Acoustic Signals and Hearing: A Time-Envelope and Phase Spectral Approach

Cover
Acoustic Signals and
Hearing:
A Time-Envelope and Phase
Spectral Approach
Copyright
Contents
List of figures
Biography
Preface
Acknowledgments
1 Introduction
	1.1 Sinusoidal function
		1.1.1 Instantaneous magnitude and phase
		1.1.2 Complex forms for sinusoidal functions
		1.1.3 Period and harmonics
		1.1.4 Autocorrelation function of periodic function
		1.1.5 Orthogonality of sinusoidal functions and Fourier series expansion
	1.2 Response of linear system to sinusoidal input
		1.2.1 Linear system
		1.2.2 Impulse response and convolution
		1.2.3 Transient and steady-state responses to sinusoidal input
	1.3 Sinusoidal sequence
		1.3.1 Orthogonality of sinusoidal sequences
		1.3.2 Discrete Fourier transform and filter bank
	1.4 Models of sound sources
		1.4.1 Symmetric spherical wave
		1.4.2 Spherical source for spherical wave
		1.4.3 Radiation impedance of spherical source
	1.5 Exercises
	References
2 Resonance systems
	2.1 Single resonator
		2.1.1 Single-degree-of-freedom system
		2.1.2 Loudspeaker cabinet as a single-degree-of-freedom system
	2.2 Coupled oscillator
		2.2.1 Two-degree-of-freedom system
		2.2.2 Coupled oscillator modeling for bass-reflection loudspeaker system
		2.2.3 Zeros and transfer function
	2.3 Response to sinusoidal input
		2.3.1 Steady-state response and poles of transfer function
		2.3.2 Magnitude response and resonance
		2.3.3 Frequency selectivity by resonance
		2.3.4 Impulse and transient responses
	2.4 Wave equation and sound propagation in a one-dimensional system
		2.4.1 Wave equation
		2.4.2 General solution of wave equation
		2.4.3 Traveling of sinusoidal wave
	2.5 Wave propagation in an acoustic tube
		2.5.1 Sinusoidal wave in an open tube
		2.5.2 Magnitude and phase responses to a sinusoidal source in an open tube
		2.5.3 Sinusoidal wave excited by a velocity source in an acoustic tube
		2.5.4 Poles and zeros of driving-point impedance
	2.6 Exercises
	References
3 Modulation waveform and masking effect
	3.1 Analytic signals and envelopes
		3.1.1 Analytic representation of sinusoidal function
		3.1.2 Modulation waveform by analytic signal representation
		3.1.3 Amplitude modulation
		3.1.4 Envelope and instantaneous phase
		3.1.5 Effects of noise on envelope
	3.2 Speech intelligibility under masked condition
		3.2.1 Intelligibility of noisy speech
		3.2.2 Effects of information masking on intelligibility
	3.3 Spectral fine structure of masked speech
		3.3.1 Carriers for intelligible speech
		3.3.2 Frame-wise auto-correlation sequences in spectral domain
		3.3.3 Deformation of harmonic structure
	3.4 Exercises
	References
4 Spectral and temporal effects of signals on speech intelligibility
	4.1 Frame-wise Fourier transform
		4.1.1 N-point Fourier transform
		4.1.2 Linear operation of Fourier transform
		4.1.3 Discrete Fourier transform and subsequences
		4.1.4 Magnitude and phase effects on waveform
		4.1.5 Envelope and frame-wise Fourier transforms
	4.2 Intelligibility of synthesized speech and noise spectral components
		4.2.1 Frame-wise swapping of magnitude and phase spectra between speech and random noise
		4.2.2 Sentence intelligibility scores
	4.3 Envelopes of synthesized speech material
		4.3.1 Cross-correlation between synthesized and original envelopes
		4.3.2 Phase dominance and preserving zero-crossings
	4.4 Intelligibility of time-reversing or random permutation of speech
		4.4.1 Time-reversing a waveform and its Fourier transform
		4.4.2 Intelligibility tests of time-reversing or random permutation of speech
		4.4.3 Intelligibility as a function of frame length for time-reversing or random permutation
		4.4.4 Narrowband envelopes of synthesized materials
		4.4.5 Cross-correlation of envelopes between synthesized and original materials
	4.5 Exercises
	References
5 Spectral envelope and source signature analysis
	5.1 Response of a linear system to an external source
		5.1.1 Spectral product of source signal and impulse response
		5.1.2 Frequency characteristics of steady-state vibrations of string
		5.1.3 Response to external force in the time and frequency domains
	5.2 Clustered line spectral analysis of resonance vibration
		5.2.1 Clustered line spectral modeling
		5.2.2 CLSM for piano string vibration
		5.2.3 Residual by modeling error and spectral envelope
	5.3 Clustered time sequence modeling
		5.3.1 Representation of brief sequences in the time domain
		5.3.2 Formulation of CTSM by linear equations
	5.4 Source waveform estimation from piano string vibration
		5.4.1 CTSM of the initial portion of string vibration
		5.4.2 Estimation of single cycle of cyclic wave by CTSM
	5.5 CLSM and zeros
		5.5.1 Poles and zeros
		5.5.2 CLSM for response due to a pair of poles with same-sign residues
		5.5.3 Zeros of response to excitation source
		5.5.4 Poles, zeros, and accumulated phase of response including excitation source
		5.5.5 CLSM for responses including source function
	5.6 Identification of zeros for source signature analysis
		5.6.1 Identification of zeros using linear equations
		5.6.2 Spectral trough selection
	5.7 Exercises
	References
6 Room reverberation theory and transfer function
	6.1 Reverberation time formulas
		6.1.1 Density of reflection sounds
		6.1.2 Number of collisions into surrounding walls
		6.1.3 Collisions and mean free path
