Reverberation algorithms Augusto Sarti
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
S
R
S
R
S
R
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)