University of Parma

A A ngelo ngelo Farina Farina , Paolo , Paolo Martignon Martignon , Andrea Capra, , Andrea Capra, Simone Fontana

Simone Fontana

Industrial Engineering Dept.

Industrial Engineering Dept.

University of Parma

University of Parma - - ITALY ITALY HTTP://

HTTP://www.angelofarina.it www.angelofarina.it

University of Parma

Measuring impulse Measuring impulse

responses containing responses containing

complete spatial information complete spatial information

4th Joint Meeting of the Acoustical Society of America

and the

Acoustical Society of Japan 28 November--2 December

ƒ Directional transducers, the first attempts of spatial analysis

ƒ Orthonormal decomposition of the spatial properties in spherical harmonics: the Ambisonics method

ƒ The reciprocity principle: directive microphones and directive sources

ƒ Generalization of higher-order spherical harmonics representation of both source and receiver directivity

ƒ Joining time and space: from Einstein’s view to a

comprehensive data structure representing the acoustical transfer function of a room

ƒ Practical usages of measured (or numerically simulated) temporal-spatial impulse responses

Topics

Basic

Basic sound sound propagation propagation scheme scheme

Omnidirectional receiver Direct Sound

Reflected Sound

Point Source

Direct Sound

Reverberant tail

Hardware:

Hardware: loudspeaker loudspeaker & & microphone microphone

Dodechaedron loudspeaker Omnidirectional

microphone

Aurora Plugins

Generate MLS Generate MLS

Deconvolve DeconvolveMLSMLS

Generate Sweep Generate Sweep

Deconvolve

DeconvolveSweepSweep

Convolution Convolution

Kirkeby

KirkebyInverse FilterInverse Filter

Speech

Speech TransmTransm. Index. Index

Software

Spatial

Spatial analysis analysis by by directive directive microphones microphones

ƒ ƒ The initial The initial approach approach was was to to use use directive directive microphones microphones for for gathering gathering some some information

information about about the spatial the spatial properties properties of of the sound the sound field field “as “ as perceived perceived by by the listener the listener” ”

ƒ ƒ Two Two apparently apparently different different approaches approaches emerged: emerged : binaural binaural dummy dummy heads heads and and pressure

pressure- -velocity velocity microphones: microphones :

Binaural Binaural microphone

microphone (left ( left ) )

and and

variable

variable- -directivity directivity microphone

microphone (right) (right)

“ “ objective objective ” ” spatial spatial parameters parameters

ƒ ƒ It It was was attempted attempted to to “quantify “ quantify” ” the “ the “spatiality spatiality” ” of of a room a room by by means means of of

“objective “ objective” ” parameters, parameters , based based on 2- on 2 -channels channels impulse impulse responses responses measured measured with with directive directive microphones microphones

ƒ ƒ The most The most famous famous “spatial “ spatial” ” parameter parameter is is IACC (Inter Aural IACC (Inter Aural Cross Cross Correlation

Correlation), ), based based on binaural on binaural IR measurements IR measurements

LeftLeft

Right Right

80 ms 80 ms

( )

( ) ( )

( ) ( )

p p_LL(τ(τ))

pp_RR((ττ))

[ ] ( ) ^{t t} [ ^{1 ms ... 1 ms} ]

Max IACC

d t p

d p

d t p

p

t

ms 80

0 2R ms

80

0 2L ms 80

0

R L

+

−

∈ ρ

= τ

⋅ + τ

⋅ τ

⋅ τ

τ

⋅ + τ

⋅ τ

= ρ

∫

∫

∫

“ “ objective objective ” ” spatial spatial parameters parameters

ƒ ƒ Other Other “spatial “ spatial” ” parameters parameters are the Lateral are the Lateral Energy ratios Energy ratios: LE, LF, LFC : LE, LF, LFC

ƒ ƒ These These are defined are defined from from a 2- a 2 -channels channels impulse impulse response, the first response , the first channel channel is is a a standard

standard omni omni microphone microphone , the second , the second channel channel is is a a “figure “ figure- -of of- -eight eight ” ” microphone

microphone: :

( ) ( )

∫ ( )

∫

τ

⋅ τ

τ

⋅ τ

⋅ τ

= 80 ms

ms 0

o 2 ms 80

ms 5

o 8

d h

d h

h LFC

Figure Figure

ofof88 OmniOmni

( )

∫ ( )

∫

τ

⋅ τ

τ

⋅ τ

= 80 ms

ms 0

o 2 ms 80

ms 5

8 2

d h

d h

LF

h h_oo(τ(τ))

hh₈₈((ττ))

( )

∫ ( )

∫

τ

⋅ τ

τ

⋅ τ

= 80 ms

ms 0

o 2 ms 80

ms 25

8 2

d h

d h

LE

Are Are binaural binaural measurents measurents reproducible reproducible ? ?

