E media seminar 20_12_2017_artificial_reverberation
1. Room acoustics and
Digital Artificial
Reverberation
An introduction with focus on
convolutive modal reverberators
Giacomo Vairetti
Leuven, 20th December 2017
eMedia seminar
2. Outline
1) Fundamentals of Room Acoustics
2) Introduction to Artificial Reverberation
3) Convolution algorithms
4. What is room reverberation?
Room Acoustics
o Reverberation refers to the physical phenomenon for which a
sound reaches the ears of the listeners after being reflected or
scattered by the surfaces of the room.
o The dimensions and shape of the room and the physical
characteristics of its surfaces determine the behavior of sound in
the room.
Psychoacoustics
o Reverberation is the effect for which the sound in a room is
perceived as prolonged and smeared in time.
o It provides the listener with an impression of the dimensions and
shape of the room and the physical characteristics of its surfaces
1
5. • A room can be considered as a position-dependent Linear system
• Not Time-Invariant (usually assumed TI for fixed positions)
• Linear system modelled by the room impulse response (RIR) h(t)
• Output = Input “filtered” by the RIR (convolution *)
• Artificial Reverberation: simulate the input-output behavior of a room
o Which filter for approximating the RIR?
Reverberation as a linear system
H(z)
2
6. Room Impulse Response (RIR)
a RIR can be defined as the time domain (time vs amplitude) response of
a room to an impulsive stimulus.
T0 is the acoustic delay of the direct sound (travelling time)
Early reflections: relatively sparse echoes
Late reverberation: dense and statistically random echoes
Amplitude
T0
Copyright 2015 Rational Acoustics
Echo density
increases as
3
http://acoustics.org/pressroom/httpdocs/152nd/behler.html
7. Room Impulse Response (RIR)
a RIR can be defined as the time domain (time vs amplitude) response of
a room to an impulsive stimulus.
Definition (simplified model – based on specular reflections)
Amplitude
T0
Copyright 2015 Rational Acoustics
Echo density
increases as
3
http://acoustics.org/pressroom/httpdocs/152nd/behler.html
8. Reverberation Time (RT)
• Energy decay curve (EDC)
o ratio of signal energy remaining
in the RIR h(t) at time t
• RT or T60: point where the EDC falls below -60 dB
• Sabine’s formula
4
9. Behavior of sound in a room
• Absorption
o by the air
o by the walls
• Reflection
o specular
o diffused
• Diffraction
Absorption is frequency dependent
Coloration
5 Kapralos, B., Jenkin, M., & Milios, E. (2008). Sonel mapping: a probabilistic acoustical modeling method.
Building Acoustics, 15(4), 289-313.
10. Modal theory
Room Transfer Function
(RTF)
Large absolute value for ω = ωi sum of resonant modes
RIR definition (based on modal theory)
Rectangular room
mode (1,0,0)mode (0,1,0)mode (1,1,0)mode (2,0,0)mode (2,1,0)
Lx
Ly
Lz
Eigenfunctions
Resonance
Frequency
Damping
constant
: mode index
6
http://www.soundonsound.com/techniques/room-improvement
11. Modal theory – Schroeder Frequency
Modal density and modal overlap
• Number of modes (below frequency f )
• Schroeder frequency
• Number of modes
(below frequency Fc )
7 H. Kuttruff, Room acoustics. Spon Press, 2009.
12. Modal theory – Schroeder Frequency
• The frequency response of a reverberant room can be divided in two
regions delimited by the Schroeder frequency:
o Low-frequency sparse distribution of resonant modes
o Modes packed so densely that they merge to form random
frequency response with regular statistical properties
Above Fc, statistical parameters
of frequency response curves for
all rooms are identical or depend
at most on the RT
Examples
- Concert hall V = 2700 m3, T60 = 2 s Fc = 54 Hz (44 modes below Fc)
- Bathroom V = 10 m3, T60 = 0.35 s Fc = 374 Hz (52 modes below Fc)
8
13. Reverberation
• Reverberant spaces
o St Patrick’s Church in Patrington (England)
recorded by Foteinou and Murphy
RT = 1.86 s
o Bathroom
recorded by van Saane
RT = 0.35 s
o Inchindown oil storage (Scotland)
recorded by Cox
RT = 75 s !!!
