Fifty Years of Artificial Reverberation

The first artificial reverberation algorithms were proposed in the early 1960s, and new, improved algorithms are published regularly. These algorithms have been widely used in music production since the 1970s, and now find applications in new fields, such as game audio. This overview article provides a unified review of the various approaches to digital artificial reverberation. The three main categories have been delay networks, convolution-based algorithms, and physical room models. Delay-network and convolution techniques have been competing in popularity in the music technology field, and are often employed to produce a desired perceptual or artistic effect. In applications including virtual reality, predictive acoustic modeling, and computer-aided design of acoustic spaces, accuracy is desired, and physical models have been mainly used, although, due to their computational complexity, they are currently mainly used for simplified geometries or to generate reverberation impulse responses for use with a convolution method. With the increase of computing power, all these approaches will be available in real time. A recent trend in audio technology is the emulation of analog artificial reverberation units, such as spring reverberators, using signal processing algorithms. As a case study we present an improved parametric model for a spring reverberation unit.

[1]  Pedro Novo,et al.  IKA-SIM: A System to Generate Auditory Virtual Environments , 2004 .

[2]  Manfred R. Schroeder,et al.  Natural Sounding Artificial Reverberation , 1962 .

[3]  Maic Masuch,et al.  RAY ACOUSTICS USING COMPUTER GRAPHICS TECHNOLOGY , 2007 .

[4]  Jose J. Lopez,et al.  A Comparison of Two Diffuse Boundary Models Based on Finite Differences Schemes , 2010 .

[5]  Stefan Bilbao,et al.  Computing room acoustics with CUDA - 3D FDTD schemes with boundary losses and viscosity , 2011, 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[6]  Vesa Välimäki,et al.  Interpolated rectangular 3-D digital waveguide mesh algorithms with frequency warping , 2003, IEEE Trans. Speech Audio Process..

[7]  Henry Korkes Reverberation Facilities at CBS Radio , 1959 .

[8]  Davide Rocchesso,et al.  Signal-theoretic characterization of waveguide mesh geometries for models of two-dimensional wave propagation in elastic media , 2001, IEEE Trans. Speech Audio Process..

[9]  Dinesh Manocha,et al.  FAST EDGE-DIFFRACTION FOR SOUND PROPAGATION IN COMPLEX VIRTUAL ENVIRONMENTS , 2009 .

[10]  Hynek Hermansky,et al.  Modulation Spectrum Analysis for Recognition of Reverberant Speech , 2011, INTERSPEECH.

[11]  Vesa Välimäki,et al.  Simulation of Room Acoustics using 2-D Digital Waveguide Meshes , 2006, 2006 IEEE International Conference on Acoustics Speech and Signal Processing Proceedings.

[12]  Tapio Lokki,et al.  Extreme Filters-cache-efficient implementation of long IIR and FIR filters , 2006, IEEE Signal Processing Letters.

[13]  Julius O. Smith,et al.  Physical Modeling Using Digital Waveguides , 1992 .

[14]  Damian Murphy,et al.  RenderAIR – Room Acoustics Simulation Using a Hybrid Digital Waveguide Mesh Approach , 2008 .

[15]  Bill Kapralos,et al.  Real-time GPU-based convolution: a follow-up , 2009, Future Play.

[16]  Mingsian R. Bai,et al.  Multirate synthesis of reverberators using subband filtering , 2009 .

[17]  Jordi Bonada,et al.  Method for measuring violin sound radiation based on bowed glissandi and its application to sound synthesis. , 2011, The Journal of the Acoustical Society of America.

[18]  Diemer de Vries,et al.  Improved microphone array configurations for auralization of sound fields by Wave Field Synthesis. , 2002 .

[19]  Matti Karjalainen,et al.  Efficient and Parametric Reverberator for Room Acoustics Modeling , 1997, ICMC.

[20]  Renate Heinz,et al.  Binaural room simulation based on an image source model with addition of statistical methods to include the diffuse sound scattering of walls and to predict the reverberant tail , 1993 .

[21]  S. Van Duyne,et al.  The 2-D digital waveguide mesh , 1993, Proceedings of IEEE Workshop on Applications of Signal Processing to Audio and Acoustics.

[22]  Barry A. Blesser An Interdisciplinary Synthesis of Reverberation Viewpoints , 2001 .

[23]  Rüdiger Hoffmann,et al.  The harming part of room acoustics in automatic speech recognition , 2007, INTERSPEECH.

[24]  Tapio Lokki,et al.  Engaging concert hall acoustics is made up of temporal envelope preserving reflections. , 2011, The Journal of the Acoustical Society of America.

[25]  Paulo Dias,et al.  Finite Difference Room Acoustic Modelling on a General Purpose Graphics Processing Unit , 2010 .

