Reverberation Algorithms

Post on 06-Apr-2018

235 views 0 download

Transcript of Reverberation Algorithms

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 1/123

Reverberation

algorithms

Augusto Sarti

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 2/123

Summaryn 

The Reverb Problemn  Reverb Perceptionn  Acoustic impulse response:

¨  Formation mechanisms

¨  Parameters

n  Early Reflections

n  Late Reverbn  Numerical reverberation algorithms

¨  Schroeder Reverbs

¨  Feedback Delay Network (FDN) Reverberators

¨  Waveguide Reverberators

n Geometrical reverberation algorithms

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 3/123

Impulse response

n  The sounds we perceive heavily depend on thesurrounding environment

n  Environment-related sound changes are of 

convolutive origin (filtering)

¨ Well-modeled by a space-varying impulse response

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 4/123

Direct

signal Early

reflections Reverberations 

Time 

   A  m

  p   l   i   t  u   d  e

Impulse response

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 5/123

Reverberation tf Function

n  Three sources, onelistener (two ears)

n  Filters should include

pinnae filtering

n  Filters change if anything

in the room changes

(exact model)

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 6/123

Global descriptorsn  Energy decay curve (EDC)

¨  Introduced by Schroeder to define reverberation time

¨  It measures the total signal energy remaining in thereverberator’s impulse response at time t 

¨  It decays more smoothly than the impulse response, therefore itworks better than the amplitude’s envelope for defining thereverberation time

¨  In reverberant environments a large amount of the total energy is

contained in the last portion of the impulse responsen  Reverberation time

}60)0()(:{60 dB EDC t  EDC t T  −==

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 7/123

Global descriptors

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 8/123

EDR of a violin body

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 9/123

n  In the room’s transfer function we can single out resonant modes

n  The spacing between two resonant modes is given by 

n  which is valid above the threshold frequency

Global descriptors

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 10/123

n  Number of echoes in the impulse response before time t 

n  Derivative of N t : 

n  Clarity index: ratio btw early reflections energy and latereverberation energy

Global descriptors

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 11/123

Implementation

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 12/123

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 13/123

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 14/123

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 15/123

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 16/123

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 17/123

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 18/123

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 19/123

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 20/123

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 21/123

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 22/123

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 23/123

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 24/123

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 25/123

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 26/123

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 27/123

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 28/123

Moorer reverberator 

n  accounts for late reverberations by placing anIIR filter after the FIR filter (tapped delay line)

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 29/123

Binaural impulse response

n  Our sound perception is affected by our own body

¨ Head Related Transfer Function (HRTF)

Acoustic paths can be

grouped together to

reduce cost

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 30/123

Comb filter 

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 31/123

Allpass filter 

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 32/123

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 33/123

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 34/123

Steady-state

tones (sinusoids)

really do see the

same gain at

every frequency

in an allpass,

while a comb

filter has widely

varying gains

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 35/123

Comb filters and reverberation time

n  The decay between successive samples in comband allpass filters is described by the gain

coefficient gi 

n  In order for the comb filter’s decay to correspond

to a given reverberation time, we must have

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 36/123

Combination of comb filters

n  Single comb filters do notprovide sufficient echo density

n  In order to improve the echo

density, we need to combinemultiple comb filters

¨  Cascading comb filters

corresponds to multiplying their 

transfer functions

¨  Frequency peaks not shared by all

comb filters are cancelled bymultiplication

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 37/123

Combination of comb filters

n  Better to place comb

filters in parallel

¨ Example

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 38/123

Parallel comb filters

n  The poles of comb filters are given by 

n  The poles have the same magnitudes

n  The modal density (No. of modes per Hz) is

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 39/123

Parallel comb filters

n  Modal density turns out to be the same at allfrequencies, unlike real rooms

n  Above a threshold frequency, the modal density

is constant

n  The modal density of the comb filters is then setto the modal density above the threshold

frequency

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 40/123

Parallel comb filters

n  The echo density of the comb filters isapproximatively given by

n  Relating echo density and modal density

provides:

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 41/123

Combination of allpass filters

n  Unlike comb filters, allpass filters must becascaded

¨ Multiplying freq. responses corresponds to adding

phase responses

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 42/123

Schroeder’s reverberator (1)

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 43/123

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 44/123

Schroeder’s reverberator 

n  Delays of the comb and allpass filters are chosen so thatthe ratio of the largest and smallest delay is 1.5 (typically30 and 45 ms)

n  The gains gi of the comb filters are chosen to provide adesired reverberation time T

r according to

n  Allpass filters delays are set to 5 and 1.7 ms

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 45/123

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 46/123

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 47/123

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 48/123

Feedback Delay Networks… 

at a glancen  Unitary matrix: definition

¨  A matrix is unitary if :

