Diffuse Reflections in Room Acoustics Modelling

103 Pages·2005·1.39 MB·English

HELSINKIUNIVERSITYOFTECHNOLOGY
DepartmentofElectrical andCommunications Engineering
Laboratory ofAcousticsandAudioSignalProcessing
HeliNironen
Diffuse Reflections in Room Acoustics Modelling
Master’s Thesis submitted in partial fulfillment of the requirements for the degree of
MasterofScienceinTechnology.
Espoo,October12,2004
Supervisor: ProfessorMattiKarjalainen
Instructor: D.Sc. (Tech.) TapioLokki
HELSINKIUNIVERSITY ABSTRACT OFTHE
OFTECHNOLOGY MASTER’S THESIS
Author: HeliNironen
Nameofthethesis: DiffuseReflectionsinRoomAcousticsModelling
Date: October12,2004 Numberofpages: 92
Department: ElectricalandCommunications Engineering
Professorship: S-89AcousticsandAudioSignalProcessing
Supervisor: Prof. MattiKarjalainen
Instructor: D.Sc. (Tech.) TapioLokki
Thisthesisisastudyofdiffusereflectionmodellinginroomacoustics. Theaimoftheworkisto
getfamiliarwiththemostoftenappliedphysicalprinciples andmodellingmethods. Anobjec-
tive is that the studied theory and techniques could be applied in future research work. Room
acoustics modelling methods are divided in this thesis into three categories: 1. Ray-based
methods, 2. Radiosity, and 3. Wave-based methods. When considering different modelling
methods, emphasis is on the ray- and radiosity-based approaches. Somewave-based methods
are also presented, but left out of more accurate examination. Although the approach in this
work is mainly physically-based, one totally perceptually-based method is also presented. A
simple implementation is carried out in order to get familiar with the studied principles and
methods in practice. An early response is predicted with a model which combines the image
source method and theradiosity-based approach. Theimplemented system isdescribed inde-
tail, and the modelling results are analysed. Finally, methods most applicable for estimating
acousticalqualityofaroom,methodsmostsuitableforauralisationpurposes,andrequirements
ofreal-timedynamicsystemsarediscussed.
Keywords: diffuse reflection, scattering, room acoustics modelling, ray-based modelling
methods, radiosity, auralisation
i
TEKNILLINENKORKEAKOULU DIPLOMITYÖN TIIVISTELMÄ
Tekijä: HeliNironen
Työnnimi: Diffuusitheijastukset huoneakustiikan mallinnuksessa
Päivämäärä: 12.10.2004 Sivuja: 92
Osasto: Sähkö-jatietoliikennetekniikka
Professuuri: S-89Akustiikka jaäänenkäsittelytekniikka
Työnvalvoja: ProfessoriMattiKarjalainen
Työnohjaaja: TkTTapioLokki
Tässädiplomityössätarkastellaandiffuusienheijastustenmallinnustahuoneakustiikassa. Työs-
sä käydään läpi äänen etenemiseen liittyviä käsitteitä, periaatteita ja tunnetuimpia mallinnus-
menetelmiä. Tavoitteena on, että opiskeltua teoriapohjaa voitaisiin hyödyntää myöhemmin ai-
heeseen liittyvässä tutkimuksessa. Huoneakustiikan mallinnuksessa käytetyt menetelmät jao-
tellaantässätyössäkolmeenryhmään. Ensimmäisenryhmänmenetelmissä ääniaaltojen etene-
minen mallinnetaan äänisäteiden avulla. Toisen ryhmän muodostavat radiositeettimenetelmät,
joissaääntäheijastellaandiffuusistihuoneenseiniinmuodostetunverkonsolmujenvälillä.Kol-
mannen ryhmän menetelmät perustuvat aaltoyhtälön ratkaisuun. Työn painopiste on kahteen
ensimmäiseen ryhmään kuuluvissa menetelmissä. Vaikka mallinnusmenetelmiä tarkastellaan-
kin enimmäkseen fysikaalisiin periaatteisiin tukeutuen, esitellään myös yksi menetelmä, joka
mallintaa diffuuseja heijastuksia ihmisen havitsemiseen perustuen. Työssä myös toteutetaan
yksinkertainen malli huonevasteen alkuosalle. Tässä sovelletaan kuvalähde- ja radiositeetti-
menetelmää. Toteutettu malli esitellään yksityiskohtaisesti ja sillä saatuja tuloksia analysoi-
daan. Myös työssä käsiteltyjen menetelmien soveltuvuutta erilaisiin tarkoituksiin kartoitetaan.