[26]  Minyue Fu,et al.  A Recursive Method for the Approximation of LTI Systems Using Subband Processing , 2010, IEEE Transactions on Signal Processing.

[27]  Davide Rocchesso,et al.  Circulant and elliptic feedback delay networks for artificial reverberation , 1997, IEEE Trans. Speech Audio Process..

[28]  Matti Karjalainen,et al.  Modeling of reflections and air absorption in acoustical spaces a digital filter design approach , 1997, Proceedings of 1997 Workshop on Applications of Signal Processing to Audio and Acoustics.

[29]  Thomas G. Stockham,et al.  High-speed convolution and correlation , 1966, AFIPS '66 (Spring).

[30]  D. Murphy,et al.  Acoustic Modeling Using the Digital Waveguide Mesh , 2007, IEEE Signal Processing Magazine.

[31]  Jonathan S. Abel,et al.  A hybrid reverberation crossfading technique , 2010, 2010 IEEE International Conference on Acoustics, Speech and Signal Processing.

[32]  Dinesh Manocha,et al.  AD-Frustum: Adaptive Frustum Tracing for Interactive Sound Propagation , 2008, IEEE Transactions on Visualization and Computer Graphics.

[33]  Jonathan S. Abel,et al.  A Simple, Robust Measure of Reverberation Echo Density , 2006 .

[34]  Juha Merimaa,et al.  Spatial Impulse Response Rendering I: Analysis and Synthesis , 2005 .

[35]  Cumhur Erkut,et al.  Sound Synthesis of the Harpsichord Using a Computationally Efficient Physical Model , 2004, EURASIP J. Adv. Signal Process..

[36]  J. Borish Extension of the image model to arbitrary polyhedra , 1984 .

[37]  Davide Rocchesso,et al.  Online Correction of Dispersion Error in 2D Waveguide Meshes , 2000, ICMC.

[38]  Naga K. Govindaraju,et al.  High performance discrete Fourier transforms on graphics processors , 2008, 2008 SC - International Conference for High Performance Computing, Networking, Storage and Analysis.

[39]  Yoichi Ando,et al.  ORTHOGONAL ACOUSTICAL FACTORS OF SOUND FIELDS IN A FOREST COMPARED WITH THOSE IN A CONCERT HALL , 1998 .

[40]  G.D. Cain,et al.  Approximation of FIR by IIR digital filters: an algorithm based on balanced model reduction , 1992, IEEE Trans. Signal Process..

[41]  John Vanderkooy,et al.  Transfer-Function Measurement with Maximum-Length Sequences , 1989 .

[42]  Mark R. Anderson,et al.  Direct comparison of the impact of head tracking, reverberation, and individualized head-related transfer functions on the spatial perception of a virtual speech source. , 2001, Journal of the Audio Engineering Society. Audio Engineering Society.

[43]  Michael Rettinger Reverberation Chambers for Broadcasting and Recording Studios , 1957 .

[44]  Eric Battenberg,et al.  IMPLEMENTING REAL-TIME PARTITIONED CONVOLUTION ALGORITHMS ON CONVENTIONAL OPERATING SYSTEMS , 2011 .

[45]  Luke Dahl,et al.  A REVERBERATOR BASED ON ABSORBENT ALL-PASS FILTERS , 2000 .

[46]  Jean-Marc Jot,et al.  Digital Delay Networks for Designing Artificial Reverberators , 1991 .

[47]  Jacques Martin,et al.  The prediction of echograms and impulse responses within the Epidaure software , 1993 .

[48]  T.H. Crystal,et al.  Linear prediction of speech , 1977, Proceedings of the IEEE.

[49]  David Griesinger Improving Room Acoustics Through Time-Variant Synthetic Reverberation , 1991 .

[50]  Jonathan S. Abel,et al.  An Emulation of the EMT 140 Plate Reverberator Using a Hybrid Reverberator Structure , 2009 .

[51]  Murray Hodgson,et al.  Improved algorithms and methods for room sound-field prediction by acoustical radiosity in arbitrary polyhedral rooms. , 2004, The Journal of the Acoustical Society of America.

[52]  Bengt-Inge Dalenbäck A New Model for Room Acoustic Prediction and Auralization , 1995 .

[53]  Bruce Swedien Make Mine Music , 2004 .

[54]  S. Mitra,et al.  Digital all-pass networks , 1974 .

[55]  Maarten van Walstijn,et al.  On-Line Simulation of 2D Resonators with Reduced Dispersion Error using Compact Implicit Finite Difference Methods , 2007, 2007 IEEE International Conference on Acoustics, Speech and Signal Processing - ICASSP '07.

[56]  D. V. Maercke,et al.  Binaural simulation of concert halls: A new approach for the binaural reverberation process , 1993 .

