuse
rain model. One participant used the 2018.v2 version with 500 000 rays for the calibration of the absorption
coefﬁcients and 1 000 000 rays for the coupled rooms simulations. A second entry used 2019.v1 version with
500 000 rays for all simulations. They both used image sources for specular reﬂections up to the second orderand ray-tracing parameters set to 1 m for the radius of the detection sphere with time slots of 10 ms.
Path tracing: One entry employed a geometrical acoustics simulation method based on unidirectional pathtracing from the receiver position with next event estimation, a computer graphics method of rendering imagesof three-dimensional scenes, also termed “diffuse rain" in acoustics [18]. Materials are described by a glossy
Phong reﬂectance model that is controlled by the scattering coefﬁcient. Energy decay histograms are computedfor each band at full sample rate, converted to pressure envelopes, then the per-band pressure envelopes are
multiplied by ﬁltered white noise and summed to compute the pressure IR.
SoundPLANnoise: Version 8.2 using the Sound Particle Diffraction method [20] was used. It incorporates
specular and diffuse reﬂections, transmission, room scattering, and geometrical diffraction. Diffuse reﬂections
are modeled according to the Lambert cosine law and diffraction is performed according to the uncertaintybased diffraction theory [21], which allows for arbitrary diffraction orders. The energetic impulse responses
were computed with a resolution of 1 ms.2
The main room has a large surface area of diffusing materials (characteristic roughness depth of 6 cm at fullscale, while the second room has smooth walls. For the 1 kHz band, scattering coefﬁcients of 20 % and 10 %were suggested for the two rooms respectively. However, due to differences in implementations of such parameters, this was not a controlled parameter. For example, in the wave-based methods, one participant modelledwall roughness directly with a diffuser design.
Participants were asked to submit simulated room impulse responses in audio WAV format in order to apply
the same routine for acoustical parameter calculations and thus avoid introducing another source of divergencefrom different implementations [22]. In the following results section, entries have been randomly assigned
identiﬁcation letters from A to K, to ensure anonymity.

3

RESULTS

3.1 Calibration of numerical models
In order to avoid issues regarding different implementations of absorption and impedance conditions across numerical methods, the reverberation time in each room was prescribed according to scale model measurementsin the uncoupled conﬁguration. For simplicity, participants were instructed to adjust material properties of walls
uniformly for each room (i.e. all walls of each volume have the same material deﬁnitions) to match the prescribed reverberation times. Measurements and simulations were carried out for 2 source and 2 receiver posi2 The resulting data were echograms, not impulse responses. In consequence, no 1 kHz-octave band ﬁlter was applied.

6054

tions in the reverberation chamber and 2 source and 4 receiver positions in the main room. Measured impulse
responses were numerically compensated for scaled air attenuation in the scale model. Prescribed average T30
in the main room and the reverberation chamber was 1.26 ± 0.064 s and 4.52 ± 0.065 s, respectively.
Figure 2 shows the reverberation times T30 for each source-receiver pair calculated from measured and simulated
RIRs. For both rooms, the highest relative difference is 11 %. Overall, the calibration procedure was respected.
The variances of the results from the simulations was lower than the measurements except for entry J in thereverberation chamber. The participants had the choice to only use half of the source-receiver positions due tocomputation time, only done by entry K. These variances in the calibration stage exceeded expected differences
resulting from T30 calculations from RIRs, which were on the order of 3 % to 5 % [22], and would be expected
to be even less for noise-free RIRs. The source of these discrepancies remains to be investigated.
3.2 Measured coupled system
A comparison between the physical scale model and the idealized statistical model is provided. Table 1 shows
the coupled volume acoustic parameters acquired via scale model measurements and those using the statisticalenergy balance model. As the statistical model assumes homogeneous material distribution and does not take
into account positions of the source or receivers [9], some differences are to be expected.
The decay rates DT1 and DT2 are in well agreement with relative differences of 8 % and 7 %, respectively. The
most notable difference between the statistical model and the physical model concerns the bending point. The
statistical model predicts a transition occurring later and lower in level than was measured with ΔBPt =0.2 s and
ΔBPL =7 dB, taking into account the margin of the standard deviation.
4.8

4.6

1.4

T30 (s)T30 (s)

1.6

1.2

1

4.4

4.2
(a) main room

Meas. A

B

4
C

D

E

F

G

H

I

J

K

(b) reverberation chamber

Meas. A

B

C

Entry

D

E

F

G

H

I

J

K

Entry

Figure 2. Reverberation times T30 from measured and simulated impulse responses for the two room in theuncoupled conﬁguration: (a) main room and (b) reverberation chamber. Individual S-R pair data points areshown, including 95 % conﬁdence intervals (red) and 1 Standard deviation (blue).
Table 1. Acoustical parameters for measurements in the scale model and the calibrated analytical model. Average values across the 8 source-receiver pairs with standard deviation.
Parameters
Scale model
Statistical model

