Head-Related Transfer Function and Virtual Auditory Display

Bosun Xie received a Bachelor degree in physics in 1982 and a Master of Science degree in acoustics from South China University of Technology in 1987. In 1998, he received a Doctor of Science degree in acoustics from Tongji University. Since 1982, he has been working at the South China University of Technology and is currently the director and a professor at Acoustic Lab., School of Science. Xie is also a member of The State Key Lab of Subtropical Building Science. His research interests include binaural hearing, spatial sound, acoustic signal processing, and room acoustics, has published over 150 scientific papers, and owns 5 patents in these fields. Professor Xie is a member of the Audio Engineering Society (AES), a vice-chairman of the China Audio Engineering Society and a committee member of the Acoustical Society of China.

"I find the book excellent and, as indicated by Professor Jens Blauert (whom I have known since 1986 and whose opinions I value and trust), it is extremely thorough, multifaceted, detailed, mathematically deep, yet clear - I agree. I give it an extremely positive review. The summary concluding each chapter or section is particularly valuable, an excellent idea and feature...I give the book top rank." - Wade R. Bray, HEAD acoustics, Inc.; "This book provides a thorough and comprehensive analysis of issues relevant to HRTFs. Many of them have not been covered in such a detailed, clear way in any other book. Professor Xie has devoted a considerable amount of time and effort creating a work that appeals to readers' demands. The international acoustical community will be pleased to have access to its important scientific and technological content, now available with this English translation." -Jens Blauert, Internationally renowned expert in spatial hearing

• Chapter 1: Spatial Hearing and Virtual Auditory Display 1.1. Spatial Coordinate Systems1.2. The Auditory System and Auditory Filter 1.2.1. The Auditory System and its Function 1.2.2. The Critical Band and Auditory Filter1.3. Spatial Hearing1.4. Localization Cues for a Single Sound Source 1.4.1. Interaural Time Difference 1.4.2. Interaural Level Difference 1.4.3. Cone of Confusion and Head Movement 1.4.4. Spectral Cue 1.4.5. Discussion on Directional Localization Cues 1.4.6. Auditory Distance Perception1.5. Head-Related Transfer Functions1.6. Summing Localization and Spatial Hearing with Multiple Sources 1.6.1. Summing Localization of Two Sound Sources and the Stereophonic Law of Sine 1.6.2. Summing Localization Law of More Than Two Sound Sources 1.6.3. Time Difference between Sound Sources and the Precedence Effect 1.6.4. Cocktail Party Effect1.7. Room Acoustics and Spatial Hearing 1.7.1. Sound Fields in Enclosed Spaces 1.7.2. Spatial Hearing in Enclosed Spaces1.8. Binaural Recording and Virtual Auditory Display 1.8.1. Artificial Head Models 1.8.2. Binaural Recording and Playback System 1.8.3. Virtual Auditory Display 1.8.4. Comparison with Multi-channel Surround Sound1.9. SummaryChapter 2: HRTF Measurements2.1. Transfer Function of a Linear-time-invariant (LTI) System and its Measurement Principle 2.1.1. Continuous-Time LTI System 2.1.2. Discrete-Time LTI System 2.1.3. Excitation Signals2.2. Principle and Design of HRTF Measurements 2.2.1. Overview 2.2.2. Subjects in HRTF Measurements 2.2.3. Measuring Point and Microphone Position 2.2.4. Measuring Circumstances and Mechanical Devices 2.2.5. Loudspeaker and Amplifier 2.2.6. Signal Generation and Processing 2.2.7. HRTF Equalization 2.2.8. Example of HRTF Measurement 2.2.9. Evaluation of Quality and Errors in HRTF Measurements2.3. Far-field HRTF Databases2.4. Some Specific Measurement Methods and Near-field HRTF Measurements 2.4.1 Some Specific HRTF measurement methods 2.4.2 Near-field HRTF