[57]  Elizabeth M. Wenzel,et al.  Sound Lab: A real-time, software-based system for the study of spatial hearing , 2000 .

[58]  David M. Howard,et al.  Surround-Sound Reverberation using Digital Waveguide Mesh Modelling Techniques , 2001 .

[59]  Christof Faller,et al.  Investigations on an Early-Reflection-Free Model for BRIRs , 2010 .

[60]  Dinesh Manocha,et al.  Interactive sound rendering in complex and dynamic scenes using frustum tracing , 2007, IEEE Transactions on Visualization and Computer Graphics.

[61]  Vesa Välimäki,et al.  Artificial reverberation using a hyper-dimensional FDTD mesh , 2005, 2005 13th European Signal Processing Conference.

[62]  Michael Vorländer,et al.  Virtual Reality System with Integrated Sound Field Simulation and Reproduction , 2007, EURASIP J. Adv. Signal Process..

[63]  Unto K. Laine,et al.  Splitting the Unit Delay - Tools for fractional delay filter design , 1996 .

[64]  Swen Müller,et al.  Transfer-Function Measurement with Sweeps , 2001 .

[65]  Stephen McGovern,et al.  THE IMAGE-SOURCE REVERBERATION MODEL IN AN N-DIMENSIONAL SPACE , 2011 .

[66]  Jonathan S. Abel,et al.  Estimating Room Impulse Responses from Recorded Balloon Pops , 2010 .

[67]  Jeremy J. Wells,et al.  Temporal Matching of 2-D and 3-D Wave-Based Acoustic Modeling for Efficient and Realistic Simulation of Rooms , 2009 .

[68]  Augusto Sarti,et al.  Fast Tracing of Acoustic Beams and Paths Through Visibility Lookup , 2008, IEEE Transactions on Audio, Speech, and Language Processing.

[69]  Charles Gounod,et al.  FAUST , 1791, EAMT.

[70]  Sylvain Lefebvre,et al.  Instant Sound Scattering , 2007, Rendering Techniques.

[71]  T. Lewers,et al.  A combined beam tracing and radiatn exchange computer model of room acoustics , 1993 .

[72]  Takao Tsuchiya,et al.  DISCRETE HUYGENS' MODEL APPROACH TO SOUND WAVE PROPAGATION—REVERBERATION IN A ROOM, SOUND SOURCE IDENTIFICATION AND TOMOGRAPHY IN TIME REVERSAL , 1999 .

[73]  Diemer de Vries,et al.  Applying Cochlear Modeling and Psychoacoustics in Room Acoustics , 2008 .

[74]  Vesa Välimäki,et al.  Virtual Analog Effects , 2011 .

[75]  Vesa Välimäki,et al.  Oscillator and Filter Algorithms for Virtual Analog Synthesis , 2006, Computer Music Journal.

[76]  Tobias May,et al.  Constant Complexity Reverberation for Any Reverberation Time , 2007 .

[77]  Vesa Välimäki,et al.  Spectral Delay Filters , 2009 .

[78]  Tapio Lokki,et al.  Creating Interactive Virtual Acoustic Environments , 1999 .

[79]  Julian Parker,et al.  Efficient Dispersion Generation Structures for Spring Reverb Emulation , 2011, EURASIP J. Adv. Signal Process..

[80]  Lewis S. Goodfriend,et al.  The Development and Application of Synthetic Reverberation Systems , 1959 .

[81]  David Griesinger Beyond MLS-Occupied Hall Measurement with FFT Techniques , 1996 .

[82]  Jyri Huopaniemi,et al.  Advanced AudioBIFS: virtual acoustics modeling in MPEG-4 scene description , 2004, IEEE Transactions on Multimedia.

[83]  George Drettakis,et al.  Perceptual audio rendering of complex virtual environments , 2004, ACM Trans. Graph..

[84]  Vesa Välimäki,et al.  Introduction to the Special Issue on Virtual Analog Audio Effects and Musical Instruments , 2010, IEEE Trans. Speech Audio Process..

[85]  Karlheinz Blankenbach Spatial Effects , 2012, Handbook of Visual Display Technology.

[86]  Tapio Lokki,et al.  Frequency domain acoustic radiance transfer for real-time auralization , 2009 .

[87]  Jonathan S. Abel,et al.  All Natural Room Enhancement , 2009, ICMC.

[88]  T. Ritoniemi,et al.  Headphone Sound Externalization , 2006 .

[89]  Earl Vickers,et al.  Frequency Domain Artificial Reverberation using Spectral Magnitude Decay , 2006 .

[90]  Davide Rocchesso Maximally diffusive yet efficient feedback delay networks for artificial reverberation , 1997, IEEE Signal Processing Letters.

[91]  Dinesh Manocha,et al.  Real-time sound synthesis and propagation for games , 2007, CACM.

