
- •Preface
- •Introduction
- •1.1 Spatial coordinate systems
- •1.2 Sound fields and their physical characteristics
- •1.2.1 Free-field and sound waves generated by simple sound sources
- •1.2.2 Reflections from boundaries
- •1.2.3 Directivity of sound source radiation
- •1.2.4 Statistical analysis of acoustics in an enclosed space
- •1.2.5 Principle of sound receivers
- •1.3 Auditory system and perception
- •1.3.1 Auditory system and its functions
- •1.3.2 Hearing threshold and loudness
- •1.3.3 Masking
- •1.3.4 Critical band and auditory filter
- •1.4 Artificial head models and binaural signals
- •1.4.1 Artificial head models
- •1.4.2 Binaural signals and head-related transfer functions
- •1.5 Outline of spatial hearing
- •1.6 Localization cues for a single sound source
- •1.6.1 Interaural time difference
- •1.6.2 Interaural level difference
- •1.6.3 Cone of confusion and head movement
- •1.6.4 Spectral cues
- •1.6.5 Discussion on directional localization cues
- •1.6.6 Auditory distance perception
- •1.7 Summing localization and spatial hearing with multiple sources
- •1.7.1 Summing localization with two sound sources
- •1.7.2 The precedence effect
- •1.7.3 Spatial auditory perceptions with partially correlated and uncorrelated source signals
- •1.7.4 Auditory scene analysis and spatial hearing
- •1.7.5 Cocktail party effect
- •1.8 Room reflections and auditory spatial impression
- •1.8.1 Auditory spatial impression
- •1.8.2 Sound field-related measures and auditory spatial impression
- •1.8.3 Binaural-related measures and auditory spatial impression
- •1.9.1 Basic principle of spatial sound
- •1.9.2 Classification of spatial sound
- •1.9.3 Developments and applications of spatial sound
- •1.10 Summary
- •2.1 Basic principle of a two-channel stereophonic sound
- •2.1.1 Interchannel level difference and summing localization equation
- •2.1.2 Effect of frequency
- •2.1.3 Effect of interchannel phase difference
- •2.1.4 Virtual source created by interchannel time difference
- •2.1.5 Limitation of two-channel stereophonic sound
- •2.2.1 XY microphone pair
- •2.2.2 MS transformation and the MS microphone pair
- •2.2.3 Spaced microphone technique
- •2.2.4 Near-coincident microphone technique
- •2.2.5 Spot microphone and pan-pot technique
- •2.2.6 Discussion on microphone and signal simulation techniques for two-channel stereophonic sound
- •2.3 Upmixing and downmixing between two-channel stereophonic and mono signals
- •2.4 Two-channel stereophonic reproduction
- •2.4.1 Standard loudspeaker configuration of two-channel stereophonic sound
- •2.4.2 Influence of front-back deviation of the head
- •2.5 Summary
- •3.1 Physical and psychoacoustic principles of multichannel surround sound
- •3.2 Summing localization in multichannel horizontal surround sound
- •3.2.1 Summing localization equations for multiple horizontal loudspeakers
- •3.2.2 Analysis of the velocity and energy localization vectors of the superposed sound field
- •3.2.3 Discussion on horizontal summing localization equations
- •3.3 Multiple loudspeakers with partly correlated and low-correlated signals
- •3.4 Summary
- •4.1 Discrete quadraphone
- •4.1.1 Outline of the quadraphone
- •4.1.2 Discrete quadraphone with pair-wise amplitude panning
- •4.1.3 Discrete quadraphone with the first-order sound field signal mixing
- •4.1.4 Some discussions on discrete quadraphones
- •4.2 Other horizontal surround sounds with regular loudspeaker configurations
- •4.2.1 Six-channel reproduction with pair-wise amplitude panning
- •4.2.2 The first-order sound field signal mixing and reproduction with M ≥ 3 loudspeakers
- •4.3 Transformation of horizontal sound field signals and Ambisonics
- •4.3.1 Transformation of the first-order horizontal sound field signals