ƒ ƒ Experiment Experiment performed performed in anechoic in anechoic room room - - same same loudspeaker loudspeaker , same , same source source

and receiver and receiver positions, 5 positions , 5 binaural binaural dummy dummy heads heads

Are Are binaural binaural measurents measurents reproducible reproducible ? ?

ƒ ƒ Diffuse field Diffuse field - - the difference the difference between between the heads the heads is is now now dramatic dramatic

IACCe - random incidence

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

31.5 63 125 250 500 1000 2000 4000 8000 16000

Frequency (Hz)

IACCe

B&K4100 Cortex Head Neumann

Are LF

Are LF measurents measurents reproducible reproducible ? ?

ƒ ƒ Experiment Experiment performed performed in the Auditorium of in the Auditorium of Parma - Parma - same same loudspeaker, loudspeaker ,

same same source and receiver source and receiver positions, 5 positions , 5 pressure- pressure -velocity velocity microphones microphones

Are LF

Are LF measurents measurents reproducible reproducible ? ?

ƒ ƒ At 25 m distance At 25 m distance, the , the scatter scatter is is even even larger.... larger ....

Comparison LF - measure 2 - 25m distance

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

31.5 63 125 250 500 1000 2000 4000 8000 16000

Frequency (Hz)

LF

Schoeps Neumann Soundfield B&K

3D extension 3D extension of of the the pressure- pressure -velocity velocity measurements measurements

ƒ ƒ The Soundfield The Soundfield microphone microphone allows allows for for simultaneous simultaneous measurements measurements of of the the omnidirectional

omnidirectional pressure pressure and of and of the three the three cartesian cartesian components components of of particle particle velocity

velocity (figure- (figure -of of- -8 8 patterns patterns) )

3D 3D Impulse Impulse Response Response ( ( Gerzon Gerzon , 1975) , 1975)

Portable PC with 4- channels sound board Original Room

Sound Source

SoundField Microphone

B-format 4-channels signal (WXYZ) Measurement of B-format

Impulse Responses

MLS or sweep excitation signal

Convolution of dry signals with the B-format Impulse

Responses Sound Source

Mono Mic.

B-format Imp. Resp.

of the original room

B-format 4-channels signal (WXYZ) Convolver

Ambisonics decoder

Speaker array in the reproduction room

Directivity

Directivity of of transducers transducers

Soundfield

Soundfield ST- ST -250 250 microphone microphone

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

0

30

60

90

120

150 180

210 240 270

300 330

125 Hz

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

0

30

60

90

120

150 180

210 240 270

300 330

250 Hz

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

0

30

60

90

120

150 180

210 240 270

300 330

500 Hz

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

0

30

60

90

120

150 180

210 240 270

300 330

1000 Hz

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

0

30

60

90

120

150 180

210 240 270

300 330

2000 Hz

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

0

30

60

90

120

150 180

210 240 270

300 330

4000 Hz

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

0

30

60

90

120

150 180

210 240 270

300 330

8000 Hz

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

0

30

60

90

120

150 180

210 240 270

300 330

16000 Hz

What What about about source source directivity directivity ? ?

ƒ ƒ Current Current 3D IR 3D IR sampling sampling is is still still based based on the usage on the usage of of an an “omnidirectional “ omnidirectional” ” source

source

ƒ ƒ The knowledge The knowledge of of the 3D IR measured the 3D IR measured in in this this way provide way provide no information no information about

about the soundfield the soundfield generated generated inside the room inside the room from from a directive a directive source source (i.e., a musical

(i.e., a musical instrument instrument , a singer, etc.) , a singer, etc.)