[92]  Juha Merimaa,et al.  Reproduction of Reverberation with Spatial Impulse Response Rendering , 2004 .

[93]  Tapio Lokki,et al.  A Time-Variant Reverberation Algorithm For Reverberation Enhancement Systems , 2001 .

[94]  Wolfgang Ahnert,et al.  EARS auralization software , 1993 .

[95]  Benoît Champagne,et al.  A fast subband room response simulator , 2000, 2000 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.00CH37100).

[96]  R. Vermeulen Stereo reverberation , 1956 .

[97]  K. Heinrich Kuttruff,et al.  Auralization of Impulse Responses Modeled on the Basis of Ray-Tracing Results , 1993 .

[98]  Dana S. Hougland,et al.  Concert and Opera Halls: How They Sound , 1996 .

[99]  Julius O. Smith,et al.  Spring Reverb Emulation Using Dispersive Allpass Filters in a Waveguide Structure , 2006 .

[100]  A Lewis,et al.  THE SCIENCE OF SOUND , 1997 .

[101]  Maarten van Walstijn,et al.  A Phase Grating Approach to Modeling Surface Diffusion in FDTD Room Acoustics Simulations , 2011, IEEE Transactions on Audio, Speech, and Language Processing.

[102]  Barry D. Kulp,et al.  Digital Equalization Using Fourier Transform Techniques , 1988 .

[103]  Guillermo Garcia Optimal Filter Partition for Efficient Convolution with Short Input/Output Delay , 2002 .

[104]  Kiyoshi Nakagawa,et al.  An improved geometrical sound field analysis in rooms using scattered sound and an audible room acoustic simulator , 1993 .

[105]  Vesa Välimäki,et al.  Parametric Spring Reverberation Effect , 2010 .

[106]  Matti Karjalainen,et al.  Compilation of unified physical models for efficient sound synthesis , 2003, 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03)..

[107]  Julius O. Smith A new approach to digital reverberation using closed waveguide networks , 1985 .

[108]  Ka Calamia,et al.  19th INTERNATIONAL CONGRESS ON ACOUSTICS MADRID, 2-7 SEPTEMBER 2007 CULLING INSIGNIFICANT DIFFRACTION COMPONENTS FOR INTERACTIVE ACOUSTIC SIMULATIONS , 2007 .

[109]  Julius O. Smith,et al.  A Digital Model of the Echoplex Tape Delay , 2008 .

[110]  Vesa Välimäki,et al.  Automated calibration of a parametric spring reverb model , 2011 .

[111]  Tapio Lokki,et al.  The perceptual effects of dispersion error on room acoustic model auralization , 2011 .

[112]  Guilherme Campos,et al.  The Meshotron: A Network of Specialized Hardware Units for 3-D Digital Waveguide Mesh Acoustic Model Parallelization , 2010 .

[113]  L. Beranek,et al.  Analysis of Sabine and Eyring equations and their application to concert hall audience and chair absorption. , 2006, The Journal of the Acoustical Society of America.

[114]  Matti Karjalainen,et al.  Body Modeling Techniques for String Instrument Synthesis , 1996, ICMC.

[115]  Tapio Lokki,et al.  Investigations on the balloon as an impulse source. , 2011, The Journal of the Acoustical Society of America.

[116]  Augusto Sarti,et al.  Two-Dimensional Beam Tracing from Visibility Diagrams for Real-Time Acoustic Rendering , 2010, EURASIP J. Adv. Signal Process..

[117]  V. Ralph Algazi,et al.  Headphone-Based Spatial Sound , 2011, IEEE Signal Processing Magazine.

[118]  Augusto Sarti,et al.  Virtual Analog Modeling in the Wave-Digital Domain , 2010, IEEE Transactions on Audio, Speech, and Language Processing.

[119]  James A. Moorer,et al.  About This Reverberation Business , 1978 .

[120]  Julius O. Smith,et al.  Automated Physical Modeling of Nonlinear Audio Circuits For Real-Time Audio Effects—Part I: Theoretical Development , 2010, IEEE Transactions on Audio, Speech, and Language Processing.

[121]  Lauri Savioja,et al.  REAL-TIME 3D FINITE-DIFFERENCE TIME-DOMAIN SIMULATION OF LOW- AND MID-FREQUENCY ROOM ACOUSTICS , 2010 .

[122]  Udo Zoelzer Digital Audio Signal Processing , 2008 .

[123]  Cumhur Erkut,et al.  Synthesis of Hand Clapping Sounds , 2007, IEEE Transactions on Audio, Speech, and Language Processing.

[124]  Hideki Tachibana,et al.  Calculation of impulse responses and acoustic parameters in a hall by the finite-difference time-domain method , 2008 .