DT1 (s)1.39 ± 0.16
1.29

DT2 (s)3.46 ± 0.09
3.71

BPt (s)0.48 ± 0.04
0.73

BPL (dB)-22.6 ± 1.3
-30.8

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0

0
Statistical model
A
B
C

-20
-30
-40
-50

Statistical model
G-10

Energy (dB)

Energy (dB)

-10

D
E
F

H
I

J
K

-20
-30
-40

0

0.5

1

Time (s)

1.5

2

-50

0

0.5

1

1.5

2

Time (s)Figure 3. Statistical and simulated energy decay curves of the coupled conﬁguration for the 1 kHz-octave bandfor S1-R3 position. Results are split across 2 ﬁgures to improve readability.
3.3 Simulated coupled system
An example of the energy decay curves obtained from the measured and simulated room impulse responses forone source-receiver pair in the octave band of interest is presented in Fig. 3. The double-slope decay behavior
expected for a coupled volume system is clearly visible for all entries and, based on visual impression, they
seem to be in general agreement with the statistical model’s EDC.
The results for all source-receiver pairs in the coupled volume conﬁguration are summarized in Fig. 4. The
remarks made earlier in the comparison between the physical model and the statistical model still apply in thiscase. Of primary interest are the decay rates of the different simulations, which approach those of the statisticalmodel. For the main volume, DT1 of entries A,C, D, I, J, K show good agreement with the statistical model,
while the remaining entries over estimated it. The scale results are slightly higher than the statistical model, but
not to the same degree. In almost perfect contrast, those performing well for DT1 signiﬁcantly underestimatedDT2 , while the remaining entries, except H, provided comparable values to the statistical model.
Regarding the bending point, those methods correctly modelling DT2 also matched the statistical model of
BPt , while the remaining entries result tend more towards the results of the scale model. Regarding BPL , allmethods overestimated with respect to the statistical model, with the same group A,C, D, I, J, K resembling more
the results of the scale model.
The differences present for the uncoupled calibration phase are found in the coupled decay times as a generaltrend, but it is noted that entries with the highest calibration differences did not have the most extreme parameter
predictions, e.g. entry I. In addition, entry H appears to have a signiﬁcantly stronger direct sound component(see Fig. 3) which accounts for it being a relative outlier for BPL .
Regarding trends across similar methods, while maintaining anonymity, it can be said that Wave-based methods
were relatively consistent with respect to double-slope parameter results. The commonalities of the remaining
methods makes it difﬁcult to separate them further in any attempt to explain the observed data groupings.
Variances for parameter DT1 are smaller than observed for the measured data, except for entry J. For otherparameters, numerical simulations exhibit larger variances, except entries H and I; entries B and D have similarvariances compared to measurements. All entries simulated the 8 source-receiver pairs, except K that only usedsource S1. Considering the same positions, this entry has a higher variance only for DT2 .

4

CONCLUSION

This study presented a simpliﬁed test case to compare the ability of various numerical methods for room acoustic simulations to reproduce or predict classical coupled volume behavior. Contrary to a previous study in

6056

1.8
4

3.5

1.4

DT2 (s)DT1 (s)

1.6

1.2
1

3
(a)
2.5

0.8
0.9

A

B

C

D

E

F

G

H

I

J

K

Entry

C

D

E

F

G

H

I

J

K

Entry
(d)

-22

BPL (dB)

BPt (s)

B

-20

0.7

-24

0.6

-26

0.5

0.3

A
-18

0.8

0.4

(b)

-28
(c)

A

-30
B

C

D

E

F

Entry

G

H

I

J

K

-32

A

B

C

D

E

F

G

H

I

J

K

Entry

Figure 4. Comparison of resulting acoustical parameters from simulated RIRs. Individual S-R pairs are shown,including 95 % conﬁdence intervals (in red) and 1 Standard deviation (in blue). Black dashed lines represent
predicted values from the statistical model.
2013 [8], these results show that the tested methods are capable of representing coupled volume behavior, although not all results are consistent with statistical theory or comparable to measurements. Comparisons ofmethods shows the range of values (variance) across the 8 source-receive pairs varies signiﬁcantly, potentiallyhighlighting issues regarding local variations being poorly represented for some methods.
Perceptual thresholds regarding double-slope decay parameters have been examined [23]. For a system of coupled volumes with a conﬁguration comparable to the one used in the present work, just noticeable differenceswere around 10 % for DT1 and 20 % for DT2 , BPt , and BPL . Overall, differences observed among simulations
exceeded these thresholds for at least one parameter compared with the statistical or the physical model.
We are now examining the feasibility of the next phase of this study, providing a more detailed geometricalmodel with speciﬁc material properties determined though laboratory measurements. Such input data should
allow for direct comparisons of simulated results to the physical scale model, which is not appropriate in thecurrent study due to the simpliﬁcations in the model and homogeneous application of material properties.