Measurement 2.5. SummaryChapter 3: Primary Features of HRTFs3.1. Time- and Frequency-domain Features of HRTFs 3.1.1. Time-domain Features of Head-related Impulse Responses (HRIRs) 3.1.2. Frequency-domain Features of HRTFs 3.1.3. Minimum-phase Characteristics of HRTFs3.2. Interaural Time Difference (ITD) Analysis 3.2.1. Methods for Evaluating ITD 3.2.2. Calculation Results for ITD3.3. Interaural Level Difference (ILD) Analysis3.4. Spectral Features of HRTFs 3.4.1. Pinna-related Spectral Notches 3.4.2. Torso-related Spectral Cues3.5. Spatial Symmetry in HRTFs 3.5.1. Front-back Symmetry 3.5.2. Left-right Symmetry 3.5.3. Symmetry of ITD3.6. Near-field HRTFs and Distance Perception Cues3.7. HRTFs and Other Issues Related to Binaural Hearing3.8. SummaryChapter 4: Calculation of HRTFs 4.1. Spherical Head Model for HRTF Calculation 4.1.1. Determining Far-field HRTFs and their Characteristics on the Basis of a Spherical Head Model 4.1.2. Analysis of Interaural Localization Cues 4.1.3. Influence of Ear Location 4.1.4. Effect of Source Distance 4.1.5. Further Discussion on the Spherical Head Model4.2. Snowman Model for HRTF Calculation 4.2.1. Basic Concept of the Snowman Model 4.2.2. Results for the HRTFs of the Snowman Model4.3. Numerical Methods for HRTF Calculation 4.3.1. Boundary Element Method (BEM) for Acoustic Problems 4.3.2. Calculation of HRTFs by BEM 4.3.3. Results for BEM-based HRTF Calculation 4.3.4 Simplification of Head Shape 4.3.5. Other Numerical Methods for HRTF Calculation 4.4. SummaryChapter 5: HRTF Filter Models and Implementation5.1. Error Criteria for HRTF Approximation5.2. HRTF Filter Design: Model and Considerations 5.2.1. Filter Model for Discrete-time Linear-time-invariant (LTI) System 5.2.2. Basic Principles and Model Selection in HRTF Filter Design 5.2.3. Length and Simplification of Head-related Impulse Responses (HRIRs) 5.2.4. HRTF Filter Design Incorporating Auditory Properties 5.3. Methods for HRTF Filter Design 5.3.1. Finite Impulse Response (FIR) Representation 5.3.2. Infinite Impulse Response (IIR) Representation by Conventional Methods 5.3.3. Balanced Model Truncation for IIR Filter 5.3.4. HRTF Filter Design Using the Logarithmic Error Criterion 5.3.5. Common-acoustical-pole and Zero Model of HRTFs 5.3.6. Comparison of Results of HRTF Filter Design 5.4. Structure and Implementation of HRTF Filter5.5. Frequency-warped Filter for HRTFs 5.5.1. Frequency Warping 5.5.2. Frequency-warped Filter for HRTFs5.6. SummaryChapter 6: Spatial Interpolation and Decomposition of HRTFs 6.1. Directional Interpolation of HRTFs 6.1.1. Basic Concept of HRTF Directional Interpolation 6.1.2. Some Common Schemes for HRTF Directional Interpolation 6.1.3. Performance Analysis of HRTF Directional Interpolation 6.1.4. Problems and Improvements of HRTF Directional Interpolation6.2. Spectral Shape Basis Function Decomposition of HRTFs 6.2.1. Basic Concept of Spectral Shape Basis Function Decomposition 6.2.2. Principal Components Analysis (PCA) of HRTFs 6.2.3. Discussion of Applying PCA to HRTFs 6.2.4. PCA Results for HRTFs 6.2.5. Directional Interpolation under PCA Decomposition of HRTFs 6.2.6. Subset Selection of HRTFs6.3. Spatial Basis Function Decomposition of HRTFs 6.3.1. Basic Concept of Spatial Basis Function Decomposition 6.3.2. Azimuthal Fourier Analysis and Sampling Theorem of HRTFs 6.3.3. Analysis of Required Azimuthal Measurements of HRTFs 6.3.4. Spherical Harmonic Function Decomposition of HRTFs 6.3.5. Spatial Principal Components Analysis and Recovery of HRTFs from a Small Set of Measurements6.4. HRTF Spatial Interpolation and Signal Mixing for Multi-channel Surround Sound 6.4.1. Signal Mixing for Multi-channel Surround Sound 6.4.2. Pairwise Signal Mixing 6.4.3. Sound Field Signal Mixing 6.4.4. Further Discussion on Multi-channel Sound Reproduction6.5. Simplification