Preface ....................................................... vii
Part I. Digital Signal Processing for Audio and Acoustics
1. Foundations of Digital Signal Processing for Audio and
Acoustics .................................................... 3
1.1. Basics of Digital Signal Processing ..................... 3
1.1.1. Discrete Time Signals and Sequences .............. 4
1.1.2. Linear Systems ................................... 6
1.1.3. Time-Invariant Systems ........................... 6
1.1.4. Linear and Time-Invariant Systems ................ 6
1.2. Fourier Transforms ...................................... 8
1.2.1. Transfer Function Representation ................ 10
1.3. The z-Transform ........................................ 14
1.4. Sampling and Reconstruction ............................ 16
1.4.1. Ideal Sampling .................................. 17
1.4.2. Reconstruction of Continuous Time Signals
from Discrete Time Sequences .................... 18
1.4.3. Sampling Rate Reduction by an Integer Factor .... 19
1.4.4. Increasing the Sampling Rate by an Integer
Factor .......................................... 21
1.4.5. Resampling for Audio Applications ............... 22
1.5. Discrete Fourier Transform ............................. 23
1.6. Bilinear Transform ..................................... 24
1.7. Summary ................................................ 25
2. Filter Design for Audio Applications ........................ 27
2.1. Filter Design Process .................................. 27
2.1.1. Desired Response Specification .................. 27
2.1.2. Approximating Error Function .................... 28
2.2. FIR Filter Design ...................................... 28
2.2.1. Linear Phase Filter Design ...................... 29
2.2.2. Least Squares FIR Filter Design ................. 29
2.2.3. FIR Windows for Filter Design ................... 30
2.2.4. Adaptive FIR Filters ............................ 35
2.3. IIR Filter Design ...................................... 36
2.3.1. All-Pass Filters ................................ 37
2.3.2. Butterworth Filters ............................. 37
2.3.3. Chebyshev Filters ............................... 38
2.3.4. Elliptic Filters ................................ 40
2.3.5. Shelving and Parametric Filters ................. 40
2.3.6. Autoregressive or All-Pole Filters .............. 44
2.4. Summary ................................................ 46
Part II. Acoustics and Auditory Perception
3. Introduction to Acoustics and Auditory Perception ........... 49
3.1. Sound Propagation ...................................... 49
3.2. Acoustics of a Simple Source in Free-Field ............. 50
3.3. Modal Equations for Characterizing Room Acoustics at
Low Frequencies ........................................ 51
3.3.1. Axial, Tangential, Oblique Modes and
Eigenfrequencies ................................ 53
3.4. Reverberation Time of Rooms ............................ 54
3.5. Room Acoustics from Schroeder Theory ................... 60
3.6. Measurement of Loudspeaker and Room Responses .......... 61
3.6.1. Room Response Measurement with Maximum Length
Sequence (MLS) .................................. 61
3.6.2. Room Response Measurement with Sweep Signals .... 63
3.7. Psychoacoustics ........................................ 65
3.7.1. Structure of the Ear ............................ 65
3.7.2. Loudness Perception ............................. 66
3.7.3. Loudness Versus Loudness Level .................. 68
3.7.4. Time Integration ................................ 68
3.7.5. Frequency Selectivity of the Ear ................ 70
3.8. Summary ................................................ 72
Part III. Immersive Audio Processing
4. Immersive Audio Synthesis and Rendering Over
Loudspeakers ................................................ 75
4.1. Introduction ........................................... 75
4.2. Immersive Audio Synthesis .............................. 77
4.2.1. Microphone Signal Synthesis ..................... 77
4.2.2. Subjective Evaluation of Virtual Microphone
Signals ......................................... 80
4.2.3. Spot Microphone Synthesis Methods ............... 80
4.2.4. Summary and Future Research Directions .......... 82
4.3. Immersive Audio Rendering .............................. 83
4.3.1. Rendering Filters for a Single Listener ......... 83
4.3.2. Rendering Filters for Multiple Listeners ........ 87
4.3.3. Simulation Results .............................. 94
4.3.4. Summary ......................................... 96
5. Multiple Position Room Response Equalization ................ 99
5.1. Introduction .......................................... 100
5.2. Background ............................................ 101
5.3. Single-Point Room Response Equalization ............... 102
5.4. Multiple-Point (Position) Room Response
Equalization .......................................... 103
5.5. Designing Equalizing Filters Using Pattern
Recognition ........................................... 105
