Theory and Applications of Spherical Microphone Array Processing

201 Pages·2017·7.03 MB·English

by  Daniel P. Jarrett

Springer Topics in Signal Processing
Daniel P. Jarrett
Emanuël A.P. Habets
Patrick A. Naylor
Theory and
Applications
of Spherical
Microphone
Array Processing
Springer Topics in Signal Processing
Volume 9
Series editors
Jacob Benesty, Montreal, Canada
Walter Kellermann, Erlangen, Germany
More information about this series at http://www.springer.com/series/8109
ë
Daniel P. Jarrett Emanu l A.P. Habets
(cid:129)
Patrick A. Naylor
Theory and Applications
of Spherical Microphone
Array Processing
123
DanielP. Jarrett Patrick A.Naylor
Kilburn& StrodeLLP Department ofElectrical andElectronic
London Engineering
UK Imperial CollegeLondon
London
EmanuëlA.P. Habets UK
International AudioLaboratories Erlangen
Erlangen
Germany
ISSN 1866-2609 ISSN 1866-2617 (electronic)
SpringerTopics inSignal Processing
ISBN978-3-319-42209-1 ISBN978-3-319-42211-4 (eBook)
DOI 10.1007/978-3-319-42211-4
LibraryofCongressControlNumber:2016944322
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Preface
The topic of spherical microphone array signal processing has been gaining
importance since the publications of Meyer and Elko around 2002, and fuelled by
many others since.
Sound is unavoidably influenced by the space in which it is rendered, as we all
knowfrompersonalexperience,andthecapabilityofmicrophonearraystocapture
the spatial information is both fascinating and intriguing. The English physicist
Charles Wheatstone is credited with the first use of the term ‘microphone’.
However, it was not until the carbon microphone, invented by David Hughes and
demonstrated in 1877, that the concept of capturing sound as an electrical signal
becameestablished.TheinventionbyGerhardSesslerandJimWestoftheelectret
microphone in 1962, and further developments of condenser microphone technol-
ogy in particular, led to a significant improvement in quality and reliability.
These early microphones were principally targeting the capture of acoustic
signalsinaclose-talkingmode,lessthanaround10cmfromthetalker’sorsinger’s
lips. Would their inventors have considered that the spatial information associated
withthesoundcouldbeuseful,exploitedtolocalizesourcesofsound,discriminate
desired sounds from interferences, or even infer the geometry of an acoustic space
and navigate within it? We could only guess but certainly the potential to achieve
thesegoalshasbeenalwayspresent.Thecatalystformorerecentdevelopmentshas
been the happy marriage of high quality, synchronized multichannel
analogue-to-digital conversion with powerful digital signal processing hardware
and software, facilitating arrays with elements numbering from a handful to hun-
dreds, or even thousands. Given the availability of numerous sensors, many
alternative geometries can be considered, the spherical geometry being one such
with considerable merits. It is the algorithms to process the signals from these
numerous microphones that are the key focus of this book.
Weofferthereaderaviewofthetheoreticalaspects ofmicrophone arraysignal
processing for spherical geometries and some examples of applications of the
ensuing algorithms. Our intention is to present the methods in a general form
allowing the ideas to be further developed. It is a well known feeling that digging
v
vi Preface
deeper into a subject only serves toreveal greaterdepths and further potential. We
hope, nevertheless, that this book will at the same time provide satisfaction to the
mind of the curious reader but also serve to equip the researchers of the future to
develop and exploit the great potential of spherical microphone arrays and their
associated signal processing.
WegratefullyacknowledgethecontributionsofSebastianBraun,MajaTaseska,
Oliver Thiergart and Mark Thomas to the work presented in this book. We would
also like to express our gratitude to Hamza Javed and Maja Taseska for their
attentive reading of our drafts, and to Sira Gonzalez and Felicia Lim for providing
helpful feedback and suggestions throughout the writing process.
London Daniel P. Jarrett
Erlangen Emanuël A.P. Habets
London Patrick A. Naylor
April 2016
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Background and Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Microphone Array Signal Processing . . . . . . . . . . . . . . . . . . . . 2
1.3 Organization of the Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2 Theoretical Preliminaries of Acoustics . . . . . . . . . . . . . . . . . . . . . . 11
2.1 Fundamentals of Acoustics . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2 Sound Field Representation Using Spherical Harmonic
Expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3 Sign Convention . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.4 Sound Intensity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.5 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3 Spatial Sampling and Signal Transformation . . . . . . . . . . . . . . . . . 23
3.1 Time-Frequency Domain Processing . . . . . . . . . . . . . . . . . . . . . 23
3.2 Complex Spherical Harmonic Domain Processing . . . . . . . . . . . . 25
3.3 Real Spherical Harmonic Domain Processing . . . . . . . . . . . . . . . 27
3.4 Spatial Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.4.1 Sampling Schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.4.2 Array Configurations . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.5 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4 Spherical Array Acoustic Impulse Response Simulation . . . . . . . . . 39
4.1 Allen and Berkley’s Image Method . . . . . . . . . . . . . . . . . . . . . 40
4.1.1 Green’s Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.1.2 Image Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.2 SMIR Method in the Spherical Harmonic Domain . . . . . . . . . . . 42
