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Abstract (Front Matter PDF )
Summary
Vision and hearing
Hearing points
Inferring the auditory image
Putting the system together
Spatial blur
Auditory blur and coherence
The modulation transfer function
Coherence conservation and the phase locked loop
Auditory imaging concepts
Auditory accommodation and impairments
List of acronyms
List of symbols
Mathematical conventions
Preface
Preface to v6
Preface to v7
About the author
Acknowledgments
About the text
Chapter overview
1 Background (PDF )
1.1 The scope and state of hearing theory
1.2 Elements of hearing theory
1.3 Hearing theoretical development and vision
1.4 Objects and images in hearing research
1.4.1 The acoustic object
1.4.2 The auditory image
1.4.3 The perceived auditory object
1.4.4 Discussion
1.4.5 A note about subsequent auditory imaging terminology
1.5 Rigorous analogies between hearing and vision
1.5.1 The prominence of direct versus reflected radiation
1.5.2 Anatomy and physiology
1.5.2 Equal-level receptors
1.5.2 Equal-level ganglion cells
1.5.2 Equal-level cortex and thalamus
1.5.3 Imaging theory
1.5.4 Information and communication
1.5.5 Coherence
1.6 Conclusion
2 The anatomy and physiology of the mammalian ear (PDF )
2.1 Introduction
2.2 The peripheral ear
2.2.1 The outer ear
2.2.2 The middle ear
2.2.3 The inner ear
2.2.3 The cochlea
2.2.3 The auditory nerve
2.3 Organizing principles and common threads in the central auditory system
2.3.1 Tonotopy
2.3.2 Synchronized responses
2.3.3 Generalizations from single unit recordings
2.3.4 Dual-stream models
2.4 Central auditory neuroanatomy
2.4.1 Medulla and pons
2.4.2 Midbrain
2.4.3 Thalamus and cortex
2.5 Hearing in humans and other mammals
2.5.1 Outer and middle ear differences
2.5.2 Cochlear and auditory nerve differences
2.5.3 Central differences
3 The acoustic source and environment (PDF )
3.1 Introduction
3.2 Physical waves
3.2.1 Linear analysis
3.2.2 Dispersion analysis
3.2.3 Conclusion
3.3 Acoustic sources
3.3.1 Primitive sound sources
3.3.1 Solid objects
3.3.1 Modal dispersion
3.3.1 Resonators
3.3.1 Mode-Locking
3.3.1 Airflow generators
3.3.1 Stochastic sources
3.3.2 Speech and other animal sounds
3.3.3 Complex source modulation
3.3.3 Explicit forced modulation
3.3.3 Implicit modulation
3.3.3 Transient response
3.4 The acoustic environment
3.4.1 Radiation patterns
3.4.2 Acoustic information propagation in air
3.4.3 Reflections
3.4.4 Room acoustics
3.4.4 Steady-state response
3.4.4 Transient response
3.5 Transitioning from waves to stimuli
4 Optical imaging (PDF )
4.1 Introduction
4.2 Optical imaging theory
4.2.1 Geometrical optics
4.2.2 Diffraction and Fourier optics
4.3 The human eye
4.4 Some links between imaging optics and acoustics
5 Three approaches to information transfer (PDF )
5.1 Introduction
5.2 Information
5.2.1 Information theory in a nutshell
5.2.1 Discrete communication
5.2.1 Continuous communication
5.2.2 The physicality of information
5.2.3 Information theory and hearing
5.2.4 Auditory information
5.3 Communication
5.3.1 Communication theory basics
5.3.2 Acoustic and auditory communication
5.4 Imaging and communication
5.4.1 Imaging as communication
5.4.2 Similarities and differences between imaging and communication
6 Physical signals (PDF )
6.1 Introduction
6.2 The analytic signal
6.3 The narrowband approximation and the complex envelope
6.4 Auditory envelope and phase