[125]  Jyri Tapani Pakarinen,et al.  A Review of Digital Techniques for Modeling Vacuum-Tube Guitar Amplifiers , 2009, Computer Music Journal.

[126]  Mendel Kleiner,et al.  Auralization-An Overview , 1993 .

[127]  Ming C. Lin,et al.  Precomputed wave simulation for real-time sound propagation of dynamic sources in complex scenes , 2010, ACM Trans. Graph..

[128]  Jonathan S. Abel,et al.  A Digital Reverberator Modeled After the Scattering of Acoustic Waves by Trees in a Forest , 2008 .

[129]  Niels Jørgen Christensen,et al.  Photon maps in bidirectional Monte Carlo ray tracing of complex objects , 1995, Comput. Graph..

[130]  Jont B. Allen,et al.  Image method for efficiently simulating small‐room acoustics , 1976 .

[131]  Matti Karjalainen,et al.  Frequency-Zooming ARMA Modeling of Resonant and Reverberant Systems , 2002 .

[132]  Stefan Bilbao,et al.  Numerical Sound Synthesis , 2009 .

[133]  Alan V. Oppenheim,et al.  Discrete-time signal processing (2nd ed.) , 1999 .

[134]  Jan Plogsties,et al.  Sparse Frequency-Domain Reverberator , 2010 .

[135]  William G. Gardner,et al.  Efficient Convolution without Input/Output Delay , 1995 .

[136]  B. Katz,et al.  Framework for Real-Time Auralization in Architectural Acoustics , 2008 .

[137]  Vesa Välimäki,et al.  Analysis and modeling of piano sustain-pedal effects. , 2007, The Journal of the Acoustical Society of America.

[138]  Thomas Hélie,et al.  Volterra Series and State Transformation for Real-Time Simulations of Audio Circuits Including Saturations: Application to the Moog Ladder Filter , 2010, IEEE Transactions on Audio, Speech, and Language Processing.

[139]  Nicolas Tsingos,et al.  Precomputing Geometry-Based Reverberation Effects for Games , 2009 .

[140]  Dinesh Manocha,et al.  Use of GPUs in room acoustic modeling and auralization , 2010 .

[141]  Ning Xiang,et al.  Binaural scale modelling for auralisation and prediction of acoustics in auditoria , 1993 .

[142]  Federico Fontana,et al.  A Modal-Based Real-Time Piano Synthesizer , 2010, IEEE Transactions on Audio, Speech, and Language Processing.

[143]  P. Vaidyanathan,et al.  The digital all-pass filter: a versatile signal processing building block , 1988, Proc. IEEE.

[144]  Bobby Owsinski The Mixing Engineer's Handbook , 1999 .

[145]  Lars G. Johansen,et al.  Artificial Reverberation Based on a Pseudo-Random Impulse Response II , 1999 .

[146]  D. Griesinger Concert Hall Acoustics and Audience Perception [Applications Corner] , 2007, IEEE Signal Processing Magazine.

[147]  W. G. Gardner,et al.  A real‐time multichannel room simulator , 1992 .

[148]  Udo Zölzer,et al.  Parametric approximation of room impulse responses by multirate systems , 1993, 1993 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[149]  Angelo Farina,et al.  Real-time partitioned convolution for Ambiophonics surround sound , 2001, Proceedings of the 2001 IEEE Workshop on the Applications of Signal Processing to Audio and Acoustics (Cat. No.01TH8575).

[150]  Stefan Bilbao,et al.  MODELING METHODS FOR THE HIGHLY DISPERSIVE SLINKY SPRING: A NOVEL MUSICAL TOY , 2010 .

[151]  Itai Neoran,et al.  Capturing Manipulation and Reproduction of Sampled Acoustic Impulse Responses , 2004 .

[152]  Matti Karjalainen,et al.  Reverberation Modeling Using Velvet Noise , 2007 .

[153]  Finn Jacobsen,et al.  A note on the physical interpretation of frequency dependent boundary conditions in a digital Waveguide Mesh , 2007 .

[154]  Mingsian R. Bai,et al.  Comparative Study of Design and Implementation Strategies of Automotive Virtual Surround Audio Systems , 2010 .

[155]  S. Strøm,et al.  Fifteen years' experience with computerized ray tracing , 1983 .

[156]  Thomas A. Funkhouser,et al.  Modeling acoustics in virtual environments using the uniform theory of diffraction , 2001, SIGGRAPH.

[157]  A. Kulowski Algorithmic representation of the ray tracing technique , 1985 .

[158]  Tapio Lokki,et al.  The room acoustic rendering equation. , 2007, The Journal of the Acoustical Society of America.

[159]  Fritz Menzer Binaural Reverberation Using Two Parallel Feedback Delay Networks , 2010 .

[160]  Wenyu Jiang,et al.  Using Programmable Graphics Hardware for Acoustics and Audio Rendering , 2009 .