- •4.3.2 The first-order horizontal Ambisonics
- •4.3.3 The higher-order horizontal Ambisonics
- •4.3.4 Discussion and implementation of the horizontal Ambisonics
- •4.4 Summary
- •5.1 Outline of surround sounds with accompanying picture and general uses
- •5.2 5.1-Channel surround sound and its signal mixing analysis
- •5.2.1 Outline of 5.1-channel surround sound
- •5.2.2 Pair-wise amplitude panning for 5.1-channel surround sound
- •5.2.3 Global Ambisonic-like signal mixing for 5.1-channel sound
- •5.2.4 Optimization of three frontal loudspeaker signals and local Ambisonic-like signal mixing
- •5.2.5 Time panning for 5.1-channel surround sound
- •5.3 Other multichannel horizontal surround sounds
- •5.4 Low-frequency effect channel
- •5.5 Summary
- •6.1 Summing localization in multichannel spatial surround sound
- •6.1.1 Summing localization equations for spatial multiple loudspeaker configurations
- •6.1.2 Velocity and energy localization vector analysis for multichannel spatial surround sound
- •6.1.3 Discussion on spatial summing localization equations
- •6.1.4 Relationship with the horizontal summing localization equations
- •6.2 Signal mixing methods for a pair of vertical loudspeakers in the median and sagittal plane
- •6.3 Vector base amplitude panning
- •6.4 Spatial Ambisonic signal mixing and reproduction
- •6.4.1 Principle of spatial Ambisonics
- •6.4.2 Some examples of the first-order spatial Ambisonics
- •6.4.4 Recreating a top virtual source with a horizontal loudspeaker arrangement and Ambisonic signal mixing
- •6.5 Advanced multichannel spatial surround sounds and problems
- •6.5.1 Some advanced multichannel spatial surround sound techniques and systems
- •6.5.2 Object-based spatial sound
- •6.5.3 Some problems related to multichannel spatial surround sound
- •6.6 Summary
- •7.1 Basic considerations on the microphone and signal simulation techniques for multichannel sounds
- •7.2 Microphone techniques for 5.1-channel sound recording
- •7.2.1 Outline of microphone techniques for 5.1-channel sound recording
- •7.2.2 Main microphone techniques for 5.1-channel sound recording
- •7.2.3 Microphone techniques for the recording of three frontal channels
- •7.2.4 Microphone techniques for ambience recording and combination with frontal localization information recording
- •7.2.5 Stereophonic plus center channel recording
- •7.3 Microphone techniques for other multichannel sounds
- •7.3.1 Microphone techniques for other discrete multichannel sounds
- •7.3.2 Microphone techniques for Ambisonic recording
- •7.4 Simulation of localization signals for multichannel sounds
- •7.4.1 Methods of the simulation of directional localization signals
- •7.4.2 Simulation of virtual source distance and extension
- •7.4.3 Simulation of a moving virtual source
- •7.5 Simulation of reflections for stereophonic and multichannel sounds
- •7.5.1 Delay algorithms and discrete reflection simulation
- •7.5.2 IIR filter algorithm of late reverberation
- •7.5.3 FIR, hybrid FIR, and recursive filter algorithms of late reverberation
- •7.5.4 Algorithms of audio signal decorrelation
- •7.5.5 Simulation of room reflections based on physical measurement and calculation
- •7.6 Directional audio coding and multichannel sound signal synthesis
- •7.7 Summary
- •8.1 Matrix surround sound
- •8.1.1 Matrix quadraphone
- •8.1.2 Dolby Surround system
- •8.1.3 Dolby Pro-Logic decoding technique
- •8.1.4 Some developments on matrix surround sound and logic decoding techniques
- •8.2 Downmixing of multichannel sound signals
- •8.3 Upmixing of multichannel sound signals
- •8.3.1 Some considerations in upmixing
- •8.3.2 Simple upmixing methods for front-channel signals
- •8.3.3 Simple methods for Ambient component separation