Teoriapohjan perusteella analysoidaan, mitämenetelmistä voidaan käyttää huoneen akustisten
ominaisuuksien arviointiin, mitkämenetelmistäsopivatparhaitenauralisaatioon jaminkälaisia
kompromisseja vaativatdynaamiset reaaliaikasysteemit.
Avainsanat:diffuusiheijastus, äänensironta,huoneakustiikan mallinnus,sädemenetelmät, ra-
diositeettimenetelmä, auralisaatio
ii
Acknowledgements
This Master’s thesis was carried out for the Uni-verse project at the Telecommunications
Software and Multimedia Laboratory, Helsinki University of Technology, during the year
2004.
Theworkwasinstructed byD.Sc. (Tech.) TapioLokki. IwouldliketothankTapioforhis
guidance. Hehas provided mewithmany valuable insights during the course ofthe work.
I also thank Tapio for his comments and suggestions on the structure and content of this
thesis. Hehaspatiently givenmefeedback onvariousversionsofthethesis.
I also want to thank my supervisor Prof. Matti Karjalainen for his helpful comments and
supportive discussions. Prof. Lauri Savioja I would like to thank for employing mein the
Uni-verseprojectandforproviding mewithaninteresting topicformythesis.
I would also like to give special thanks to Sami Kiminki, my co-worker in the Uni-verse
project, for numerous helpful discussions, valuable insights, and all the practical help that
he offered me during this work. Sampo Vesa and Iikka Olli, who have shared the office
withme,Iwouldliketothankforgoodcompanyandforarelaxedworkingenvironment.
Furthermore,IwishtothankmyfriendsforallthefunIhaveexperiencedwiththemduring
mystudies. SharafHameedIwanttothankforbringinganIndiancontribution tomycircle
offriends.
Finally, I would like to express my gratitude to my family. I want to thank my parents for
theirpatience,encouragement, andallthesupportthatIhavegotduringmyalmostendless
studies. Also, I would like to thank my dear sisters Satu and Kati for their contribution.
My beloved Teemu I deeply thank for his understanding, support, and love. His positive
attitudetowardslifehasencouraged meoverthepastfewyears.
Otaniemi,October12,2004,
HeliNironen
iii
Contents
Symbols ix
Abbreviations x
1 Introduction 1
2 Background 4
2.1 Characteristics ofSoundWaves. . . . . . . . . . . . . . . . . . . . . . . . 4
2.1.1 VelocityofSound . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1.2 SomeBasicRelations . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.3 PlaneWaves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1.4 SphericalWaves . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.5 EnergyandEnergyDensity . . . . . . . . . . . . . . . . . . . . . 8
2.1.6 Intensity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 ReflectionofSound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.1 PrincipalLawsofSoundReflection . . . . . . . . . . . . . . . . . 10
2.2.2 Diffraction, Scattering, andDiffuseReflection . . . . . . . . . . . 13
2.2.3 DiffuseSoundField . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2.4 Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3 Expressing SurfaceDiffusion . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3.1 Lambert’sLaw . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3.2 Theoretically CalculatedScattering Functions . . . . . . . . . . . . 19
iv
2.3.3 Measured ScatteringFunctions . . . . . . . . . . . . . . . . . . . . 25