6.4.1 Auditory sensitivity to temporal envelope
6.4.2 Auditory sensitivity to phase
6.4.2 ``Phase deafness'' and its discontents
6.4.2 Frequency modulation
6.4.3 The envelope and the temporal fine structure
6.4.4 A final remark
6.5 Challenges to the analytic signal formulation
6.5.1 Auditory challenges
6.5.1 Empirical methods
6.5.1 Bandwidth
6.5.2 Mathematical challenges
6.5.3 Frequency and instantaneous frequency
6.6 Hearing, modulation, and demodulation
6.6.1 Real and complex envelopes
6.6.2 Two spectra
7 Toward a unified view of coherence (PDF )
7.1 Introduction
7.2 Perspectives on coherence
7.2.1 Optics
7.2.2 Communication
7.2.3 Acoustics
7.2.4 Hearing: Psychoacoustics
7.2.5 Neuroscience
7.2.6 Hearing: Neurophysiology
7.3 Synthesis
8 Acoustic coherence theory suitable for hearing (PDF )
8.1 Introduction
8.2 Coherence and interference
8.2.1 The coherence function
8.2.2 Temporal coherence and spatial coherence
8.2.3 The cross-spectral density and spectrum
8.2.4 Coherence time and coherence length
8.2.5 The wave equation for the coherence functions
8.2.6 Spectral coherence
8.2.7 Broadband interference with spectral coherence
8.2.8 Narrowband filtering and coherence
8.2.9 Nonstationary coherence
8.2.9 Beating
8.2.10 Discussion
8.3 Coherence of typical acoustic sources
8.3.1 Mathematical sounds and realistic light sources
8.3.2 Effective duration of realistic acoustic sources
8.3.3 Coherence time of realistic sources
8.3.4 Discussion
8.4 Decoherence through reflections and reverberation
8.4.1 Coherence and reflections
8.4.2 Coherence and reverberation
8.5 Interaural coherence
8.6 Coherence processing in the brain
8.7 Discussion
9 Synchronization and phase-locked loops (PDF )
9.1 Introduction
9.2 Background
9.3 The phase-locked loop (PLL)
9.4 The linearized PLL model
9.5 PLL coherence
9.6 Motivation for an auditory PLL
9.7 Nonlinear synchronization recast as a PLL
9.7.1 Nonlinear oscillators and PLLs
9.7.2 Auditory neural phase locking
9.7.3 The origin of auditory phase locking
9.8 The organ of Corti as a PLL
9.8.1 Identifying the PLL components
9.8.1 The phase detector
9.8.1 The loop filter
9.8.1 The local oscillator
9.8.2 Putting together the auditory PLL
9.8.3 Interim discussion
9.9 Corollaries to the PLL
9.9.1 What signals can acquire lock?
9.9.2 Is there any spurious or residual phase locking even if the PLL receives incoherent signals?
9.9.3 What is the approximate pull-in time?
9.9.4 What is the pull-in (capture) frequency range for a given auditory channel?
9.9.5 What changes in the input signal can pull the PLL out of lock?
9.9.5 Phase step
9.9.5 Frequency step
9.9.5 Frequency ramp
9.9.5 Conclusion
9.9.6 Can the PLL become unstable?
9.9.7 What is the effect of the input level on the PLL response?
9.9.8 Conclusion
9.10 Further PLLs downstream
9.11 Detection schemes with and without phase locking
9.12 Conclusion
10 The paratonal equation (PDF )
10.1 Background
10.2 The ``paraxial'' approximation of the dispersion equation
10.3 The time lens
10.4 Summary of assumptions
10.5 Conclusion
11 Estimating the auditory imaging parameters (PDF )
11.1 Introduction
11.2 The outer ear
11.2.1 The waveguide approximation
11.2.2 Higher-order modes
11.2.3 The group-velocity dispersion of the outer ear
11.3 The middle ear
11.3.1 The middle ear vibrational modes
11.3.2 Middle ear group-velocity dispersion
11.4 The inner ear: oval window to the outer hair cells
11.4.1 Single-mode traveling wave