- •8.3.4 Model and statistical characteristics of two-channel stereophonic signals
- •8.3.5 A scale-signal-based algorithm for upmixing
- •8.3.6 Upmixing algorithm based on principal component analysis
- •8.3.7 Algorithm based on the least mean square error for upmixing
- •8.3.8 Adaptive normalized algorithm based on the least mean square for upmixing
- •8.3.9 Some advanced upmixing algorithms
- •8.4 Summary
- •9.1 Each order approximation of ideal reproduction and Ambisonics
- •9.1.1 Each order approximation of ideal horizontal reproduction
- •9.1.2 Each order approximation of ideal three-dimensional reproduction
- •9.2 General formulation of multichannel sound field reconstruction
- •9.2.1 General formulation of multichannel sound field reconstruction in the spatial domain
- •9.2.2 Formulation of spatial-spectral domain analysis of circular secondary source array
- •9.2.3 Formulation of spatial-spectral domain analysis for a secondary source array on spherical surface
- •9.3 Spatial-spectral domain analysis and driving signals of Ambisonics
- •9.3.1 Reconstructed sound field of horizontal Ambisonics
- •9.3.2 Reconstructed sound field of spatial Ambisonics
- •9.3.3 Mixed-order Ambisonics
- •9.3.4 Near-field compensated higher-order Ambisonics
- •9.3.5 Ambisonic encoding of complex source information
- •9.3.6 Some special applications of spatial-spectral domain analysis of Ambisonics
- •9.4 Some problems related to Ambisonics
- •9.4.1 Secondary source array and stability of Ambisonics
- •9.4.2 Spatial transformation of Ambisonic sound field
- •9.5 Error analysis of Ambisonic-reconstructed sound field
- •9.5.1 Integral error of Ambisonic-reconstructed wavefront
- •9.5.2 Discrete secondary source array and spatial-spectral aliasing error in Ambisonics
- •9.6 Multichannel reconstructed sound field analysis in the spatial domain
- •9.6.1 Basic method for analysis in the spatial domain
- •9.6.2 Minimizing error in reconstructed sound field and summing localization equation
- •9.6.3 Multiple receiver position matching method and its relation to the mode-matching method
- •9.7 Listening room reflection compensation in multichannel sound reproduction
- •9.8 Microphone array for multichannel sound field signal recording
- •9.8.1 Circular microphone array for horizontal Ambisonic recording
- •9.8.2 Spherical microphone array for spatial Ambisonic recording
- •9.8.3 Discussion on microphone array recording
- •9.9 Summary
- •10.1 Basic principle and implementation of wave field synthesis
- •10.1.1 Kirchhoff–Helmholtz boundary integral and WFS
- •10.1.2 Simplification of the types of secondary sources
- •10.1.3 WFS in a horizontal plane with a linear array of secondary sources
- •10.1.4 Finite secondary source array and effect of spatial truncation
- •10.1.5 Discrete secondary source array and spatial aliasing
- •10.1.6 Some issues and related problems on WFS implementation
- •10.2 General theory of WFS
- •10.2.1 Green’s function of Helmholtz equation
- •10.2.2 General theory of three-dimensional WFS
- •10.2.3 General theory of two-dimensional WFS
- •10.2.4 Focused source in WFS
- •10.3 Analysis of WFS in the spatial-spectral domain
- •10.3.1 General formulation and analysis of WFS in the spatial-spectral domain
- •10.3.2 Analysis of the spatial aliasing in WFS
- •10.3.3 Spatial-spectral division method of WFS
- •10.4 Further discussion on sound field reconstruction
- •10.4.1 Comparison among various methods of sound field reconstruction
- •10.4.2 Further analysis of the relationship between acoustical holography and sound field reconstruction
- •10.4.3 Further analysis of the relationship between acoustical holography and Ambisonics
- •10.4.4 Comparison between WFS and Ambisonics
- •10.5 Equalization of WFS under nonideal conditions