¨  We can also write that a matrix is unitary if 

|||||||| uuM =⋅

1|||||||| == MMMMT T 

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 49/123

FDN

•  Stability of the feedback loop is guaranteed if A = gM where M is an unitarymatrix and |g|<1

•  Outputs will be mutually incoherent: we can use the FDN to render the diffusesoundfield with a 4 loudspeaker system

•  The early reverbeartions can be simulated by appropriately injecting the inputsignal into the delay lines

⎥⎥⎥⎥

⎢⎢⎢⎢

=

44434241

34333231

24232221

14131211

aaaa

aaaa

aaaa

aaaa

A

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 50/123

Jot’s reverberator 

⎥⎥⎥⎥

⎢⎢⎢⎢

=

 N  N 

 N 

 N 

aaa

aaa

aaa

4421

22221

11211

A

⎥⎥⎥

⎢⎢⎢

=

 N b

b

1

b

[ ]=c

⎥⎥⎥

⎢⎢⎢

=

 N c

c

1

c

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 51/123

Jot’s reverberator 

The input-output relation of Jot’s reverberator is given by

with and

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 52/123

Jot’s reverberator 

n  System transfer function:

n  Zeros:

n  Poles:

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 53/123

Jot’s reverberator 

n  Moorer noted that convolving exponentiallydecaying white noise with source signals

produces a very natural sounding

n  As a consequence, by introducing absorptive

losses into a lossless prototype, we shouldobtain a natural sounding reverberator 

n  This is accomplished by associating a gain with

each delay:

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 54/123

Jot’s reverberator 

n  The logarithm of the gain is proportional to the length of the delay:

n  The above modification has the effect of replacing z with

z/γ in the transfer function

n  The lossless prototype response h[n] will be multiplied byan exponential envelope γn

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 55/123

Modeling the

Environment 

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 56/123

Modeling the environment

n  Simulate reverberations due to

environment

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 57/123

Motivations

Acoustical environment provides ...n  Sense of presence

n  Comprehension of space

n  Localization of auditory cues

n  Selectivity of audio signals (“cocktail party

effect”)

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 58/123

Geometric acoustic modeling

n  Spatialize sound by computing reverberationpaths from source to receiver 

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 59/123

Similarities to Graphics

n  Both model wave propagatation 

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 60/123

Differences from Graphics I

n  Sound has longer wavelengths than light¨ Diffractions are significant

¨ Specular reflections dominate diffuse reflections

¨ Occlusions by small objects have little effect

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 61/123

Differences from Graphics II

n  Sound waves are coherent¨ Modeling phase is important

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 62/123

n  Sound travels more slowly than light¨ Reverberations are perceived over time

Differences from Graphics III

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 63/123

Overview of approaches

n  Finite element methodsn  Boundary element methods

n  Image source methods

n  Ray tracing

n  Beam tracing 

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 64/123

Finite element methods

n  Solve wave equation over grid-alignedmesh 

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 65/123

Boundary element methods

n  Solve wave equation over discretizedsurfaces 

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 66/123

Boundary Element Trade-offs

n  Advantages¨ Works well for low frequencies

¨ Simple formulation

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 67/123

n  Disadvantages¨ Complex function stored with each element

¨ Form factors must model diffractions &

specularities

¨ Elements must be much smaller thanwavelength

Boundary Element Trade-offs

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 68/123

Image source methods

n  Consider direct paths from “virtualsources” 

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 69/123

Image source trade-offs

n  Advantages¨ Simple for rectangular rooms

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 70/123

n  Disadvantages¨ O(nr ) visibility checks in arbitrary

environments

¨ Specular reflections only

Image source trade-offs

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 71/123

Path tracing

n  Trace paths between source andreceiver  

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 72/123

Path Tracing Trade-offs

n  Advantages¨ Models all types of surfaces and scattering

¨ Simple to implement

Incoming ray

Sampledreverberation

s

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 73/123

Path Tracing Disadvantages

n  Disadvantages¨ Subject to sampling errors (aliasing)