11.4.2 Cochlear dispersion and group-velocity dispersion
11.4.3 Estimating the cochlear group-delay dispersion
11.5 Total group-delay dispersion of the inner ear
11.6 The inner ear: time lensing by the outer hair cells
11.6.1 Stiffness-dependent traveling-wave phase modulation
11.6.2 Phase modulation evidence
11.6.2 Negative resistance due to outer hair cell activity
11.6.2 Olivocochlear efferent bundle effects
11.6.2 Radial displacement of inner hair cell stereocilia
11.6.2 Vibration ``hotspots'' in the organ of Corti
11.6.2 Angle-dependence phase measurements of the organ of Corti
11.6.3 Estimation of the auditory time-lens curvature
11.6.4 Extrapolation of time-lens curvature to human hearing
11.6.4 Constant focal time
11.6.4 Analogous focal time target
11.6.4 Filter bandwidth scaling
11.6.4 Guinea pig and gerbil \(Q_{10}\) spread
11.6.4 Frequency selectivity in humans
11.6.4 Human time-lens curvature estimation
11.6.4.6 Large-curvature scaling
11.6.4.6 Small-curvature scaling
11.6.5 Discussion
11.7 Neural dispersion
11.7.1 The inferior colliculus is the candidate auditory retina
11.7.2 The existence of the neural dispersion
11.7.3 Neural dispersion estimation
11.8 Discussion
12 The temporal imaging equations (PDF )
12.1 Introduction
12.2 Temporal imaging with a single time lens
12.2.1 Ideal temporal imaging
12.2.2 Nonideal imaging of a Gaussian pulse
12.3 The imaging condition and the auditory system
12.4 Psychoacoustic glides in temporal imaging
12.4.1 Modeling of Schroeder-phase complex curvature measurements
12.4.2 Initial estimates of the phase curvature and \(t_0\)
12.5 The temporal aperture based on psychoacoustic glide data
12.5.1 The entrance pupil, temporal aperture, and exit pupil
12.5.2 The low-frequency correction
12.5.3 Comparison with temporal windows from psychoacoustic literature
12.5.4 Comparison with physiological chinchilla data
12.5.5 Comparison with psychoacoustic beating data
12.6 The global quadratic phase term
12.7 Discussion
12.7.1 The imaging equations
12.7.2 Inherent auditory defocus
12.7.3 The temporal aperture
12.7.4 The auditory dispersion parameters
12.7.5 Pinhole camera design
12.7.6 Absorption and high-order dispersive aberrations
13 The impulse response and its associated modulation transfer functions (PDF )
13.1 Introduction
13.2 The impulse response of the imaging system
13.2.1 Imaging condition satisfied
13.2.2 Imaging condition not satisfied
13.3 The Modulation transfer functions
13.3.1 Gaussian pupil
13.3.2 Rectangular pupil
13.3.3 Power modulation spectra and bandwidths
13.4 The modulation transfer function in hearing
13.4.1 Low-frequency modulation bandwidth correction
13.4.2 Empirical TMTF data from literature
13.4.3 Tonal TMTFs
13.4.4 Broadband TMTFs
13.4.5 Narrowband TMTFs
13.5 Modulation and partially coherent sound
13.6 Discussion and conclusion
14 The use of sampling for imaging continuous signals (PDF )
14.1 Introduction
14.2 Sampling in hearing theory
14.3 Basic aspects of ideal sampling
14.4 Auditory sampling and imaging
14.4.1 Impulse sampling
14.4.2 Natural sampling and images
14.4.3 Flat-top sampling
14.5 Auditory coding or sampling?
14.6 ``It from bit''
14.7 Nonuniform undersampling
14.8 The effect of sampling on the modulation transfer function
14.9 Discussion
15 Auditory image fundamentals (PDF )
15.1 Introduction
15.2 Sharpness and blur in the hearing literature
15.3 Sharpness, blur, and aberrations of auditory images