- •10.6 Summary
- •11.1 Basic principles of binaural reproduction and virtual auditory display
- •11.1.1 Binaural recording and reproduction
- •11.1.2 Virtual auditory display
- •11.2 Acquisition of HRTFs
- •11.2.1 HRTF measurement
- •11.2.2 HRTF calculation
- •11.2.3 HRTF customization
- •11.3 Basic physical features of HRTFs
- •11.3.1 Time-domain features of far-field HRIRs
- •11.3.2 Frequency domain features of far-field HRTFs
- •11.3.3 Features of near-field HRTFs
- •11.4 HRTF-based filters for binaural synthesis
- •11.5 Spatial interpolation and decomposition of HRTFs
- •11.5.1 Directional interpolation of HRTFs
- •11.5.2 Spatial basis function decomposition and spatial sampling theorem of HRTFs
- •11.5.3 HRTF spatial interpolation and signal mixing for multichannel sound
- •11.5.4 Spectral shape basis function decomposition of HRTFs
- •11.6 Simplification of signal processing for binaural synthesis
- •11.6.1 Virtual loudspeaker-based algorithms
- •11.6.2 Basis function decomposition-based algorithms
- •11.7.1 Principle of headphone equalization
- •11.7.2 Some problems with binaural reproduction and VAD
- •11.8 Binaural reproduction through loudspeakers
- •11.8.1 Basic principle of binaural reproduction through loudspeakers
- •11.8.2 Virtual source distribution in two-front loudspeaker reproduction
- •11.8.3 Head movement and stability of virtual sources in Transaural reproduction
- •11.8.4 Timbre coloration and equalization in transaural reproduction
- •11.9 Virtual reproduction of stereophonic and multichannel surround sound
- •11.9.1 Binaural reproduction of stereophonic and multichannel sound through headphones
- •11.9.2 Stereophonic expansion and enhancement
- •11.9.3 Virtual reproduction of multichannel sound through loudspeakers
- •11.10.1 Binaural room modeling
- •11.10.2 Dynamic virtual auditory environments system
- •11.11 Summary
- •12.1 Physical analysis of binaural pressures in summing virtual source and auditory events
- •12.1.1 Evaluation of binaural pressures and localization cues
- •12.1.2 Method for summing localization analysis
- •12.1.3 Binaural pressure analysis of stereophonic and multichannel sound with amplitude panning
- •12.1.4 Analysis of summing localization with interchannel time difference
- •12.1.5 Analysis of summing localization at the off-central listening position
- •12.1.6 Analysis of interchannel correlation and spatial auditory sensations
- •12.2 Binaural auditory models and analysis of spatial sound reproduction
- •12.2.1 Analysis of lateral localization by using auditory models
- •12.2.2 Analysis of front-back and vertical localization by using a binaural auditory model
- •12.2.3 Binaural loudness models and analysis of the timbre of spatial sound reproduction
- •12.3 Binaural measurement system for assessing spatial sound reproduction
- •12.4 Summary
- •13.1 Analog audio storage and transmission
- •13.1.1 45°/45° Disk recording system
- •13.1.2 Analog magnetic tape audio recorder
- •13.1.3 Analog stereo broadcasting
- •13.2 Basic concepts of digital audio storage and transmission
- •13.3 Quantization noise and shaping
- •13.3.1 Signal-to-quantization noise ratio
- •13.3.2 Quantization noise shaping and 1-Bit DSD coding
- •13.4 Basic principle of digital audio compression and coding
- •13.4.1 Outline of digital audio compression and coding
- •13.4.2 Adaptive differential pulse-code modulation
- •13.4.3 Perceptual audio coding in the time-frequency domain
- •13.4.4 Vector quantization
- •13.4.5 Spatial audio coding
- •13.4.6 Spectral band replication
- •13.4.7 Entropy coding
- •13.4.8 Object-based audio coding
- •13.5 MPEG series of audio coding techniques and standards
- •13.5.1 MPEG-1 audio coding technique
- •13.5.2 MPEG-2 BC audio coding