¨ Depends on receiver position

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 74/123

Beam Tracing

n  Trace beams (bundles of rays) fromsource 

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 75/123

Beam Tracing Trade-offs

n  Advantages¨ Takes advantage of spatial coherence

¨ Predetermines visible virtual sources

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 76/123

Beam Tracing Disadvantages

n  Disadvantages¨ Difficult for curved surfaces or refractions

¨ Requires efficient polygon sorting and

intersection

BSPsCell adjacency graphs

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 77/123

Complex 3D Environments

n  Precompute beam tree for stationarysource 

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 78/123

Interactive Performance

n  Lookup beams containing moving receiver  

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 79/123

Summary

n  FEM/BEM¨ best for low frequencies

n  Image source methods

¨ best for rectangular rooms (very common)

n  Path tracing

¨ best for high-order reflections (very common)

n  Beam tracing

¨ best for precomputation

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 80/123

Current research in

interactive audio

spatialization

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 81/123

81

Back to the problem

n  Path/ray tracingaccording to the laws of geometric optics

n  Applications to

¨  Simulation of acoustic

reverberations incomplex environments

¨  Prediction of EMpropagation for wirelesssystems (multipathfading)

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 82/123

82

n  Construction of the beam tree through space

subdivision

n  Construction of paths through beam tree lookup

Beam tracing

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 83/123

83

Using space subdivision

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 84/123

84

What is missing?

n  Traditional beam tracing assumes that thesource be fixed

¨ Every time the source moves, the BT needs tobe rebuilt from scratch (lengthy process basedon space subdivision)

n  Is it possible to avoid space subdivision?

n  Is it possible to settle all visibility issues inadvance (irrespective of the source

location)?n  Is it ultimately possible to build the BT

through a simple lookup process?

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 85/123

85

Reformulating the problem

n  Define environment’s visibility

independently from the source’s

location

n  Compute the environment’s visibilityn  Build the beam tree using

¨ Visibility info

¨ Source’s location

n  Build the paths using

¨ Beam tree

¨ Receiver’s location

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 86/123

86

Environment’s characterizationn  Sources and Receivers

¨  Assumed to be point-like

n  Reflectors

¨  Oriented surface of a reflecting wall

n  A reflecting wall defines two reflectors

n  Assumed as flat

n  Identified by an indexn  Byproducts:

¨  Beams

n  Compact bundle of rays originated by the same source

n  Identified by a source (real or virtual) and the illuminatedportion of a reflector 

¨  Active reflectors

n  That portion of a reflector illuminated by a beam

n  Identified by a beam and a reflector 

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 87/123

87

Visibility

n  Visibility function¨  Function that associates the index of the visible

reflector to a viewpoint and a viewing direction

¨  Piece-wise constant function that takes on values in theparameter space that characterizes viewpoint andviewing direction

n  Visibility function from a reflector ¨  Visibility function where viewpoints are constrained on

the pts of the reflector 

n  Environment’s visibility description

¨  Set of the visibility functions associated to all the

environment’s reflectorsn  M reflecting walls => 2M visibility functions

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 88/123

88

Defining the parameter spacen 

Parameter space: viewpoint and viewing direction¨  If the point lies on a reflector 

n  4D parameter space in the 3D case

n  2D parameter space in the 2D case

¨  Reflector’s normalization

n  affine transformation (rigid motion + scaling) of the

geometric space that remaps the reflector onto thesegment that goes from (0,-1) to (0,1), with reflectingsurface facing x≥0

¨  This way viewpoint and viewing direction can bedescribed by the eq. y = a x + b, where -1≤b≤1describes the point on the reflector and a the viewing

directionn  Parameter space: (a,b)

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 89/123

89

Visibility region

n  The visibility region of a given reflector w.r.t. a reference reflector is the region of 

the parameter space (a,b) that

corresponds to viewpoints on the

reference reflector from which the givenone results as visible

¨ Due to occlusions, this region can be empty or 

made of a set of convex polygons

n  The visibility region of reflector i is the

region where the visibility function is equal

to i 

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 90/123

90

Visibility region

n  A generic reflector can be described by x = e t + f 

y = g t + h

0≤t ≤1

Substituting in y=ax+b we obtaing t + h = a (e t + f) + b, 0≤t ≤1

-1≤b≤1

Visibility region:

Intersection btw a bundle of rays (a beam inparameter space) and the strip -1≤b≤1

(f,h)

(e+f,g+h)

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 91/123

91

Examples

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 92/123

92

Visibility regionn  Potential visibility region: visibility region with no other reflectors

n  Potential visibility regions may overlapn  Actual visibility region is contained within the potential one

¨  Overlaps must be resolved considering occlusions

n  Approach for evaluating visibility function

¨  Compute potential visibility regions

¨  Resolve overlaps and identify actual visibility regions¨  Label actual visibility regions

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 93/123

93

Resolving overlaps

n  When two potential visibility regionsoverlap, the corresponding reflectors

exhibit a partial occlusion w.r.t. the

reference reflector 

n  Who occludes who decides which regioneats which on the overlap

n  This can be done by tracing a sample ray

within the overlapping region

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 94/123

94

Parameter space (dual space)

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 95/123

95

Reflectors in the dual space

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 96/123

96

Normalized dual space

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 97/123

97

Building a beam tree from visibility

n Evaluating the global visibility of theenvironment corresponds to building

one visibility function per reflector 

¨ This corresponds to constructing and

labeling all the actual visibility regions for each reflector 

n  All this ignores the location of the source

n  Given source location and visibility,

how do we build the beam tree?