15.3.1 The two limits of optical blur
15.3.2 Contrast and blur
15.3.3 Auditory blur and aberrations
15.4 Suprathreshold masking, contrast, and blur
15.5 The auditory defocus
15.6 The temporal resolution of the auditory system
15.6.1 Temporal acuity
15.6.2 Envelope acuity
15.7 Polychromatic images
15.8 Pitch as an image
15.9 Higher-order monochromatic auditory aberrations
15.9.1 General considerations
15.9.2 Physiological evidence
15.9.3 Psychoacoustic evidence
15.9.4 Further psychoacoustic evidence
15.10 Chromatic aberration
15.10.1 ``Transverse'' chromatic aberration
15.10.2 Temporal chromatic aberration
15.11 Auditory depth of field?
15.11.1 The auditory f-number
15.11.2 Auditory depth of field (time)
15.11.3 Auditory depth of field (coherence)
15.11.3 Nonsimultaneous masking
15.11.3 Nonsimultaneous masking as depth of field
15.11.4 Discussion
15.12 Aberrations not found in hearing
15.13 Aberrations due to nonlinearities
15.14 Rules of thumb for auditory imaging
15.15 Discussion
16 Auditory accommodation (PDF )
16.1 Introduction
16.2 Ocular accommodation
16.3 What may auditory accommodation be like?
16.3.1 Relevant empirical evidence
16.3.2 Synthesis
16.4 The hypothetical accommodating component(s)
16.4.1 Cochlear group-delay dispersion
16.4.2 Time-lens curvature and the phase-locked loop
16.4.2 The medial olivocochlear reflex
16.4.2 Time-lens curvature
16.4.2 The phase-locked loop
16.4.2.3 Motivation
16.4.2.3 Empirical evidence
16.4.2.3 Synthesis
16.4.2 PLL and time-lens accommodation
16.4.3 The temporal aperture duration and shape
16.4.4 Neural group-delay dispersion
16.4.5 Filter bandwidth
16.4.6 Sampling rate
16.4.7 Synchronization accommodation
16.4.7 Phase-lock coupling strength and noise
16.4.7 Jitter
16.4.7 Dither
16.4.7 Relation to tinnitus?
16.4.8 Coherent and incoherent stream mixing
16.5 What informs auditory accommodation?
16.6 Listening effort and accommodation
16.7 Discussion
17 Dispersive and synchronization hearing impairments (PDF )
17.1 Introduction
17.2 The missing dimensions of hearing impairments
17.3 Evidence for dispersive shifts in hearing impairments
17.3.1 Changes in the total group-velocity dispersion
17.3.1 Schroeder phase curvature drift
17.3.1 Derived-band auditory brainstem response changes
17.3.1 Filter broadening and group-delay dispersion changes
17.3.2 Changes in cochlear dispersion as a result of impairment
17.3.3 Static changes in the OHC (time lens) curvature
17.3.3 Forward masking and depth of field
17.3.3 Binaural diplacusis
17.3.4 Impairments in neural group-delay dispersion
17.3.4 Direct evidence for neural group dispersive changes
17.3.4 Effects on the temporal modulation transfer function (TMTF)
17.3.4 Auditory neuropathy
17.4 Phase locking and coherent detection impairments
17.4.1 Loss of balance between coherent and noncoherent detection
17.4.2 OHC impairment
17.4.3 Neural impairment
17.4.4 Excessive phase locking
17.5 Sampling rate and clocking impairments
17.6 Excessive aberrations
17.6.1 Excessive transverse chromatic aberration
17.6.2 Neural syncrhony: Excessive temporal chromatic aberration
17.6.3 Higher-order aberrations and adjacent-filter phase mismatch
17.7 Impairments of auditory accommodation
17.7.1 Neural synchrony: Loss of defocus amplitude
17.7.1 Presbyopia and prebycusis
17.7.1 Hypothetical effects of medial olivocochlear reflex impairment
17.7.1 Medial olivocochlear reflex and aging