- •13.5.3 MPEG-2 advanced audio coding
- •13.5.4 MPEG-4 audio coding
- •13.5.5 MPEG parametric coding of multichannel sound and unified speech and audio coding
- •13.5.6 MPEG-H 3D audio
- •13.6 Dolby series of coding techniques
- •13.6.1 Dolby digital coding technique
- •13.6.2 Some advanced Dolby coding techniques
- •13.7 DTS series of coding technique
- •13.8 MLP lossless coding technique
- •13.9 ATRAC technique
- •13.10 Audio video coding standard
- •13.11 Optical disks for audio storage
- •13.11.1 Structure, principle, and classification of optical disks
- •13.11.2 CD family and its audio formats
- •13.11.3 DVD family and its audio formats
- •13.11.4 SACD and its audio formats
- •13.11.5 BD and its audio formats
- •13.12 Digital radio and television broadcasting
- •13.12.1 Outline of digital radio and television broadcasting
- •13.12.2 Eureka-147 digital audio broadcasting
- •13.12.3 Digital radio mondiale
- •13.12.4 In-band on-channel digital audio broadcasting
- •13.12.5 Audio for digital television
- •13.13 Audio storage and transmission by personal computer
- •13.14 Summary
- •14.1 Outline of acoustic conditions and requirements for spatial sound intended for domestic reproduction
- •14.2 Acoustic consideration and design of listening rooms
- •14.3 Arrangement and characteristics of loudspeakers
- •14.3.1 Arrangement of the main loudspeakers in listening rooms
- •14.3.2 Characteristics of the main loudspeakers
- •14.3.3 Bass management and arrangement of subwoofers
- •14.4 Signal and listening level alignment
- •14.5 Standards and guidance for conditions of spatial sound reproduction
- •14.6 Headphones and binaural monitors of spatial sound reproduction
- •14.7 Acoustic conditions for cinema sound reproduction and monitoring
- •14.8 Summary
- •15.1 Outline of psychoacoustic and subjective assessment experiments
- •15.2 Contents and attributes for spatial sound assessment
- •15.3 Auditory comparison and discrimination experiment
- •15.3.1 Paradigms of auditory comparison and discrimination experiment
- •15.3.2 Examples of auditory comparison and discrimination experiment
- •15.4 Subjective assessment of small impairments in spatial sound systems
- •15.5 Subjective assessment of a spatial sound system with intermediate quality
- •15.6 Virtual source localization experiment
- •15.6.1 Basic methods for virtual source localization experiments
- •15.6.2 Preliminary analysis of the results of virtual source localization experiments
- •15.6.3 Some results of virtual source localization experiments
- •15.7 Summary
- •16.1.1 Application to commercial cinema and related problems
- •16.1.2 Applications to domestic reproduction and related problems
- •16.1.3 Applications to automobile audio
- •16.2.1 Applications to virtual reality
- •16.2.2 Applications to communication and information systems
- •16.2.3 Applications to multimedia
- •16.2.4 Applications to mobile and handheld devices
- •16.3 Applications to the scientific experiments of spatial hearing and psychoacoustics
- •16.4 Applications to sound field auralization
- •16.4.1 Auralization in room acoustics
- •16.4.2 Other applications of auralization technique
- •16.5 Applications to clinical medicine
- •16.6 Summary
- •References
- •Index

634 Spatial Sound
SAOC possesses a high coding efficiency. MPS and SAOC allow for a 5.1-channel signal coding at a low bit rate of 48 kbit/s. SAOC enables the independent manipulation of the gain, equalization, and effect of each object. Because its coding and transmission are independent from reproduction, SAOC is appropriate for different reproduction manners (different numbers and configurations of loudspeakers or headphones). SAOC is applicable to teleconferences, personalized music remixed in interactive reproduction, and games.