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 98/123

98

Sources in parameter space

n  A source in parameter space is a line (dual of a pt)

n  Source and active portion of a reflector define a beam¨  The branching of a beam is defined by the intersection btw

the line and the actual visibility regions

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 99/123

99

Beam tracing

n  Given a beam reflected by the i-threflector, use visibility to to determine itsbranching in sub-beams (one per visiblereflector)

¨ Determine virtual source location in thewarped space corresponding to i-th reflector 

¨ Determine illuminated portion of reflector andthe corresponding “narrowed” reference strip

¨ Scan actual visibility regions over the line

corresponding to the source in parameter space

¨ Update beam tree

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 100/123

100

Beam tracing

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 101/123

101

Computational efficiency

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 102/123

102

Computational efficiency

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 103/123

103

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 104/123

104

Modeling diffraction

n  Use geometric theory of diffractionn  Diffraction modeled by placing sources

(and the relative beam trees) at diffracting

wedges

n  Beam trees computed in advance jointly

with visibility information

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 105/123

A comparison btw imp.

responsesSim.

Meas.

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 106/123

Comparison 

n  Parameters:

¨  EDC

¨  Early Decay Time (EDT): time that imp. resp. takes to dim down of 

10 dB.

¨  Center Time (CT): centroid of squared impulse response

n  Imp. Resp. envelope:

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 107/123

EDC

Simulated refl. only

Sim. of refl. + diffr. Complete simulation

recorded

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 108/123

EDT

Simulated refl. only

Sim. of refl. + diffr. Complete simulation\

recorded

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 109/123

Centre TimeSimulated refl. only

Sim. of refl. + diffr. Complete simulation

recorded

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 110/123

110

Auralization

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 111/123

Active Beamshaping

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 112/123

112

Rendering beams  Physical approach: WFS

  Huygens principle

  data-based (needs

wavefield acquisition)

  Works on wavefronts

  Geometric appraoch:

Beam Tracing

  Implements general

solution according to

geometric propagation

principles

  Boundary conditions

become components

of the implementation

G l

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 113/123

113

Goal  Reconstruction of an arbitrary source (arbitrary

radiation function) in an arbitrary location using an array

of speaker in close range

Si l t f

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 114/123

114

Signal transfer 

bhG =

=

Nx1

Mx1NxM

Matrix form

Example (1) central beam

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 115/123

115

Example (1) – central beam

n M = 16;

n f = 700Hz

n  Δy = not uniform

n Gaussian mask

Example 2 skewed beam

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 116/123

116

Example 2 – skewed beam

n M = 64;

n f = 700Hz

n  Δy = 10 cm

n Maschera Gauss

Rendered beam

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 117/123

Rendered beam

Wid b d t i

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 118/123

118

Wideband extension

¨ Instead of setting constraints at a singlefrequency, we apply them to multiplefrequencies (wideband minimization)

¨ 4 parameters:n  F, No. of frequencies where we minimize

n  M, No. of speakers

n  N, No. of angles

n  T, No. of taps of the filter 

E l 3 k d b

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 119/123

119

Example 3 – skewed beam

Interface

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 120/123

Interface

120

Testing in a dry room

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 121/123

121

Testing in a dry room

15-speaker non-uniform array

Multiple audio cards in daisy-chain configuration

8-16-24 synchronized outputs

Results

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 122/123

Resultsn  Expected contrasting needs

¨ Low frequencies require extensive arrays

¨ High frequencies require closely-spaced

speakers

¨ Cost constrains limit the No. of speakers

n  With 15-16 speakers we do not go beyond

17-18 db of attenuation btw main lobe and

side lobes with a limited frequency range

(300Hz-6kHz)

122

C l i

8/3/2019 Reverberation Algorithms

http://slidepdf.com/reader/full/reverberation-algorithms 123/123

Conclusions

n  Results are comparable to those achievedwith WFS but we control them in a

geometric fashion. Therefore we can

¨ Reconstruct an arbitrary source in an arbitrary

location¨ Combine multiple beams through

superposition principle, therefore it can be

used as a geometric engine for synthesizing

the response of the environment as well (earlyreverberation for spatial impression)