Immersive audio signal processing

This graduate-level text lays out the foundation of DSP for audio and the fundamentals of auditory perception, then goes on to discuss immersive audio rendering and synthesis, the digital equalization of room acoustics, and various DSP implementations. It covers a variety of topics and up-to-date results in immersive audio processing research: immersive audio synthesis and rendering, multichannel room equalization, audio selective signal cancellation, multirate signal processing for audio applications, surround sound processing, psychoacoustics and its incorporation in audio signal processing algorithms for solving various problems, and DSP implementations of audio processing algorithms on semiconductor devices.

Preface	p. vii
Part I Digital Signal Processing for Audio and Acoustics
1 Foundations of Digital Signal Processing for Audio and Acoustics	p. 3
1.1 Basics of Digital Signal Processing	p. 3
1.1.1 Discrete Time Signals and Sequences	p. 4
1.1.2 Linear Systems	p. 6
1.1.3 Time-Invariant Systems	p. 6
1.1.4 Linear and Time-Invariant Systems	p. 6
1.2 Fourier Transforms	p. 8
1.2.1 Transfer Function Representation	p. 10
1.3 The z-Transform	p. 14
1.4 Sampling and Reconstruction	p. 16
1.4.1 Ideal Sampling	p. 17
1.4.2 Reconstruction of Continuous Time Signals from Discrete Time Sequences	p. 18
1.4.3 Sampling Rate Reduction by an Integer Factor	p. 19
1.4.4 Increasing the Sampling Rate by an Integer Factor	p. 21
1.4.5 Resampling for Audio Applications	p. 22
1.5 Discrete Fourier Transform	p. 23
1.6 Bilinear Transform	p. 24
1.7 Summary	p. 25
2 Filter Design for Audio Applications	p. 27
2.1 Filter Design Process	p. 27
2.1.1 Desired Response Specification	p. 27
2.1.2 Approximating Error Function	p. 28
2.2 FIR Filter Design	p. 28
2.2.1 Linear Phase Filter Design	p. 29
2.2.2 Least Squares FIR Filter Design	p. 29
2.2.3 FIR Windows for Filter Design	p. 30
2.2.4 Adaptive FIR Filters	p. 35
2.3 IIR Filter Design	p. 36
2.3.1 All-Pass Filters	p. 37
2.3.2 Butterworth Filters	p. 37
2.3.3 Chebyshev Filters	p. 38
2.3.4 Elliptic Filters	p. 40
2.3.5 Shelving and Parametric Filters	p. 40
2.3.6 Autoregressive or All-Pole Filters	p. 44
2.4 Summary	p. 46
Part II Acoustics and Auditory Perception
3 Introduction to Acoustics and Auditory Perception	p. 49
3.1 Sound Propagation	p. 49
3.2 Acoustics of a Simple Source in Free-Field	p. 50
3.3 Modal Equations for Characterizing Room Acoustics at Low Frequencies	p. 51
3.3.1 Axial, Tangential, Oblique Modes and Eigenfrequencies	p. 53
3.4 Reverberation Time of Rooms	p. 54
3.5 Room Acoustics from Schroeder Theory	p. 60
3.6 Measurement of Loudspeaker and Room Responses	p. 61
3.6.1 Room Response Measurement with Maximum Length Sequence (MLS)	p. 61
3.6.2 Room Response Measurement with Sweep Signals	p. 63
3.7 Psychoacoustics	p. 65
3.7.1 Structure of the Ear	p. 65
3.7.2 Loudness Perception	p. 66
3.7.3 Loudness Versus Loudness Level	p. 68
3.7.4 Time Integration	p. 68
3.7.5 Frequency Selectivity of the Ear	p. 70
3.8 Summary	p. 72
Part III Immersive Audio Processing
4 Immersive Audio Synthesis and Rendering Over Loudspeakers	p. 75
4.1 Introduction	p. 75
4.2 Immersive Audio Synthesis	p. 77
4.2.1 Microphone Signal Synthesis	p. 77
4.2.2 Subjective Evaluation of Virtual Microphone Signals	p. 80
4.2.3 Spot Microphone Synthesis Methods	p. 80
4.2.4 Summary and Future Research Directions	p. 82
4.3 Immersive Audio Rendering	p. 83