As stated in Section 13.4.1, general audio coding techniques are different from speech coding techniques. They were developed separately. Audio compression and coding are realized by removing the physical and perceptual redundancy in signals. Speech coding is usually based on the time-varying filter (linear prediction) model of the human vocal system. MPEG specified the standard of MPEG-D Unified Speech and Audio coding (USAC) [ISO/IEC 23003-1 (2012); Neuendorf et al., 2013] to adapt to the applications of digital radio, streaming multimedia, audio book, mobile devices. The USAC combines the enhanced HE-AAC v2 audio coding technique and speech coding technique AMR-WB+ into a unified system. According to the signal component, USAC flawlessly transits between two coding modes. HE-AAC v2 is improved in many aspects, including a time-warped MDCT, additional 50% window lengths of 512 and 1,024 samples (block lengths of 256 and 512 samples) for MDCT with 50% overlap, enhanced SBR bandwidth extension, unified stereo coding. USAC distinguishes from MPS in the following aspects:
1.In addition to interchannel level difference and interchannel correlation, interchannel phase difference is added as the side information of the USAC.
2.In contrast to MPS in which residual signals are coded independently from the downmixing signals, the USAC couples the coding of downmixing and residual signals closely to improve the transmission quality.
3.At higher bit rates, because the core coder can discretely handle a wider bandwidth and code multiple channels, the tools of SBR and parametric coding can be not used. In this case, complex prediction stereo coding is used to improve the efficiency of stereo coding.
The USAC can operate at a bit rate as low as 8 kbit/s for mono signal. Within the bit rate ranging from 8 kbit/s for mono to 64 kbit/s for stereophonic sound, the quality of the USAC exceeds that of HE-AAC v2.
13.5.6 MPEG-H 3D audio
Multichannel spatial surround sound with height in Chapter 6 is next-generation spatial sound technique and system. Various multichannel spatial surround sound systems have been proposed. These systems differ in performance and complexity. The prospect of these systems depends on their acceptability by consumers. The diversity of systems and formats causes serious problems of compatibility in program making, coding, and reproduction. Therefore, the standard for multichannel spatial sound should be developed.
MPEG-H 3D Audio is a coding technique and standard for new-generation spatial sounds. It has the advantages of high flexibility, quality, and efficiency [ISO/IEC 23008-3 (2015); Herre et al., 2014, 2015]. It was called for proposal in 2013 and published in 2015. The MPEG-H 3D Audio coding supports channel-based, objected-based, and higher-order Ambisonic signal inputs. After decoding is completed, it supports various reproduction methods, such as 2-channel, 5.1-channel to 22.2-channel, or even more channel reproduction. It also supports headphone presentation. The reproduction methods are basically independent from the input format, which avoids the problem of compatibility among different spatial sound systems. Therefore, MPEG-H 3D Audio is a universal standard that unites different

Storage and transmission of spatial sound signals 635
spatial sound techniques and formats rather than a coding technique only. This feature distinguishes the MPEG-H 3D Audio from the previous MPEG standards such as MPEG-1 and MPEG-2 AAC audio coding.
The MPEG-H3D core coding uses many previous techniques, especially USAC in Section 13.5.5. Compared with USAC, the main enhancements of MPEG-H 3D core coding are as follows:
1.Joint coding of quadruple input channels
2.Enhanced noise filling
Therefore, the development of MPEG-H 3D Audio focuses on the conversion of various spatial sound signals and rendering/reproduction after coding and decoding. Figure 13.23 illustrates the block diagram of MPEG-H 3D Audio. After USAC-3D core decoding, the following signals and data are separated from the MPEG-H 3D Audio bit stream:
1.Channel-based signals
2.Object-based signals
3.Compressed object metadata
4.SAOC transmission channel signals and side information
5.Higher-order Ambisonics (scene-based) signals and side information
On the basis of the aforementioned signals and data, the decoder generates the reproduced signals that are mixed and then reproduced by loudspeakers or converted for headphone presentation.