of Signal Processing for Binaural Virtual Source Synthesis 6.5.1. Virtual Loudspeaker-based Algorithms 6.5.2. Basis Function Decomposition-based Algorithms6.6. Beamforming Model for Synthesizing Binaural Signals and HRTFs 6.6.1. Spherical Microphone Array for Synthesizing Binaural Signals 6.6.2. Other Array Beamforming Models for Synthesizing Binaural Signals and HRTFs 6.7. SummaryChapter 7: Customization of Individualized HRTFs7.1. Anthropometric Measurements and their Correlation with Localization Cues 7.1.1. Anthropometric Measurements 7.1.2. Correlations among Anthropometric Parameters and HRTFs or Localization Cues7.2. Individualized Interaural Time Difference (ITD) Model and Customization 7.2.1. Extension of the Spherical Head ITD Model 7.2.2. ITD Model Based on Azimuthal Fourier Analysis7.3. Anthropometry-based Customization of HRTFs 7.3.1. Anthropometry Matching Method 7.3.2. Frequency Scaling Method 7.3.3. Anthropometry-based Linear Regression Method7.4. Subjective Selection-based HRTF Customization7.5. Notes on Individualized HRTF Customization7.6. Structural Model of HRTFs 7.6.1. Basic Idea and Components of the Structural Model 7.6.2. Discussion and Improvements of the Structural Model7.7. SummaryChapter 8: Binaural Reproduction through Headphones8.1. Equalization of the Characteristics of Headphone-to-Ear Canal Transmission 8.1.1. Principle of Headphone Equalization 8.1.2. Free-field and Diffuse-field Equalization8.2. Repeatability and Individuality of Headphone-to-ear-canal Transfer Functions (HpTFs) 8.2.1. Repeatability of HpTF Measurement 8.2.2. Individuality of HpTFs8.3. Directional Error in Headphone Reproduction8.4. Externalization and Control of Perceived Virtual Source Distance in Headphone Reproduction 8.4.1. In-head Localization and Externalization 8.4.2. Control of Perceived Virtual Source Distance in Headphone Reproduction8.5. SummaryChapter 9: Binaural Reproduction through Loudspeakers9.1. Basic Principle of Binaural Reproduction through Loudspeakers 9.1.1. Binaural Reproduction through a Pair of Frontal Loudspeakers 9.1.2. General Theory for Binaural Reproduction through Loudspeakers 9.2. Head Rotation and Loudspeaker Reproduction 9.2.1. Virtual Source Distribution in Two-Front Loudspeaker Reproduction 9.2.2. Transaural Synthesis for Four-Loudspeaker Reproduction 9.2.3. Analysis of Dynamic Localization Cues in Loudspeaker Reproduction 9.2.4. Stability of the Perceived Virtual Source Azimuth against Head Rotation9.3. Head Translation and Stability of Virtual Sources in Loudspeaker Reproduction 9.3.1. Preliminary Analysis of Head Translation and Stability 9.3.2. Stereo Dipole 9.3.3. Quantitative Analysis of Stability against Head Translation 9.3.4. Linear System Theory for the Stability of Crosstalk Cancellation9.4. Effects of Mismatched HRTFs and Loudspeaker Pairs 9.4.1. Effect of Mismatched HRTFs 9.4.2. Effect of Mismatched Loudspeaker Pairs9.5. Coloration and Timbre Equalization in Loudspeaker Reproduction 9.5.1. Coloration and Timbre Equalization Algorithms 9.5.2. Analysis of Timbre Equalization Algorithms 9.6. Some Issues on Signal Processing in Loudspeaker Reproduction 9.6.1. Causality and Stability of a Crosstalk Canceller 9.6.2. Basic Implementation Methods for Signal Processing in Loudspeaker Reproduction 9.6.3. Other Implementation Methods for Signal Processing in Loudspeaker Reproduction 9.6.4. Bandlimited Implementation of Crosstalk Cancellation9.7. Some Approximate Methods for Solving the Crosstalk Cancellation Matrix 9.7.1. Cost Function Method for Solving the Crosstalk Cancellation Matrix 9.7.2. Adaptive Inverse Filter Scheme for Crosstalk Cancellation9.8. SummaryChapter 10: Virtual Reproduction of Stereophonic and Multi-channel Surround Sound 10.1 Binaural Reproduction of Stereophonic and Multi-channel Surround Sound through