[161]  Vesa Välimäki,et al.  An Integer System for Virtual Audio Reality , 1996 .

[162]  Rudolf Rabenstein,et al.  Wave Field Simulation with the Functional Transformation Method , 2006, 2006 IEEE International Conference on Acoustics Speech and Signal Processing Proceedings.

[163]  Steve Winder Introduction to digital filters , 2002 .

[164]  Hans Hagen,et al.  Phonon tracing for auralization and visualization of sound , 2005, VIS 05. IEEE Visualization, 2005..

[165]  David Griesinger Concert Hall Acoustics and Audience Perception , 2007 .

[166]  Colin Raffel PRACTICAL MODELING OF BUCKET-BRIGADE DEVICE CIRCUITS , 2010 .

[167]  Damian Murphy,et al.  HYBRID ROOM IMPULSE RESPONSE SYNTHESIS IN DIGITAL WAVEGUIDE MESH BASED ROOM ACOUSTICS SIMULATION , 2008 .

[168]  Juha Merimaa,et al.  Analysis, synthesis, and perception of spatial sound : binaural localization modeling and multichannel loudspeaker reproduction , 2006 .

[169]  Stefan Bilbao,et al.  A Physical Model for Plate Reverberation , 2006, 2006 IEEE International Conference on Acoustics Speech and Signal Processing Proceedings.

[170]  Miller S. Puckette,et al.  Designing Multi-Channel Reverberators , 1982 .

[171]  Maarten van Walstijn,et al.  Modeling Frequency-Dependent Boundaries as Digital Impedance Filters in FDTD and K-DWM Room Acoustics Simulations , 2008 .

[172]  T. Lokki,et al.  Digital Signal Processing Techniques for Non-exponentially Decaying Reverberation , 1998 .

[173]  Tapio Lokki,et al.  Creating Interactive Virtual Auditory Environments , 2002, IEEE Computer Graphics and Applications.

[174]  Julian Parker A SIMPLE DIGITAL MODEL OF THE DIODE-BASED RING-MODULATOR , 2011 .

[175]  Jose J. Lopez,et al.  On the Implementation of a Room Acoustics Modeling Software Using Finite-Differences Time-Domain Method , 2007 .

[176]  A. Krokstad,et al.  Calculating the acoustical room response by the use of a ray tracing technique , 1968 .

[177]  Angelo Farina AURALIZATION SOFTWARE FOR THE EVALUATION OF THE RESULTS OBTAINED BY A PYRAMID TRACING CODE: RESULTS OF SUBJECTIVE LISTENING TESTS , 2000 .

[178]  Christof Faller,et al.  Unitary Matrix Design for Diffuse Jot Reverberators , 2010 .

[179]  Marco Civolani,et al.  Modeling of the EMS VCS3 Voltage-Controlled Filter as a Nonlinear Filter Network , 2010, IEEE Transactions on Audio, Speech, and Language Processing.

[180]  Toshiyuki Gotoh,et al.  On 'Out-of-Head Localization' in Headphone Listening , 1975 .

[181]  M. R. Schroeder,et al.  Digital simulation of sound transmission in reverberant spaces (part 1) , 1969 .

[182]  David Griesinger,et al.  Practical Processors and Programs for Digital Reverberation , 1989 .

[183]  Judicaël Picaut,et al.  Experimental study of sound propagation in a street , 2005 .

[184]  William L. Martens,et al.  Simulating the Cues of Spatial Hearing in Natural Environments , 1984, ICMC.

[185]  J. Borish,et al.  An efficient algorithm for measuring the impulse response using pseudorandom noise , 1983 .

[186]  Jean Laroche A new analysis/synthesis system of musical signals using Prony's method-application to heavily damped percussive sounds , 1989, International Conference on Acoustics, Speech, and Signal Processing,.

[187]  Michael Vorländer,et al.  OPTIMAL FILTER PARTITIONS FOR REAL-TIME FIR FILTERING USING UNIFORMLY-PARTITIONED FFT-BASED CONVOLUTION IN THE FREQUENCY-DOMAIN , 2011 .

[188]  Angelo Farina,et al.  Recording Concert Hall Acoustics for Posterity , 2003 .

[189]  Michael Jenkin,et al.  Acoustical Modeling with Sonel Mapping , 2007 .

[190]  M. Kleiner,et al.  Computation of edge diffraction for more accurate room acoustics auralization. , 2001, The Journal of the Acoustical Society of America.

[191]  Eric A. Lehmann,et al.  Diffuse Reverberation Model for Efficient Image-Source Simulation of Room Impulse Responses , 2010, IEEE Transactions on Audio, Speech, and Language Processing.

[192]  M. Schroeder Integrated‐impulse method measuring sound decay without using impulses , 1979 .