5.5.1. Review of Cluster Analysis in Relation to
Acoustical Room Responses ...................... 105
5.5.2. Fuzzy c-means for Determining the Prototype .... 105
5.5.3. Cluster Validity Index ......................... 107
5.5.4. Multiple Listener Room Equalization with Low
Filter Orders .................................. 107
5.6. Visualization of Room Acoustic Responses .............. 109
5.7. The Sammon Map ........................................ 110
5.8. Results ............................................... 112
5.9. The Influence of Reverberation on Room Equalization ... 121
5.9.1. Image Method ................................... 121
5.9.2. RMS Average Filters ............................ 121
5.9.3. Results ........................................ 122
5.10.Summary ............................................... 123
6. Practical Considerations for Multichannel Equalization ..... 125
6.1. Introduction .......................................... 126
6.2. Objective Function-Based Crossover Frequency
Selection ............................................. 130
6.3. Phase Interaction Between Noncoincident
Loudspeakers .......................................... 132
6.3.1. The Influence of Phase on the Net Magnitude
Response ....................................... 134
6.4. Phase Equalization with All-Pass Filters .............. 134
6.4.1. Second-Order All-Pass Networks ................. 134
6.4.2. Phase Correction with Cascaded All-Pass
Filters ........................................ 136
6.4.3. Results ........................................ 139
6.5. Objective Function-Based Bass Management Filter
Parameter Optimization ................................ 139
6.5.1. Results ........................................ 144
6.6. Multiposition Bass Management Filter Parameter
Optimization .......................................... 146
6.6.1. Results ........................................ 147
6.7. Spectral Deviation and Time Delay-Based Correction .... 150
6.7.1 Results for Spectral Deviation and Time Delay-
Based Crossover Correction ...................... 152
6.8. Summary ............................................... 153
7. Robustness of Equalization to Displacement Effects:
Part I ..................................................... 157
7.1. Introduction .......................................... 157
7.2. Room Acoustics for Simple Sources ..................... 161
7.3. Mismatch Analysis for Spatial Average Equalization .... 162
7.3.1. Analytic Expression for Mismatch Performance
Function ....................................... 162
7.3.2. Analysis of Equalization Error ................. 165
7.4. Results ............................................... 166
7.5. Summary ............................................... 168
8. Robustness of Equalization to Displacement Effects:
Part II .................................................... 171
8.1. Introduction .......................................... 171
8.2. Modal Equations for Room Acoustics .................... 172
8.3. Mismatch Analysis with Spatial Average Equalization ... 172
8.3.1. Spatial Averaging for Multiple Listener
Equalization ................................... 172
8.3.2. Equalization Performance Due to Mismatch ....... 173
8.4. Results ............................................... 177
8.4.1. Magnitude Response Spatial Averaging ........... 177
8.4.2. Computation of the Quantum Numbers ............. 178
8.4.3. Theoretical Results ............................ 180
8.4.4. Validation ..................................... 181
8.4.5. Magnitude Response Single-Listener
Equalization ................................... 183
8.5. Summary ............................................... 185
9. Selective Audio Signal Cancellation ........................ 187
9.1. Introduction .......................................... 187
9.2. Traditional Methods for Acoustic Signal
Cancellation .......................................... 189
9.2.1. Passive Techniques ............................. 189
9.2.2. Active Techniques .............................. 190
9.2.3. Parametric Loudspeaker Array ................... 191
9.3. Eigenfilter Design for Conflicting Listener
Environments .......................................... 191
9.3.1. Background ..................................... 191
9.3.2. Determination of the Eigenfilter ............... 192
9.3.3. Theoretical Properties of Eigenfilters ......... 195
9.4. Results ............................................... 198
9.4.1. Eigenfilter Performance as a Function of
Filter Order M ................................. 198
9.4.2. Performance Sensitivity as a Function of the
Room Response Duration ......................... 202
9.5. Summary ............................................... 205
References .................................................... 209
Index ......................................................... 213
Index ......................................................... 351
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