9
Carmen
Anechoic room
16. Artificial Reverberation
• Simulate the acoustic behavior of a room
• Approaches
o Echo chambers
• play dry sound inside a reverberant room
and record it with a microphone
o Electromechanical (tape delays, springs, plates) - analog
• Springs/plate: excite vibrations in the structure
and add them to the dry signal
• Tape delays: generate echoes by record and
playback on a tape loop at the same time
o Digital synthesis – Digital Artificial Reverberation
10
Echo chamber of the Dresden University of Technology
Välimäki, et al. (2012). Fifty years of artificial reverberation. IEEE
Transactions on Audio, Speech, and Language Processing
Välimäki, et al. (2016). More Than 50 Years of Artificial
Reverberation. In Proc. 60th Int. Conf. DREAMS, AES
20. Delay networks methods
• Perceptual approach based on networks of delay lines and digital filters
• Early reflections (first 100 ms) influence spatial impression (geometry)
o Sparse first echoes
o Implemented using tapped delay lines (+ low-pass filter for losses)
• Late reverberation influences the impression of size (volume)
o Desired qualities:
• Smooth time decay (enough echo density, not too regular, faster at high-frequency)
• Smooth frequency response (enough mode density, not too regular)
o Implemented using comb and all-pass filters
https://ccrma.stanford.edu/~jos/pasp/Artificial_Reverberation.html12
22. Wave-based methods
• Approximate the wave equation in order to recreate a particular
soundfield using numerical methods (physical approach)
• Finite/Boundary Element Method (FEM/BEM)
o Discretize frequency and volume/surfaces
o The elements interact with each other
according to the basics of wave propagation
• Finite Difference Time Domain (FDTD) method
o Discretize volume and time
o Use finite differences to approximate derivatives
in the wave equation
• Grid size smaller than wavelength - Methods valid at low frequencies
13
http://www.onlineacoustics.com/acoustical-modelling/
23. Geometrical Acoustics
• Assumes a ray-like behavior of sound
o Valid only at high frequencies, where the wavelength of the sound waves
is small compared to the dimension of the space
o Sound reflections are modeled either as specular or diffuse reflections
(plus absorption)
Specular reflection – Image Source Method (ISM) and Ray-Tracing
Diffuse reflection – Ray-Tracing
Specular Diffuse
14
24. Geometrical Acoustics
Image-Source Method (ISM) • Only feasible for early reflections
due to the exponential increase of the
number of image sources
• Easy and computationally efficient for
simple geometries
• For each path from source to receiver,
compute the distance-dependent
propagation delay and attenuation of
sound, as well as each reflection
• Finally the responses of each path are
summed together
MIS
MIS MIS MIS
MIS
MISMISMIS
MIS
15 Image: Ville Pulkki , http://users.spa.aalto.fi/ville/diffrvisual/basicidea.html
25. Geometrical Acoustics
Hybrid model – example (ODEON)
o Ray tracing used to detect reflective surfaces
of interest
o ISM models early reflections
o Ray-Tracing for late reverberation
o Absorption and diffusion coefficients chosen to
match the expected reverberation time
o Example:
St Patrick’s Church in Patrington (England)
More sound examples: http://www.openairlib.net/
More detail here: video Ray tracing and hybrid methods in room acoustics (ODEON)
Fointenou A. and Murphy D., "Investigation of factors influencing acoustic characteristics in geometric acoustics
based auralization", Proc. of the 13th Int. Conf. on Digital Audio Effects (DAFx-10), Graz, Austria, Sept. 6-10, 201016
33. Linear convolution
• Provides the output of a LTI system
with impulse response h(t) for a
given input sequence x(t)
• defined as the integral of the
product of the two functions after
one is reversed and shifted
• In discrete time (FIR filtering)
Wikipedia
21
34. Linear convolution
• Provides the output of a LTI system
with impulse response h(t) for a
given input sequence x(t)
• defined as the integral of the
product of the two functions after
one is reversed and shifted
• In discrete time (FIR filtering)
21
35. Convolution algorithms
• Direct convolution :
o no inherent latency Use for very short RIRs (and in NUPOLS)
• FFT convolution :
o Perform circular convolution with proper zero-padding = linear convolution
o large latency = Nx = length input signal
• Block convolution (OLA/OLS) :
o Perform FFT convolution one signal block at a time
o Use for medium length filters (Nh similar to block length L), Latency = L
• Partitioned convolution : use for long filters
o The RIR is partitioned into P sub-filters
o Each sub-filter is treated as a separate RIR (OLS performed for each sub-filter)
o Uniform (UPOLS) :
• Sub-filters of same length
o Non-uniform (NUPOLS) :
• No latency and reduced computational cost, but more complex implementation
• Combines direct convolution and UPOLS
22
37. Parametric modeling of Room Acoustics
• Another solution to the complexity problem of FIR-based direct convolution is
to use IIR (infinite impulse response) filters, such that a long room impulse
response can be achieved with fewer filter coefficients.