4.3.1 Rendering Filters for a Single Listener	p. 83
4.3.2 Rendering Filters for Multiple Listeners	p. 87
4.3.3 Simulation Results	p. 94
4.3.4 Summary	p. 96
5 Multiple Position Room Response Equalization	p. 99
5.1 Introduction	p. 100
5.2 Background	p. 101
5.3 Single-Point Room Response Equalization	p. 102
5.4 Multiple-Point (Position) Room Response Equalization	p. 103
5.5 Designing Equalizing Filters Using Pattern Recognition	p. 105
5.5.1 Review of Cluster Analysis in Relation to Acoustical Room Responses	p. 105
5.5.2 Fuzzy c-means for Determining the Prototype	p. 105
5.5.3 Cluster Validity Index	p. 107
5.5.4 Multiple Listener Room Equalization with Low Filter Orders	p. 107
5.6 Visualization of Room Acoustic Responses	p. 109
5.7 The Sammon Map	p. 110
5.8 Results	p. 112
5.9 The Influence of Reverberation on Room Equalization	p. 121
5.9.1 Image Method	p. 121
5.9.2 RMS Average Filters	p. 121
5.9.3 Results	p. 122
5.10 Summary	p. 123
6 Practical Considerations for Multichannel Equalization	p. 125
6.1 Introduction	p. 126
6.2 Objective Function-Based Crossover Frequency Selection	p. 130
6.3 Phase Interaction Between Noncoincident Loudspeakers	p. 132
6.3.1 The Influence of Phase on the Net Magnitude Response	p. 134
6.4 Phase Equalization with All-Pass Filters	p. 134
6.4.1 Second-Order All-Pass Networks	p. 134
6.4.2 Phase Correction with Cascaded All-Pass Filters	p. 136
6.4.3 Results	p. 139
6.5 Objective Function-Based Bass Management Filter Parameter Optimization	p. 139
6.5.1 Results	p. 144
6.6 Multiposition Bass Management Filter Parameter Optimization	p. 146
6.6.1 Results	p. 147
6.7 Spectral Deviation and Time Delay-Based Correction	p. 150
6.7.1 Results for Spectral Deviation and Time Delay-Based Crossover Correction	p. 152
6.8 Summary	p. 153
7 Robustness of Equalization to Displacement Effects: Part I	p. 157
7.1 Introduction	p. 157
7.2 Room Acoustics for Simple Sources	p. 161
7.3 Mismatch Analysis for Spatial Average Equalization	p. 162
7.3.1 Analytic Expression for Mismatch Performance Function	p. 162
7.3.2 Analysis of Equalization Error	p. 165
7.4 Results	p. 166
7.5 Summary	p. 168
8 Robustness of Equalization to Displacement Effects: Part II	p. 171
8.1 Introduction	p. 171
8.2 Modal Equations for Room Acoustics	p. 172
8.3 Mismatch Analysis with Spatial Average Equalization	p. 172
8.3.1 Spatial Averaging for Multiple Listener Equalization	p. 172
8.3.2 Equalization Performance Due to Mismatch	p. 173
8.4 Results	p. 177
8.4.1 Magnitude Response Spatial Averaging	p. 177
8.4.2 Computation of the Quantum Numbers	p. 178
8.4.3 Theoretical Results	p. 180
8.4.4 Validation	p. 181
8.4.5 Magnitude Response Single-Listener Equalization	p. 183
8.5 Summary	p. 185
9 Selective Audio Signal Cancellation	p. 187
9.1 Introduction	p. 187
9.2 Traditional Methods for Acoustic Signal Cancellation	p. 189
9.2.1 Passive Techniques	p. 189
9.2.2 Active Techniques	p. 190
9.2.3 Parametric Loudspeaker Array	p. 191
9.3 Eigenfilter Design for Conflicting Listener Environments	p. 191
9.3.1 Background	p. 191
9.3.2 Determination of the Eigenfilter	p. 192
9.3.3 Theoretical Properties of Eigenfilters	p. 195
9.4 Results	p. 198
9.4.1 Eigenfilter Performance as a Function of Filter Order M	p. 198
9.4.2 Performance Sensitivity as a Function of the Room Response Duration	p. 202
9.5 Summary	p. 205
References	p. 209
Index	p. 213

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