ACKNOWLEDGEMENTS
The authors would like to thank all those who took time out of their schedules to participated in this study.

REFERENCES[1] Vorländer, M. International round robin on room acoustical computer simulation, Proc of 15th International
Congress on Acoustics, Trondheim, May, 1995, pp 577-580.

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[2] Bork, I. A comparison of room simulation software - The 2nd round robin on room acoustical computer
simulation, Acta Acust Acust, Vol 86, 2000, pp 740-752.
[3] Bork, I. Report on the 3rd round robin on room acoustical computer simulation - Part I: Measurements,
Acta Acust Acust, Vol 91, 2005, pp 740-752.
[4] Bork, I. Report on the 3rd round robin on room acoustical computer simulation - Part II: Calculations, Acta
Acust Acust, Vol 91, 2005, pp 753-763.
[5] Cremer, L.; Müller, H.A. Principles and Applications of Room Acoustics, Vol 1, Applied Science Publishers,
New York (USA), 1982.
[6] Summers, J.A. Technical note: Remark on the formal identity of two statistical-acoustics models of coupledrooms, Building Acoustics, Vol 12(1), 2005, pp 41-50.
[7] Luizard, P.; Katz, B.F.G. Coupled volume multi-slope room impulse responses: a quantitative analysis
method, Proc Intl Conf on Auditorium Acoustics, Inst of Acous, Dublin, May, 2011, pp 169-176.
[8] Luizard, P.; Otani, M.; Botts, J.; Savioja, L.; Katz, and B.F. Comparaison of the sound ﬁeld measurements
and prediction in coupled volumes between numerical methods and scale model measurements, Proc of
Meetings on Acoustics, Vol 19, 2013.
[9] Luizard, P.; Polack, J.-D.; Katz, B.F. Sound energy decay in coupled spaces using a parametric analyticalsolution of a diffusion equation, J Acous Soc Am, Vol 135, 2014, pp 2765–2776.
[10] Xiang, N.; Goggans, P.M. Evaluation of decay times in coupled spaces: Bayesian parameter estimation, J
Acous Soc Am, Vol 110(3), 2001, pp 1415-1424.
[11] Picaut J.; Fortin N. SPPS, a particle-tracing numerical code for indoor and outdoor sound propagation
prediction. Proc Acoustics 2012, Nantes, April, 2012, pp 1423-1428.
[12] Kowalczyk, K.; van Walstijn, M. Room acoustics simulation using 3-D compact explicit FDTD schemes,IEEE Trans Audio Speech Language Proc, Vol 19, 2011, pp 34-46.
[13] Tsuchiya, T.; Maruta, N.Three-dimensional compact explicit-ﬁnite difference time domain scheme withdensity variation. Japanese Journal of Applied Physics, Vol 57(7S1) 2018, pp 07LC01-1-6.
[14] Bilbao, S.; Hamilton, B. Wave-based room acoustics simulation: explicit/implicit ﬁnite volume modelingof viscothermal losses and frequency-dependent boundaries, J Aud Eng Soc, Vol 65(1), 2017, pp 78-89.
[15] Farina, A. RAMSETE - a new Pyramid Tracer for medium and large acoustic problems, Proc Euronoise,
Lyon, March, 1995.
[16] CATT-Acoustic, TUCTTM v2.0a User’s manual, 2016.
[17] Odeon A/S, ODEON Room Acoustics Software User’s manual Version 15, 2018.
[18] Schröder, D. Physically based real-time auralization of interactive virtual environments, Ph.D. thesis,
RTWH Aachen, 2011.
[19] Schröder, D.; Vorländer, M. RAVEN: A real-time framework for the Auralization of interactive virtualenvironments, Proc Forum Acusticum, Aalborg, June, 2011, pp 1541-1546.
[20] Stephenson U. Simulation of multiple Sound Particle Diffraction based on the Uncertainty Relation - arevolution in noise immission prognosis; Part I: Principle and Method, Proc Euronoise, Heraklion, May,
2018, pp 2063-2076.
[21] Stephenson, U. M. An energetic approach for the simulation of diffraction within ray tracing based on theuncertainty relation, Acta Acust Acust, Vol 96 (3), 2010, pp 516–535.
[22] Katz, B.F.G. International round robin on room acoustical impulse response analysis software 2004, Applied Research Letters Online, Vol 5, 2004, pp 158–164.
[23] Luizard, P.; Katz, B. F.; Guastavino, C. Perceptual thresholds for realistic double-slope decay reverberationin large coupled spaces, J Acous Soc Am, Vol 137(75), 2015, pp 75–84.

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