2.4 MainMethodsofRoomAcoustics Modelling . . . . . . . . . . . . . . . . 27
2.4.1 GeneralIssuesaboutRoomAcoustics Modelling . . . . . . . . . . 27
2.4.2 Ray-BasedModelling Methods . . . . . . . . . . . . . . . . . . . 29
2.4.3 Radiosity Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.4.4 Wave-BasedMethods . . . . . . . . . . . . . . . . . . . . . . . . . 34
3 ModellingDiffuseReflections 37
3.1 MethodsBasedonRayTracing . . . . . . . . . . . . . . . . . . . . . . . . 37
3.2 CombiningBeamTracingandRadiosity . . . . . . . . . . . . . . . . . . . 40
3.3 Approach BasedontheApproximateConeTracing . . . . . . . . . . . . . 43
3.4 UtilisingSchroeder Diffusersin2D . . . . . . . . . . . . . . . . . . . . . 48
3.5 Perceptually-Based Approach . . . . . . . . . . . . . . . . . . . . . . . . 51
4 ExperimentalPart 56
4.1 Implemented System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.1.1 Modelling ofSpecularReflectionResponse . . . . . . . . . . . . . 57
4.1.2 Modelling ofDiffuseReflectionResponse . . . . . . . . . . . . . . 64
4.1.3 CombiningSpecularandDiffuseReflectionResponses . . . . . . . 69
4.2 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.2.1 EffectoftheScattering Coefficient . . . . . . . . . . . . . . . . . . 70
4.2.2 EffectofthePatchSize . . . . . . . . . . . . . . . . . . . . . . . . 72
4.2.3 Discussion aboutImplementation . . . . . . . . . . . . . . . . . . 72
5 Discussion 76
5.1 DiffuseReflectionModelling whenPredicting Acoustical
QualityofaRoom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.2 DiffuseReflectionsinContextofAuralisation . . . . . . . . . . . . . . . . 79
5.3 Real-timeDynamicDiffuseReflectionModelling . . . . . . . . . . . . . . 81
6 ConclusionsandFutureWork 83
v
Symbols
a Attenuation constant
b Numberofzeroesinanallpassfilter
c Velocityofsound
d Diffusioncoefficient
d ActualdepthofthenthwellinaSchroederdiffusor
n
f Frequency
g Numberofgridnodesonasurface
h Numberoftriangular beamsemittedfromagridnode
i √ 1
−
i Symbolofsurfaceelement
j Symbolofsurfaceelement
k Wavenumber
k Specularreflectionscalar
s
k Diffusereflectionscalar
d
k Variabledetermining levelofdiffusedreflectioncomponents inaresponse
diff
l Integervariable
l ,l ,l CoefficientsrelatedtoLambert’slawincontextofimplemented system
sp pp pl
m Formfactorbetweensurfaceelements jandi
j i
→
n Surfacenormal
n Integervariable
n Totalnumberofnonempty patches
p
p Soundpressure
p Staticvalueofapressure
0
p Initialsoundpressure
0
p Soundpressure ofanincidentwave
i
p Soundpressure ofareflectedwave
r
p Soundpressure onpartially diffusing surfacereceiver
sc
p Soundpressure obtained fortotallydiffusely reflectingsurface
dif
vi
p Soundpressure obtained fortotally specularly reflectingsurface
spec
r Distancevariable
r Distancebetweenasoundsourceandasurfacepatch
sp
r Distancebetweentwosurfacepatches
pp
r Distancefromasurfacepatchtoalistener
pl
r Distancebetweensurfaceelements jandi
j i
→
r,r Locationvectorsofwallelements
0
r Locationvectorofareceiver
r
r Locationvectorofasource
0
r Locationvectorofapointonasurface
s
s Scattering coefficient
s RelativedepthofthenthwellinaSchroederdiffusor
n
t Time
v Valueofparticle velocity
v Particlevelocity
v Particlevelocity ofanincidentwave
i
v Particlevelocity ofareflectedwave
r