ƒ ƒ Dave Dave Malham Malham suggested suggested to to represent represent also also the source directivity the source directivity with with a set a set of of spherical spherical harmonics, harmonics , called called O- O -format format - - this this is is perfectly perfectly reciprocal reciprocal to to the the representation

representation of of the microphone the microphone directivity directivity with with the B the B- -format format signals signals (Soundfield ( Soundfield microphone). microphone ).

ƒ ƒ Consequently Consequently , a complete and reciprocal , a complete and reciprocal spatial spatial transfer function transfer function can be can be defined

defined, , employing employing a 4- a 4 -channels channels O O- -format format source and a 4- source and a 4 -channels channels B B- - format

format receiver: receiver :

Portable PC with 4in-4out channels sound board O-format 4-channels source

B-format 4-channels microphone (Soundfield)

1st 1st order order MIMO MIMO impulse impulse response response

ƒ ƒ If If only only spherical spherical harmonics harmonics of of order order 0 and 1 are taken 0 and 1 are taken into into account, account, a complete

a complete spatial spatial transfer function transfer function measurement measurement requires requires 16 impulse 16 impulse responses: responses :

{ } ^y [ ] ^h { } ^x

or x

x x x

h h

h h

h h

h h

h h

h h

h h

h h

y y y y

z y x w

zz zy

zx zw

yz yy

yx yw

xz xy

xx xw

wz wy

wx ww

z y x w

⊗

=

⎪ ⎪

⎭

⎪ ⎪

⎬

⎫

⎪ ⎪

⎩

⎪ ⎪

⎨

⎧

⊗

⎥ ⎥

⎥ ⎥

⎥

⎦

⎤

⎢ ⎢

⎢ ⎢

⎢

⎣

⎡

=

⎪ ⎪

⎭

⎪ ⎪

⎬

⎫

⎪ ⎪

⎩

⎪ ⎪

⎨

⎧

ƒ ƒ Once these Once these 16 16 IRs IRs have have been been measured, measured , it it is is possible possible to to compute compute the response the response of of the room the room with with a source and a receiver a source and a receiver having having

arbitrary

arbitrary directivity directivity patterns, patterns , given given by by the O the O- -format format source functions source functions {r { r

, r , r

, r , r

, r , r

}, and the B }, and the B- -format format receiver receiver functions functions {r { r

, r , r

, r , r

, r , r

}: }:

{ } { } { } ^{r y r} [ ] ^h { } ^s

t _sr = ⊗ = ⊗ ⊗

ƒ ƒ In In which which also also each each of of {s} and {r} are sets {s} and {r} are sets of of 4 impulse 4 impulse responses, responses , representing

representing the frequency the frequency- -dependent dependent directivities directivities of of the source the source

and and of of the receiver the receiver

Limits

Limits of of the 1 the 1 ^{st st} - - order order method method

ƒƒ AlbeitAlbeitmathematicallymathematicallyelegantelegantand easy toand easy to implementimplementwithwithcurrently-currently-existingexistinghardware, hardware, the 1

the 1^stst-order -order methodmethod presentedpresentedhereherecannotcannot representrepresent faithfullyfaithfullythe the complexcomplex directivitydirectivity pattern

pattern ofofananhumanhumanvoice or ofvoice or ofananhumanhumanear:ear:

-20 -15 -10 -5 0 5

0

15

30

45

60

75

90

105

120

135

150 165

180 195

210 225 240 255 270

285 300

315 330

345

Real

1st order approx.

W X Y

1.421 0.289 0.000

Limits

Limits of of the 1 the 1 ^{st st} - - order order method method

ƒƒ The polarThe polar pattern ofpattern ofa a binauralbinauraldummydummyhead ishead isevenevenmore complexmore complex, , asas shownshown herehere(1 kHz, right ear(1 kHz, right ear):):

-20 -15 -10 -5 0

0

5 10 15 20 2530

35 40

45 50

55 60

65 70

75 80

85 90 95 100 105 110 115 120 125 130 135 140 150145 160155 170165 175 190185

200195 210205 215 220 225 230 235 240 245 250 255 260 265 270 275 280

285 290

295 300

305 310

315

320325330335340345350355

Measured

W X Y

0.395 -0.015 0.191

How to get better spatial resolution?

How to get better spatial resolution?