• Pole-Zero models
• IIR modeling
+ filtering
Gain = b0
Poles = resonances + decay time constants
Zeros = anti-resonances + time delays
23
39. Room Impulse Response (RIR) – from modal theory
IDEA:
Use a digital filter whose impulse response is a linear combination of
a finite number of exponentially decaying sinusoids
• discrete time
• finite summation
24
Modal Reverberator
40. Room Transfer Function (RTF) – from modal theory
IDEA:
Use an IIR digital filter whose transfer function is a linear combination
of a finite number of modes
Use a parallel of resonant filters
25
Modal Reverberator
Eigenfunctions
Resonance
Frequency
Damping
constant
41. • Parallel form of IIR filter
• Explicit control over the
parameters of each mode
• Frequency (mode oscillation)
• Damping constant (decay time)
• Mode amplitude (complex)
• Real-time interactive control
of individual modes
• Allows source and listener
movement within the space
• Modify mode amplitudes according
to the mode spatial pattern
26
Modal Reverberator
Abel, J. S., Coffin, S., & Spratt, K. (2014, October). A Modal Architecture for Artificial Reverberation with Application
to Room Acoustics Modeling. In Audio Engineering Society Convention 137. AES
Complex updates
Real signal if
42. 27
Modal Reverberator - design
• Choose the number of modes, and the values for the mode
frequencies, dampings and amplitudes.
• Possible approaches
o behavioral
• fit parameters to system measurements (approximation of a
target RIR)
o analytical
• derive parameters from system physics (room dimensions and
absorption coefficients – see modal theory)
o perceptual
• select parameters according to desired equalization and T60
(arbitrary mode frequencies)
Abel, J. S., Coffin, S., & Spratt, K. (2014, October). A Modal Architecture for Artificial Reverberation with Application
to Room Acoustics Modeling. In Audio Engineering Society Convention 137. AES
43. 28
Modal Reverberator - design
• Behavioral Approach
• Estimate the mode frequencies as the frequencies of spectral peaks
• Peaks in the magnitude spectrum occur roughly at the mode frequencies
• Capture the most perceptually important modes
• model only the spectral peaks having magnitudes that exceed the critical-band
smoothed magnitude by a given ratio
Abel, J. S., Coffin, S., & Spratt, K. (2014, October). A Modal Architecture for Artificial Reverberation with Application
to Room Acoustics Modeling. In Audio Engineering Society Convention 137. AES
44. 28
Modal Reverberator - design
• Behavioral Approach
• Estimate the mode frequencies as the frequencies of spectral peaks
• Peaks in the magnitude spectrum occur roughly at the mode frequencies
• Capture the most perceptually important modes
• model only the spectral peaks having magnitudes that exceed the critical-band
smoothed magnitude by a given ratio
• Approximate mode damping using
the RIR decay time measured in a
subband around that frequency
Abel, J. S., Coffin, S., & Spratt, K. (2014, October). A Modal Architecture for Artificial Reverberation with Application
to Room Acoustics Modeling. In Audio Engineering Society Convention 137. AES
45. 29
Modal Reverberator - design
• Behavioral Approach
• mode amplitudes are found by a least-squares fit to the measured RIR
Φ is an M-column matrix of
complex mode responses of
length N samples
W : positive-definite weighting
matrix, e.g. used to emphasize
a good fit to early reflections
Abel, J. S., Coffin, S., & Spratt, K. (2014, October). A Modal Architecture for Artificial Reverberation with Application
to Room Acoustics Modeling. In Audio Engineering Society Convention 137. AES
h : target RIR : Modal approximation