v Componentofparticlevelocity, radialone
rad
v Componentofparticlevelocity, paralleltox-axis
x
v Componentofparticlevelocity, normaltoawall
n
w Energydensity
w Energydensity, directcontribution fromsomesoundsourcetoareceiver
d
w Kineticenergydensity
kin
w Potentialenergy density
pot
x,y,z Locationvariables
x Locationvariableinarotatedcoordinate system
0
x Inputsignalincontextofallpassfilter
y Outputsignalincontextofallpassfilter
x ,y ,z Locationvariables ofareceiver
r r r
x ,y ,z Locationvariables ofasource
0 0 0
x ,y ,z Locationvariables ofapointonasurface
s s s
z Acousticimpedance ofacapataclosedendofapipe
d
A Areaofanemittingsurface
es
A Areaofareceiving surface
rs
D A Areaofanelementinasurfacewhichisemittingsound
es
A Cross-sectional areaofabeam
i
A Areaofasurface, visiblefromareceiver
vis
vii
B Irradiation strength
B Irradiation strength, directcontribution fromasoundsourcetoareceiver
d
E Energy
E Initialenergy atasoundsource
0
E Energyarrivingtoalistener
l
E Energyarrivingtoasinglepatch
p
ENV Envelope ofanallpassfilter
G Green’sfunction
I Intensity
I Intensity ofanincident wave
0
I Incident soundintensity atasurface elementi
i
I Intensity, contribution fromasinglesurfaceelement jtoasurfaceelementi
j
I Directcontribution fromsomesoundsourceatasurfaceelementi
0 i
→
dI Intensity ofenergyre-radiated betweensurface elements
I Surfaceintensity
∗
I Intensity atareceiver
R
K Constant
L Straightlineconnecting twosurfaceelements
L Straightlineconnecting asurfaceelementandareceiver
0
M Non-negative oddprimenumber
N Integervariable
P Pointinsidearoom
P Powerofabeamemanating fromanimagesource
i
P Powerofabeamemanating fromasource
s
Q Volumevelocity
R Reflectionfactor
R Energyreflectionfactor
e
RG Exteriorregion,external toasurface
e
RG Regioninasurface
s
RG Interior region,internal toasurface
i
R Specularreflection
s
R Diffusereflection
d
D R Anareaofasurfacereceiver
S Areaofasurface
dS,dS’ Surfaceareaelements
D S Areaofsurface element
T Periodoftime
viii
V Pressurewave,travelling inpositivex-direction
W Pressurewave,travelling innegativex-direction
X Randomnumber
Z Wallimpedance
Z Impedanceatanentrance ofnthpipeincontextofSchroederdiffusor
n
a Absorptioncoefficient
b Surfaceadmittance, outwardpointing surfacenormal
b Surfaceadmittance, inwardpointingsurface normal
0
c Phaseangleofreflectionfactor
g Splittingcoefficient
k Adiabaticexponent
l Designwavelength ofaSchroederdiffusor
0
µ Optimumdecayrateofanallpass filter.
w Angularfrequency
y Coefficientofanallpassfilter.
r Gasdensity
r Staticvalueofagasdensity
0
s Reflectioncoefficient
s Energyreflectioncoefficientatsurfaceelementj
j
q Angleofanincident wave
0
q Angleofareflectedwave
q Angleofsoundraywhichilluminatessurface elementi
i
q Angleofsoundraywhichirradiatesfromsurfaceelement j
j
q Angleofsoundraywhichirradiatesfromsurfaceelementtoreceiver
r
q Angleofanincident wave,fromsourcetopatch
sp
q Angleofreflectedwave,frompatchtolistener
pl
q Angleofreflectedwave,frompatchtoanother patch
pp
V AnglebetweenLandsurfacenormalatsurface elementdS
V AnglebetweenLandsurfacenormalatsurface elementdS’
0
V AnglebetweenL andsurfacenormalatsurfaceelementdS
00 0
z Specificacoustic impedance
W Solidanglepresented byasurfacetoareceiving point
DW Asolidanglethatithbeamencloses inbeamtracing
i
Q Temperature
ix