[193]  Stefan Bilbao A Digital Plate Reverberation Algorithm , 2007 .

[194]  Stefan Bilbao,et al.  Spring Reverberation: A Physical Perspective , 2010 .

[195]  Jens Blauert,et al.  Principles of binaural room simulation , 1992 .

[196]  N.H Fletcher,et al.  Wave propagation on helices and hyperhelices: a fractal regression , 2001, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[197]  Jacques Martin,et al.  Binaural room acoustics simulation: Practical uses and applications , 1992 .

[198]  Matti Karjalainen,et al.  Digital Waveguide Networks for Room Response Modeling and Synthesis , 2005 .

[199]  D. Botteldooren Finite‐difference time‐domain simulation of low‐frequency room acoustic problems , 1995 .

[200]  Unto K. Laine,et al.  Splitting the unit delay [FIR/all pass filters design] , 1996, IEEE Signal Process. Mag..

[201]  Nam Ik Cho,et al.  A New Overlap Save Algorithm for Fast Block Convolution and Its Implementation Using FFT , 2011, J. Signal Process. Syst..

[202]  Dinesh Manocha,et al.  GSound: Interactive Sound Propagation for Games , 2011 .

[203]  Samuli Laine,et al.  Accelerated beam tracing algorithm , 2009 .

[204]  Nicolas Tsingos,et al.  Topological Sound Propagation with Reverberation Graphs , 2008 .

[205]  Young-Cheol Park,et al.  Design of Time-Varying Reverberators for Low Memory Applications , 2008, IEICE Trans. Inf. Syst..

[206]  Zoran Cvetkovic,et al.  Scattering Delay Network: An Interactive Reverberator for Computer Games , 2011 .

[207]  Tapio Takala,et al.  Simulation of Room Acoustics with a 3-D Finite Difference Mesh , 1994, ICMC.

[208]  Stefan Bilbao,et al.  A Virtual Model of Spring Reverberation , 2010, IEEE Transactions on Audio, Speech, and Language Processing.

[209]  Guy-Bart Stan,et al.  Comparison of different impulse response measurement techniques , 2002 .

[210]  A. W. M. van den Enden,et al.  Discrete Time Signal Processing , 1989 .

[211]  Maarten van Walstijn,et al.  Room Acoustics Simulation Using 3-D Compact Explicit FDTD Schemes , 2011, IEEE Transactions on Audio, Speech, and Language Processing.

[212]  Barry A. Blesser,et al.  An Audio Delay System Using Digital Technology , 1971 .

[213]  David Stanley Mcgrath,et al.  Convolution Processing for Realistic Reverberation , 1995 .

[214]  M. Vorländer Simulation of the transient and steady‐state sound propagation in rooms using a new combined ray‐tracing/image‐source algorithm , 1989 .

[215]  Peter Svensson,et al.  Errors in MLS Measurements Caused by Time Variance in Acoustic Systems , 1999 .

[216]  Manfred R. Schroeder,et al.  -Colorless- Artificial Reverberation , 1960 .

[217]  Stefan Bilbao,et al.  Virtual Room Acoustics: A Comparison of Techniques for Computing 3D-FDTD Schemes Using CUDA , 2011 .

[218]  Rebecca Stewart,et al.  A Hybrid Artificial Reverberation Algorithm , 2007 .

[219]  Dinesh Manocha,et al.  An efficient GPU-based time domain solver for the acoustic wave equation , 2012 .

[220]  Anders Gade,et al.  Acoustics in Halls for Speech and Music , 2014 .

[221]  Vesa Välimäki,et al.  Recent Advances in Real-Time Musical Effects, Synthesis, and Virtual Analog Models , 2011, EURASIP J. Adv. Signal Process..

[222]  Chris Kyriakakis,et al.  Using Subband Filters to Reduce the Complexity of Real-time Signal Processing , 2002 .

[223]  Ton Kalker,et al.  Reverberation Assessment in Audioband Speech Signals for Telepresence Systems , 2008, SIGMAP.

[224]  Angelo Farina,et al.  Simultaneous Measurement of Impulse Response and Distortion with a Swept-Sine Technique , 2000 .

[225]  Maic Masuch,et al.  Waveguide-based Room Acoustics through Graphics Hardware , 2006, ICMC.

[226]  Tatsuya Kawahara,et al.  Robust Speech Recognition Based on Dereverberation Parameter Optimization Using Acoustic Model Likelihood , 2010, IEEE Transactions on Audio, Speech, and Language Processing.

[227]  Samuel Siltanen,et al.  Spatial Room Impulse Responses with a Hybrid Modeling Method , 2011 .

[228]  Thomas A. Funkhouser,et al.  A beam tracing approach to acoustic modeling for interactive virtual environments , 1998, SIGGRAPH.