17.7.1 Aging-related hearing and accommodation impairments
17.7.2 Loss of depth-of-field control
17.7.3 Tinnitus as an accommodative impairment
17.8 Conclusion
18 General model and discussion (PDF )
18.1 Introduction
18.2 A provisional functional model of the mammalian auditory system
18.2.1 Introduction
18.2.2 The model
18.3 Known gaps and weaknesses in the proposed theory
18.3.1 Analytical approximations of the dispersive paratonal equation
18.3.2 Multiple roles assigned to the organ of Corti
18.3.3 Neural group-delay dispersion
18.3.4 Modulation filtering
18.3.5 The role of the PVCN
18.3.6 Accommodation
18.3.7 Coherence model
18.3.8 No simulation
18.3.9 Across-channel response
18.3.10 Lateral inhibition
18.3.11 Binaural hearing
18.3.12 Neuromodulation
18.3.13 Multiple time lenses and PLLs
18.4 Novel contributions to auditory theory
18.4.1 Temporal auditory imaging
18.4.2 Sampling
18.4.3 Modulation domain
18.4.4 Coherence and defocus
18.4.5 Coherent and noncoherent detection
18.5 Missing experimental data
18.5.1 Human dispersion parameters
18.5.2 Behavioral data
18.5.3 Acoustics
18.5.4 Cross-disciplinary digging
18.6 Overarching themes
18.6.1 Imaging as a unifying sensory principle
18.6.2 Perception and sensation
18.6.3 Analog and digital computation in service of sensation
18.6.4 Fast and slow processing
18.6.5 The auditory literature
A Examples of realistic coherence functions of acoustic sources (PDF )
A.1 Introduction
A.2 White noise and the cohering effect of two filter types
A.3 Effect of integration time
A.4 Stationarity and nonstationarity
A.5 Four narrowband coherence-time examples
A.6 The effects of room acoustics on coherence
A.6.1 Effect of position and frequency
A.6.2 Decoherence as a function of position and frequency
A.6.3 Cross-spectral coherence
A.7 Conclusion
B Waves (PDF )
B.1 Group-velocity dispersion
B.2 Group-velocity absorption
B.3 Complex pulse calculus
C Linear canonical transform approach to the dispersion integral (PDF )
D Impulse response of rectangular pupil with positive defocus (PDF )
E Evidence of discrete sampling in hearing through aliasing of double- and triple-pulse sequences (PDF )
E.1 Introduction
E.1.1 Continuous and discrete auditory temporal models
E.1.2 The present study
E.2 Experiments
E.2.1 Experiment 1: Confusion between one, two, and three pulses
E.2.1 Introduction
E.2.1 Methods
E.2.1.2 Subjects
E.2.1.2 Setup
E.2.1.2 Stimuli
E.2.1.2 Procedure
E.2.1 Results
E.2.1 Discussion
E.2.2 Experiment 2: Within-channel adaptive two-three numerosity threshold
E.2.2 Introduction
E.2.2 Methods
E.2.2.2 Stimuli
E.2.2.2 Procedure
E.2.2 Results
E.2.2 Discussion
E.2.3 Experiment 3: The possibility of nonuniform sampling
E.2.3 Introduction
E.2.3 Methods
E.2.3.2 Procedure
E.2.3.2 Stimuli
E.2.3 Results
E.2.3 Discussion
E.3 General discussion
E.3.1 Relationship to continuous temporal processing models
E.3.2 Physiological correlates of the results
E.3.3 Individual variation and resemblance to informational masking
E.3.4 No intensity effects
E.3.5 Discrete or continuous sampling in the auditory system
E.4 Conclusion
F Dispersion parameter estimation from psychoacoustic data (PDF )
F.1 Introduction
F.1.1 Beating
F.1.2 Phase curvature
F.1.3 Stretched octave
F.1.4 Double-pulse gap detection
F.1.5 Solving for \(v\)
F.2 Results and discussion
F.2.1 Root selection
F.2.2 Complex solutions?
F.2.3 Low-frequency inversion
F.2.4 Magnification
F.3 General discussion