4.2.1 Green’s Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.2.2 Neumann Green’s Function . . . . . . . . . . . . . . . . . . . . . . 44
vii
viii Contents
4.2.3 Scattering Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.2.4 SMIR Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.3 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.3.1 Truncation Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.3.2 Computational Complexity . . . . . . . . . . . . . . . . . . . . . . 50
4.3.3 Algorithm Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.4 Examples and Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.4.1 Diffuse Sound Field Energy . . . . . . . . . . . . . . . . . . . . . 51
4.4.2 Binaural Interaural Time and Level Differences . . . . . . . . 54
4.4.3 Mouth Simulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.5 Chapter Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . 61
Appendix: Spatial Correlation in a Diffuse Sound Field. . . . . . . . . . . . 61
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5 Acoustic Parameter Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.1 Direction of Arrival Estimation . . . . . . . . . . . . . . . . . . . . . . . . 65
5.1.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5.1.2 Steered Response Power . . . . . . . . . . . . . . . . . . . . . . . . 68
5.1.3 Intensity-Based Method . . . . . . . . . . . . . . . . . . . . . . . . 69
5.1.4 Subspace Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
5.1.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.2 Signal-to-Diffuse Ratio Estimation . . . . . . . . . . . . . . . . . . . . . . 80
5.2.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.2.2 Coefficient-of-Variation Method . . . . . . . . . . . . . . . . . . . 82
5.2.3 Coherence-Based Method . . . . . . . . . . . . . . . . . . . . . . . 83
5.2.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.3 Chapter Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . 88
Appendix: Relationship Between the Zero-Order Eigenbeam
and the Omnidirectional Reference Microphone Signal . . . . . . . . . . . . 88
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
6 Signal-Independent Array Processing . . . . . . . . . . . . . . . . . . . . . . 93
6.1 Signal Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
6.2 Design Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
6.2.1 Directivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
6.2.2 Front-to-Back Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
6.2.3 White Noise Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
6.2.4 Spatial Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
6.3 Signal-Independent Beamformers . . . . . . . . . . . . . . . . . . . . . . . 102
6.3.1 Farfield Beamformers . . . . . . . . . . . . . . . . . . . . . . . . . . 102
6.3.2 Nearfield Beamformers . . . . . . . . . . . . . . . . . . . . . . . . . 110
6.4 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
Contents ix
7 Signal-Dependent Array Processing . . . . . . . . . . . . . . . . . . . . . . . . 113
7.1 Signal Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
7.2 Performance Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
7.2.1 Speech Distortion Index . . . . . . . . . . . . . . . . . . . . . . . . 117
7.2.2 Noise Reduction Factor . . . . . . . . . . . . . . . . . . . . . . . . . 118
7.2.3 Array Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
7.2.4 Mean Square Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
7.3 Signal-Dependent Beamformers . . . . . . . . . . . . . . . . . . . . . . . . 120
7.3.1 Maximum SNR Filter . . . . . . . . . . . . . . . . . . . . . . . . . . 120
7.3.2 Wiener Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
7.3.3 Minimum Variance Distortionless Response Filter . . . . . . 122
7.3.4 Parametric Wiener Filter . . . . . . . . . . . . . . . . . . . . . . . . 126
7.3.5 Linearly Constrained Minimum Variance Filter . . . . . . . . 127
7.3.6 Generalized Sidelobe Canceller Structure . . . . . . . . . . . . 129
7.4 Relative Transfer Function Estimation . . . . . . . . . . . . . . . . . . . . 133
7.4.1 Covariance Subtraction Method . . . . . . . . . . . . . . . . . . . 134
7.4.2 Generalized Eigenvector Method . . . . . . . . . . . . . . . . . . 134
7.4.3 Temporal Averaging Method . . . . . . . . . . . . . . . . . . . . . 135
7.5 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
8 Parametric Array Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
8.1 Signal Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
8.2 Parameter Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
8.3 Sound Pressure Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
8.4 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
8.4.1 Directional Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
8.4.2 Dereverberation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
8.5 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
9 Informed Array Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
9.1 Noise Reduction Using Narrowband DOA Estimates . . . . . . . . . 152
9.1.1 Signal Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
9.1.2 Tradeoff Beamformer . . . . . . . . . . . . . . . . . . . . . . . . . . 155
9.1.3 Signal Statistics Estimation . . . . . . . . . . . . . . . . . . . . . . 156
9.1.4 Desired Speech Presence Probability Estimation . . . . . . . . 159
9.1.5 Algorithm Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
9.1.6 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
9.2 Dereverberation Using Signal-to-Diffuse Ratio Estimates . . . . . . . 169
9.2.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . 170
9.2.2 Informed Filter for Dereverberation . . . . . . . . . . . . . . . . 173