ƒƒ The answer is simple: analyze the spatial distribution of both source and receiver by The answer is simple: analyze the spatial distribution of both source and receiver by means of higher

means of higher--order spherical harmonics expansionorder spherical harmonics expansion

ƒƒ Spherical harmonics analysis is the equivalent, in space domain,Spherical harmonics analysis is the equivalent, in space domain,of the Fourier of the Fourier analysis in time domain

analysis in time domain

ƒ

ƒ As a complex time-As a complex time-domain waveform can be thought as the sum of a number of domain waveform can be thought as the sum of a number of sinusoidal and cosinusoidal functions, so a complex spatial dist

sinusoidal and cosinusoidal functions, so a complex spatial distribution around a ribution around a given notional point can be expressed as the sum of a number of

given notional point can be expressed as the sum of a number of spherical harmonic spherical harmonic functions

functions

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

0 0.5 1 1.5 2 2.5 3

dc Cos(5) Sin(5) Cos(10) Sin(10)

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

0 0.5 1 1.5 2 2.5 3

Sum

-20 0 0

5 10 1520 25

30 35

40 45

50 55

60 65

70 75

80 85 90 95 100 105 110 115 120 125 130 135 140 145 215

220 225 230 235 240 245 250 255 260 265 270 275 280 285 290

295 300

305 310

315 320

325

330335340345 350355 0

0.35 0

5 10 1520 25

30 35

40 45

50 55

60 65

70 75

80 85 90 95 100 105 110 115 120 125 130 135 140 145 150 160155 170165 175 180 190185 200195 205 210 215 220 225 230 235 240 245 250 255 260 265 270 275 280 285

290 295

300 305

310 315

320 325

330335340345350355

Higher

Higher - - order spherical harmonics expansion order spherical harmonics expansion

Complete high

Complete high - - order MIMO method order MIMO method

ƒ ƒ Employing massive arrays of transducers, it is nowaday feasible to sample Employing massive arrays of transducers, it is nowaday feasible to sample the acoustical temporal

the acoustical temporal- -spatial transfer function of a room spatial transfer function of a room

ƒ ƒ Currently available hardware and software tools make this practical up to Currently available hardware and software tools make this practi cal up to 4° 4 ° order, which means 25 inputs and 25 outputs order, which means 25 inputs and 25 outputs

ƒ ƒ A complete measurement for a given source- A complete measurement for a given source -receiver position pair takes receiver position pair takes approximately 10 minutes (25 sine sweeps of 15s each are generat

approximately 10 minutes (25 sine sweeps of 15s each are generated one ed one after the other, while all the microphone signals are sampled

after the other, while all the microphone signals are sampled simultaneously)

simultaneously)

ƒ ƒ However, it has been seen that real- However, it has been seen that real -world sources can be already world sources can be already approximated quite well with 2

approximated quite well with 2° °- -order functions, and even the human HRTF order functions, and even the human HRTF directivites are reasonally approximated with 3

directivites are reasonally approximated with 3° °- -order functions. order functions.

Portable PC with 24in-24out channels external sound card 2°-order 9-loudspeakers

source (dodechaedron)

3°-order 24-capsules microphone array

3 3 ° ° - - order microphone (Trinnov order microphone (Trinnov - - France) France)

ƒ ƒ Arnoud Laborie developed a 24- Arnoud Laborie developed a 24 -capsule compact microphone capsule compact microphone array

array - - by means of advanced digital filtering, spherical ahrmonic by means of advanced digital filtering, spherical ahrmonic signals up to 3

signals up to 3° ° order are obtained (16 channels) order are obtained (16 channels)

4 4 ° ° - - order microphone (France Telecom) order microphone (France Telecom)

ƒ ƒ Jerome Daniel and Sebastien Moreau built samples of 32- Jerome Daniel and Sebastien Moreau built samples of 32 -capsules capsules spherical arrays

spherical arrays - - these allow for extraction of microphone signals up these allow for extraction of microphone signals up

to 4° to 4 ° order (25 channels) order (25 channels)