The key strategies in MPEG-H 3D Audio include the following:
1.Channel-based reproduction and format conversion
Channel-based signals are intended for a specific loudspeaker configuration or format, and each channel corresponds to the signal of a loudspeaker at a given position.
Figure 13.23 Block diagram of MPEG-H 3D Audio coding/decoding (adapted from Herre et al., 2014).

636 Spatial Sound
However, the configurations of loudspeakers are diversiform or even nonstandard. Format converter aims to convert a set of channel-based signals for reproduction with practical loudspeaker configuration, especially to convert the signals for reproduction with a larger number of channels (such as 22.2-channel) to signals for reproduction with a smaller number of channels (such as 5.1-channel). The principle is similar to that of downmixing in Section 8.2. To ensure the reproduction quality, MPEG-H 3D Audio generates optimized downmixing matrix automatically. It supports optionally transmitted downmixing matrix to preserve the artistic contents of original signals. In addition, it uses equalization filters to preserve the timbre and uses advanced active downmixing algorithm to avoid downmixing artifacts.
The format conversion module involves two parts: rule-based initialization and active downmix algorithm. In a decoder, rule-based initialization derives the optimized downmixing matrix that converts channel-based inputs to the signals of loudspeakers in practical configuration. Derivation is implemented by iteration according to a set of tuned mapping rules for each input channel. Each rule specifies rendering of one input channel to one or more output channels. When an input channel is just consistent with an output channel (loudspeaker), the input is mapped to that output channel to avoid using the phantom source method.
In Section 8.2, for multichannel-correlated inputs with interchannel time difference, or for inputs derived from different filtered versions of the same signals, downmixing directly may lead to comb-filtering and thus timbre coloration. An active downmixing algorithm analyzes the correlation between input signals and aligns the phases if necessary to address this problem. Frequency-dependent normalization is applied to the gain of downmixing to preserve the overall power spectra of signals after downmixing. Moreover, adaptive downmixing algorithm should not alter the uncorrelated input signals.
2.Object-based rendering
USAC-3D core decoding yields object signals and object metadata. In addition to the spatial positions of objects (virtual sources), metadata of other characteristics of objects are included (Fug et al., 2014). Given the configuration of loudspeakers, the decoder feeds object signals to loudspeakers according to certain panning/mixing rules. Time-varying position data describe the spatial trajectory (or parameter equation) of a virtual source. Therefore, time-varying panning enables the simulation of a moving virtual source. The VBAP in Section 6.3 is used in MPEG-H 3D Audio for virtual source rendering. The three active loudspeakers in a spherical triangle are chosen according to the object metadata and practical loudspeaker configuration, and the gains of loudspeaker signals are calculated. However, most practical configurations lack loudspeakers below the horizontal plane. In these cases, imaginary (virtual) loudspeakers are needed for the VBAP.
3.Higher-order Ambisonics
In Chapter 9, the independent signals of higher-order Ambisonics (HOA), which are the time-varying components or coefficients of the spatial harmonic decomposition of a sound field, represent the temporal and spatial information of sound field. In reproduction, independent signals are linearly decoded to loudspeaker signals. The linearly decoded matrix depends on the configuration of loudspeakers. To improve the performance of coding, MPEG-H 3D Audio does not directly transmit the independent signals of Ambisonics. Instead, it applies a two-stage coding process to HOA data, e.g., spatial coding of components and multichannel perceptual coding.
The independent signals of HOA are decomposed into predominant and ambient components. Predominant components, which include directional sounds, can be coded as a set of plane wave incidence from certain directions. Therefore, each predominant