Headphones 10.1.1 Binaural Reproduction of Stereophonic Sound through Headphones 10.1.2 Basic Algorithm for Headphone-based Binaural Reproduction of 5.1 Channel Surround Sound 10.1.3 Improved Algorithm for Binaural Reproduction of 5.1 Channel Surround Sound through Headphones 10.1.4 Notes on Binaural Reproduction of Multi-channel Surround Sound10.2 Algorithms for Correcting Non-standard Stereophonic Loudspeaker Configurations10.3 Stereophonic Enhancement Algorithms10.4 Virtual Reproduction of Multi-channel Surround Sound through Loudspeakers 10.4.1 Virtual Reproduction of 5.1 Channel Surround Sound 10.4.2 Improvement of Virtual 5.1 Channel Surround Sound Reproduction through Stereophonic Loudspeakers 10.4.3 Virtual 5.1 Channel Surround Sound Reproduction through More than Two Loudspeakers 10.4.4 Notes on Virtual Surround Sound10.5 SummaryChapter 11: Binaural Room Modeling11.1 Physics-based Methods for Room Acoustics and Binaural Room Impulse Response (BRIR) Modeling 11.1.1 BRIR and Room Acoustics Modeling 11.1.2 Image-source Methods for Room Acoustics Modeling 11.1.3 Ray-tracing Methods for Room Acoustics Modeling 11.1.4 Other Methods for Room Acoustics Modeling 11.1.5 Source Directivity and Air Absorption 11.1.6 Calculation of Binaural Room Impulse Responses11.2 Artificial Delay and Reverberation Algorithms 11.2.1 Artificial Delay and Discrete Reflection Modeling 11.2.2 Late Reflection Modeling and Plain Reverberation Algorithm 11.2.3 Improvements on Reverberation Algorithm 11.2.4 Application of Delay and Reverberation Algorithms to Virtual Auditory Environments 11.3 SummaryChapter 12: Rendering System for Dynamic and Real-time Virtual Auditory Environments (VAEs) 12.1 Basic Structure of Dynamic VAE Systems 12.2 Simulation of Dynamic Auditory Information 12.2.1 Head Tracking and Simulation of Dynamic Auditory Information 12.2.2 Dynamic Information in Free-field Virtual Source Synthesis 12.2.3 Dynamic Information in Room Reflection Modeling 12.2.4 Dynamic Behaviors in Real-time Rendering Systems 12.2.5 Dynamic Crosstalk Cancellation in Loudspeaker Reproduction12.3 Simulation of Moving Virtual Sources12.4 Some Examples of Dynamic VAE Systems12.5 SummaryChapter 13: Psychoacoustic Evaluation and Validation of Virtual Auditory Displays (VADs) 13.1 Experimental Conditions for the Psychoacoustic Evaluation of VADs 13.2 Evaluation by Auditory Comparison and Discrimination Experiment 13.2.1 Auditory Comparison and Discrimination Experiment 13.2.2 Results of Auditory Discrimination Experiments13.3 Virtual Source Localization Experiment 13.3.1 Basic Methods for Virtual Source Localization Experiments 13.3.2 Preliminary Analysis of the Results of Virtual Source Localization Experiments 13.3.3 Results of Virtual Source Localization Experiments13.4 Quantitative Evaluation Methods for Subjective Attributes 13.5 Further Statistical Analysis of Psychoacoustic Experimental Results 13.5.1 Statistical Analysis Methods 13.5.2 Statistical Analysis Results13.6 Binaural Auditory Model and Objective Evaluation of VADs13.7 Summary Chapter 14: Applications of Virtual Auditory Displays (VADs) 14.1 VADs in Scientific Research Experiments14.2 Applications of Binaural Auralization 14.2.1 Application of Binaural Auralization in Room Acoustics 14.2.2 Existing Problems in Room Acoustic Binaural Auralization 14.2.3 Other Applications of Binaural Auralization14.3 Applications in Sound Reproduction and Program Recording14.4 Applications in Virtual Reality, Communication, and Multimedia 14.4.1 Applications in Virtual Reality 14.4.2 Applications in Communication 14.4.3 Applications in Multimedia and Mobile Products14.5 Applications in Clinical Auditory Evaluations14.6 Summary Appendix A: Spherical Harmonic FunctionsAppendix B: Multipole Re-expansions for Calculating the HRTFs of the Snowman ModelReferences Index