Multichannel software for high

Multichannel software for high- - order order

ƒƒ Plogue Bidule can be used as multichannel host software, runningPlogue Bidule can be used as multichannel host software, runninga number of VST a number of VST plugins developed by France Telecom

plugins developed by France Telecom --these include spherical harmonics extraction from these include spherical harmonics extraction from the spherical microphone arrays, rotation and manipulation of th

the spherical microphone arrays, rotation and manipulation of the multichannel Be multichannel B--format format signals, and final rendering either on head

signals, and final rendering either on head--.tracked headphones or on a static array of .tracked headphones or on a static array of loudspeakers (high

loudspeakers (high--order Ambisonics)order Ambisonics)

Verification of high

Verification of high - - order patterns order patterns

ƒ ƒ Sebastien Moreau and Olivier Warusfel verified the directivity p Sebastien Moreau and Olivier Warusfel verified the directivity p atterns of the atterns of the 4 4 °- ° -order microphone array in the anechoic room of IRCAM (Paris) order microphone array in the anechoic room of IRCAM (Paris)

5 kHz 5 kHz

10 kHz

10 kHz

High High - - order sound source order sound source

ƒ ƒ University of California Berkeley's Center for New Music and Audio University of California Berkeley's Center for New Music and Aud io Technologies (CNMAT) developed a new 120

Technologies (CNMAT) developed a new 120- -loudspeakers, digitally loudspeakers, digitally controlled sound source, capable of synthesizing sound emission controlled sound source, capable of synthesizing sound emission according to spherical harmonics patterns up to 5

according to spherical harmonics patterns up to 5° ° order. order.

Technical details of high

Technical details of high - - order source order source

ƒ ƒ Class- Class -D embedded amplifiers D embedded amplifiers

ƒ ƒ Embedded ethernet interface Embedded ethernet interface and DSP processing

and DSP processing

ƒ ƒ Long- Long -excursion special excursion special

Meyer Sound drivers

Meyer Sound drivers

Accuracy of spatial synthesis Accuracy of spatial synthesis

ƒ ƒ The spatial reconstruction error of a 120- The spatial reconstruction error of a 120 -loudspeakers array is frequency loudspeakers array is frequency dependant, as shown here:

dependant, as shown here:

Computer and sound card Computer and sound card

ƒ ƒ A complete 24 A complete 24 - - inputs, 24- inputs, 24 -outputs system can now assembled outputs system can now assembled for less than 2000 USD

for less than 2000 USD

ƒ ƒ Low Low - - noise PC case, RME Hammerfall sound card, 3 Behringer noise PC case, RME Hammerfall sound card, 3 Behringer Ultragain Pro

Ultragain Pro - - 8 digital converters slaved to the same master 8 digital converters slaved to the same master clock

clock

Advanced digital filtering techniques Advanced digital filtering techniques

ƒ ƒ A set of digital filters can be employed for sinthesizing the re A set of digital filters can be employed for sinthesizing the re quired quired spatial pattern (spherical harmonics), either when dealing with

spatial pattern (spherical harmonics), either when dealing with a a microphone array or when dealing with a loudspeaker array

microphone array or when dealing with a loudspeaker array

ƒ ƒ Whatever theory or method is chosen, we always start with N input Whatever theory or method is chosen, we always start with N inpu t signals x

signals x

, and we derive from them M output signals y , and we derive from them M output signals y

ƒ ƒ And, in any case, each of these M outputs can be expressed by: And, in any case, each of these M outputs can be expressed by:

i N

1 i

ij

j h x

y ∑

=

⊗

=

processor N inputs

M outputs

Example with a microphone array Example with a microphone array

ƒ ƒ The sound field is sampled in N points by means of a microphone array The sound field is sampled in N points by means of a microphone array

Is the time-domain sampled waveform of a wave with well defined spatial characteristics, for example:

• a spherical wave centered in a precise emission point P

• a plane wave with a certain direction

• a spherical harmonic referred to a receiver point P

Pre-calculated filters

i N

1 i

ij

j h x

y ∑

=

⊗

=

x

(t) x

(t) x

(t) x

(t)

y

(t)

Traditional design of digital filters Traditional design of digital filters

ƒ ƒ The processing filters h The processing filters h

are usually computed are usually computed following one of several, complex mathematical following one of several, complex mathematical

theories, based on the solution of the wave theories, based on the solution of the wave

equation (often under certaing simplifications), equation (often under certaing simplifications),

and assuming that the microphones are ideal and and assuming that the microphones are ideal and

identical identical

ƒ ƒ In some implementations, the signal of each In some implementations, the signal of each

microphone is processed through a digital filter microphone is processed through a digital filter

for compensating its deviation, at the expense of for compensating its deviation, at the expense of

heavier computational load

heavier computational load

Novel approach Novel approach

ƒ ƒ No theory is assumed: the set of h No theory is assumed: the set of h

filters are filters are derived directly from a set of impulse response derived directly from a set of impulse response

measurements, designed according to a least measurements, designed according to a least - -

squares principle.

squares principle.