		6.1.4 Reverberation energy decay and reverberation time
	6.2 Reverberation response to direct sound
		6.2.1 Reverberation decay curve for a linear system
		6.2.2 Buildup and decay for reverberant space
	6.3 Room transfer function
		6.3.1 Frequency characteristics and impulse response of sound field in rectangular room
		6.3.2 Complex frequency, poles and zeros of transfer function
		6.3.3 Number of eigenfrequencies and modal density
		6.3.4 Modal bandwidth and modal overlap
		6.3.5 Reverberation formula as superposition of oblique, tangential, and axial wave fields
	6.4 Minimum-phase and all-pass components for transfer functions
		6.4.1 Discrete systems and Fourier transforms
		6.4.2 Zeros and z-transforms of discrete systems
		6.4.3 Zeros and minimum-phase transfer function
		6.4.4 Poles and all-pass systems
		6.4.5 Decomposition of transfer function into product of minimum-phase and all-pass components
	6.5 Exercises
	References
7 Intelligibility and reverberation
	7.1 Superposition of direct sound and reverberation
		7.1.1 Ratio of direct sound and reverberation
		7.1.2 Intelligibility and distance from sound source under reverberant condition
	7.2 Initial decay curve of reverberation and intelligibility
		7.2.1 Initial portion of reverberation decay and sound source distance
		7.2.2 Nonexponential decay curve and intelligibility
	7.3 Multi-array loudspeaker sources and intelligibility in reverberant space
		7.3.1 Energy ratio of direct sound and reverberation for a pair of loudspeakers
		7.3.2 Energy ratio for loudspeakers in a circle
		7.3.3 Concentric circular arrays
	7.4 Modulation envelope and reverberation condition
		7.4.1 Reverberation effects on envelopes
		7.4.2 Transmission of envelope in reverberant space
		7.4.3 Spectral deformation of squared envelope by reflections
	7.5 Modulation transfer functions and linear systems
		7.5.1 Modulation index and sound source distance
		7.5.2 Spectral deformation of envelope by sound source distance
		7.5.3 Complex modulation transfer function in linear systems
	7.6 Exercises
	References
8 Subjective evaluation for coherent region in reverberant space
	8.1 Coherent length from sound source in reverberant space
		8.1.1 Wave traveling in free space
		8.1.2 Accumulated phase of traveling waves in two-dimensional reverberant space
		8.1.3 Propagation and reverberation phase in three-dimensional space
	8.2 Perception of distance from source in coherent region
		8.2.1 Frequency characteristics of transfer function as function of distance in coherent region
		8.2.2 Subjective evaluation of sound source distance
		8.2.3 Magnitude frequency characteristics for coherent and reverberation fields
	8.3 Auto-correlation analysis of musical sound
		8.3.1 Frame-wise auto-correlation functions for musical tones from a piano
		8.3.2 Auto-correlation analysis of musical sound in coherent region
	8.4 Subjective evaluation of musical sound in coherent region
		8.4.1 Conditions of subjective evaluation
		8.4.2 Subjective evaluation of loudness for musical sounds
	8.5 Envelope analysis and intelligibility of speech in the coherent region
		8.5.1 Listening tests for speech samples recorded in the coherent region
		8.5.2 Power spectral behavior of squared envelope of reverberant speech
	8.6 Exercises
	References
9 Spatial impression and binaural sound field
	9.1 Sound image localization and binaural condition of sound
		9.1.1 Head-related transfer functions and linear equations for sound image rendering
		9.1.2 Binaural filters for magnitude and time differences between two receiving points
		9.1.3 Cross-talk cancelation and spectral equalization by binaural filters
		9.1.4 Gain control of inter-aural magnitude difference
	9.2 Cross-correlation functions between a pair of receiving sounds
		9.2.1 Cross-correlation for sound pressure in sinusoidal wave field
		9.2.2 Two-dimensional random sound field
		9.2.3 Cross-correlation function in transient state
	9.3 Symmetrical sound field in a rectangular room
		9.3.1 Spatial correlation for a random sound field in a rectangular room
		9.3.2 Symmetrical sound field in a rectangular room
		9.3.3 Symmetrical binaural sound field in a rectangular room
	9.4 Spatial correlation in random sound fields and subjective diffuseness
		9.4.1 Subjective diffuseness of random sound fields
		9.4.2 Direct sound and spatial correlation
		9.4.3 Inter-aural correlation in random sound field
		9.4.4 Inter-aural correlation in a mixed sound field
		9.4.5 Inter-aural correlation of a two-channel reproduced sound field
	9.5 Reproduction of inter-aural correlations for mixed sound fields
		9.5.1 Mixing of direct sound and reverberation
		9.5.2 Reproduction of spatial correlation
		9.5.3 Decreasing positive correlation of reproduced sound by anti-phase mixing
	9.6 Binaural detection for frequency dependence of inter-aural correlation
		9.6.1 Binaural sensing of differences in frequency characteristics of inter-aural correlation
		9.6.2 Binaural sensing of inter-aural correlation for narrowband noise pairs
	9.7 Precedence effect on sound localization and envelope of signals
		9.7.1 Precedence effect
		9.7.2 Broadband noise and the precedence effect
		9.7.3 Modulation of broadband random noise and the precedence effect
		9.7.4 Envelope correlation and precedence effect
	9.8 Exercises
	References
Index
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