[229]  S.H. Foster,et al.  Real Time Synthesis of Complex Acoustic Environments , 1991, Final Program and Paper Summaries 1991 IEEE ASSP Workshop on Applications of Signal Processing to Audio and Acoustics.

[230]  R. H. Lyon,et al.  Sound propagation in urban areas , 1974 .

[231]  Jeffrey Hurchalla Low Latency Convolution in One Dimension Via Two Dimensional Convolutions: An Intuitive Approach , 2008 .

[232]  Yan Li,et al.  Spatial Sound Rendering Using Measured Room Impulse Responses , 2006, 2006 IEEE International Symposium on Signal Processing and Information Technology.

[233]  K. Teer,et al.  Bucket-brigade electronics: new possibilities for delay, time-axis conversion, and scanning , 1969 .

[234]  N. Fliege,et al.  Multirate Digital Reverberation System , 1990 .

[235]  Timo Peltonen,et al.  A Rehearsal Hall with Virtual Acoustics for Symphony Orchestras , 2009 .

[236]  Sune H. Bergman,et al.  Electrical musical instrument , 1980 .

[237]  Rudolf Rabenstein,et al.  Simulation of three-dimensional sound propagation with multidimensional wave digital filters , 1998, Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '98 (Cat. No.98CH36181).

[238]  Krzysztof Marasek,et al.  Computation of Room Acoustics using Programmable Video Hardware , 2004, ICCVG.

[239]  Izzet Kale,et al.  Motor car acoustic response modelling and order reduction via balanced model truncation , 1996 .

[240]  A. Krokstad,et al.  Extending the image method to higher-order reflections , 1993 .

[241]  L. Mcbride,et al.  A technique for the identification of linear systems , 1965 .

[242]  Jonathan S. Abel,et al.  On Peak-Detecting and RMS Feedback and Feedforward Compressors , 2003 .

[243]  Jean-Marc Jot,et al.  An analysis/synthesis approach to real-time artificial reverberation , 1992, [Proceedings] ICASSP-92: 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[244]  Tapio Lokki,et al.  An Efficient Auralization of Edge Diffraction , 2002 .

[245]  Miller Puckette,et al.  Synthetic Rehearsal: Training the Synthetic Performer , 1985, ICMC.

[246]  Barry A. Blesser,et al.  Electric reverberation apparatus , 1980 .

[247]  Marc Moonen,et al.  Fifty Years of Acoustic Feedback Control: State of the Art and Future Challenges , 2011, Proceedings of the IEEE.

[248]  Don H. Johnson,et al.  Gauss and the history of the fast Fourier transform , 1985 .

[249]  Michael Vorländer Auralization of spaces , 2009 .

[250]  Jean-Marc Jot,et al.  Analysis and synthesis of room reverberation based on a statistical time-frequency model , 1997 .

[251]  Jose J. Lopez,et al.  Simulation of Complex and Large Rooms Using a Digital Waveguide Mesh , 2007 .

[252]  Dirk Schröder,et al.  Real-time auralization of coupled rooms , 2009 .

[253]  Jean-Marc Jot,et al.  Digital Signal Processing Issues in the Context of Binaural and Transaural Stereophony , 1995 .

[254]  H. Lehnert Systematic errors of the ray-tracing algorithm , 1993 .

[255]  Stefan Bilbao,et al.  Perceptual and Numerical Aspects of Spring Reverberation Modeling , 2010 .

[256]  Antoine Chaigne,et al.  On the quality of plate reverberation , 2010 .

[257]  W. H. Wittrick On elastic wave propagation in helical springs , 1966 .

[258]  Jon Dattorro,et al.  Effect Design: Part 1: Reverberator and Other Filters , 1997 .

[259]  Matti Karjalainen,et al.  New techniques to model reverberant instrument body responses , 2001, ICMC.

[260]  Vesa Välimäki,et al.  Audio Signal Processing Using Graphics Processing Units , 2011 .

[261]  Vesa Välimäki,et al.  The Switched Convolution Reverberator , 2012 .

[262]  Davide Rocchesso,et al.  Generalized digital waveguide networks , 2003, IEEE Trans. Speech Audio Process..

[263]  Trevor J. Terrell Introduction to Digital Filters , 1980 .

[264]  Stephen G. McGovern Fast image method for impulse response calculations of box-shaped rooms , 2009 .

[265]  Hisashi Kihara,et al.  digital audio signal processing , 1990 .

[266]  M. Kuster Multichannel Room Impulse Response Generation With Coherence Control , 2009, IEEE Transactions on Audio, Speech, and Language Processing.

[267]  Harald Bode,et al.  History of Electronic Sound Modification , 1984 .

[268]  Jonathan S. Abel,et al.  Methods for Extending Room Impulse Responses Beyond Their Noise Floor , 2010 .