ƒ ƒ In practice, a matrix of filtering coefficients, is In practice, a matrix of filtering coefficients, is formed, and the matrix has to be numerically formed, and the matrix has to be numerically

inverted (usually employing some regularization inverted (usually employing some regularization

technique).

technique).

ƒ ƒ This way, the outputs of the microphone array are This way, the outputs of the microphone array are maximally close to the ideal responses prescribed maximally close to the ideal responses prescribed

ƒ ƒ This method also inherently corrects for transducer This method also inherently corrects for transducer deviations and acoustical artifacts (shielding,

deviations and acoustical artifacts (shielding, diffractions, reflections, etc.)

diffractions, reflections, etc.)

Example: synthesizing 0

Example: synthesizing 0 - - order shape order shape

The microphone array impulse responses c

, are measured for a number of P incoming directions.

…we get the filters to be applied to the microphonic signals from processing the matrix of measured impulse responses

⎥ ⎥

⎥ ⎥

⎦

⎤

⎢ ⎢

⎢ ⎢

⎣

⎡

=

N , P N

, k N

, 2 N

, 1

i , P i

, k i

, 2 i

, 1

2 , P 2

, k 2

, 2 2

, 1

1 , P 1

, k 1

, 2 1

, 1

c c

c c

c c

c c

c c

c c

c c

c c

i=1…N mikes C

k=1…P sources

c

Example: synthesizing 0

Example: synthesizing 0 - - order shape order shape

δ

=

⊗

δ

=

⊗

δ

=

⊗

δ

=

⊗

∑

∑

∑

∑

=

=

=

N

i , P 0

, i N

1 i

i , k 0

, i N

1 i

i , 2 0

, i N

1 i

i , 1 0

, i

c h

...

c h

...

c h

c h

Lets call v

the right-hand vector of known results (they will be different for higher-order shapes).

Once this matrix of N inverse filters are computed (for example, employing the Nelson/Kirkeby method), the output of the

microphone array, synthesizing the prescribed 0th-order shape, will again be simply:

∑ =

⊗

= ^N

1 i

0 , i i

0 x h

y

We design the filters in such a way that the response of the system is the prescribed theoretical function v

for the k-th source (an unit- amplitude Dirac’s Delta function in the case of the example, as the 0th-order function is omnidirectional).

So we set up a linear equation system of P equations, imposing

that:

System

System ’ ’ s least s least - - squares inversion squares inversion

ƒ ƒ For computing the matrix of N filtering coefficients h For computing the matrix of N filtering coefficients h

, a least- , a least -squares squares method is employed.

method is employed.

ƒ ƒ A “ A “total squared error total squared error” ” ε ε

is defined as: is defined as:

( )

∑ ∑ = = ⎥ ⎥

⎦

⎤

⎢ ⎢

⎣

⎡ ⊗ −

=

ε ^P

1 k

2 k N

1 i

ki 0

i

tot h c v

ƒ ƒ A set of N linear equations is formed by minimising A set of N linear equations is formed by minimising ε ε _{tot tot} , , imposing that:

imposing that:

) N ...

1 i

( h _{i 0} 0

tot = =

∂ ε

∂

Example for a 4

Example for a 4 - - channel mike channel mike

ƒ ƒ DPA DPA - - 4 A 4 A - - format microphone format microphone

ƒ ƒ 4 closely 4 closely - - spaced cardioids spaced cardioids

ƒ ƒ A set of 4x4 filters is required A set of 4x4 filters is required for getting B

for getting B - - format signals format signals

ƒ ƒ Global approach for Global approach for

minimizing errors over the minimizing errors over the

whole sphere

whole sphere

IR measurements on the DPA IR measurements on the DPA - - 4 4

84 IRs were measured, uniformly

scattered around a sphere

Computation of the inverse filters Computation of the inverse filters

ƒ ƒ A set of 16 inverse filters is required A set of 16 inverse filters is required (4 inputs, 4 outputs = 1

(4 inputs, 4 outputs = 1° °- -order B order B- -format) format)

ƒ ƒ For any of the 84 measured directions, a theoretical For any of the 84 measured directions, a theoretical response can be computed for each of the 4 output response can be computed for each of the 4 output channels (W,X,Y,Z)

channels (W,X,Y,Z)

ƒ ƒ So 84x4=336 conditions can be set: So 84x4=336 conditions can be set:

W , k Z

, 4 4

Z , 3 3

Z , 2 2

Z , 1 1

Y , k Y

, 4 4

Y , 3 3

Y , 2 2

Y , 1 1

X , k X

, 4 4

X , 3 3

X , 2 2

X , 1 1

W , k W

, 4 4

W , 3 3

W , 2 2

W , 1 1

out h

c h

c h

c h

c

out h

c h

c h

c h

c

out h

c h

c h

c h

c

out h

c h

c h

c h

c

=

⊗ +

⊗ +

⊗ +

⊗

=

⊗ +

⊗ +

⊗ +

⊗

=

⊗ +

⊗ +

⊗ +

⊗

=

⊗ +

⊗ +

⊗ +

⊗

k = 1...84

Real Real - - time implementation time implementation

4 outputs

4 inputs

Conclusions Conclusions

ƒ ƒ Traditional methods for measuring “ Traditional methods for measuring “spatial parameters spatial parameters” ” proved to be unreliable and do not provide complete proved to be unreliable and do not provide complete information

information

ƒ ƒ The 1 The 1 ° ° - - order Ambisonics method can be used for order Ambisonics method can be used for

generating and recording sound with a limited amount of generating and recording sound with a limited amount of spatial information

spatial information

ƒ ƒ For obtaining better spatial resolution, High For obtaining better spatial resolution, High - - Order Order Ambisonics can be used, limiting the spherical

Ambisonics can be used, limiting the spherical - - harmonics harmonics expansion to a reasonable order (2

expansion to a reasonable order (2 ° ° , 3 , 3 ° ° or 4 or 4 ° ° ). ).

ƒ ƒ Experimental hardware and software tools have been Experimental hardware and software tools have been

developed (mainly in France, but also in USA), allowing to developed (mainly in France, but also in USA), allowing to build an inexpensive complete measurement system

build an inexpensive complete measurement system

ƒ ƒ From the complete matrix of measured impulse responses it From the complete matrix of measured impulse responses it is easy to derive any suitable subset, including an highly is easy to derive any suitable subset, including an highly accurate binaural rendering over head

accurate binaural rendering over head- -tracked headphones. tracked headphones.

Auralization Example #1 Auralization Example #1

ƒƒ Anecoic room, one source, one Anecoic room, one source, one receiver

receiver

SS

RR xx

yy

xx

yy

Gains for IR Matrix Gains for IR Matrix

W W X X Y Y Z Z

W W 1 1 -1 - 1 0 0 0 0

X X 1 1 -1 - 1 0 0 0 0

Y Y 0 0 0 0 0 0 0 0

Z Z 0 0 0 0 0 0 0 0

Source Directivity Source Directivity

ƒ ƒ The frequency- The frequency -dpendent directivity of the human voice has dpendent directivity of the human voice has been approximated with first

been approximated with first- -order components: order components:

Human Voice Directivity

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

63 125 250 500 1000 2000 4000 8000 16000

Frequency (Hz)

Gain W

X

Auralization

Auralization Example Example #2 #2

ƒƒ ReverbersntReverbersntroom, room, oneone source, onesource, one receiver

receiver

SS

RR xx

yy

xx

yy

Gains

Gains for for IR Matrix IR Matrix

W W X X Y Y Z Z W W h h _{WW WW} h h _{XW XW} h h _{YW YW} h h _{ZW ZW}

X X h h _{WX WX} h h _{XX XX} h h _{YX YX} h h _{ZX ZX}

Y Y h h _{WY WY} h h _{XY XY} h h _{YY YY} h h _{ZY ZY}

Z Z h h _{WZ WZ} h h _{XZ XZ} h h _{YZ YZ} h h _{ZZ ZZ}