On the Conditioning of the Spherical Harmonic Matrix for Spatial Audio Applications Article Swipe
C Sandeep Reddy
,
Rajesh M. Hegde
·
YOU?
·
· 2017
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.1710.08633
YOU?
·
· 2017
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.1710.08633
In this paper, we attempt to study the conditioning of the Spherical Harmonic Matrix (SHM), which is widely used in the discrete, limited order orthogonal representation of sound fields. SHM's has been widely used in the audio applications like spatial sound reproduction using loudspeakers, orthogonal representation of Head Related Transfer Functions (HRTFs) etc. The conditioning behaviour of the SHM depends on the sampling positions chosen in the 3D space. Identification of the optimal sampling points in the continuous 3D space that results in a well-conditioned SHM for any number of sampling points is a highly challenging task. In this work, an attempt has been made to solve a discrete version of the above problem using optimization based techniques. The discrete problem is, to identify the optimal sampling points from a discrete set of densely sampled positions of the 3D space, that minimizes the condition number of SHM. This method has been subsequently utilized for identifying the geometry of loudspeakers in the spatial sound reproduction, and in the selection of spatial sampling configurations for HRTF measurement. The application specific requirements have been formulated as additional constraints of the optimization problem. Recently developed mixed-integer optimization solvers have been used in solving the formulated problem. The performance of the obtained sampling position in each application is compared with the existing configurations. Objective measures like condition number, D-measure, and spectral distortion are used to study the performance of the sampling configurations resulting from the proposed and the existing methods. It is observed that the proposed solution is able to find the sampling points that results in a better conditioned SHM and also maintains all the application specific requirements.
Related Topics
Concepts
Loudspeaker
Sampling (signal processing)
Computer science
Representation (politics)
Algorithm
Optimization problem
Set (abstract data type)
Mathematical optimization
Matrix (chemical analysis)
Harmonic
Condition number
Mathematics
Acoustics
Computer vision
Programming language
Composite material
Quantum mechanics
Filter (signal processing)
Political science
Politics
Materials science
Law
Physics
Eigenvalues and eigenvectors
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/1710.08633
- https://arxiv.org/pdf/1710.08633
- OA Status
- green
- Cited By
- 2
- References
- 20
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W2766369421
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
-
https://openalex.org/W2766369421Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.48550/arxiv.1710.08633Digital Object Identifier
- Title
-
On the Conditioning of the Spherical Harmonic Matrix for Spatial Audio ApplicationsWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2017Year of publication
- Publication date
-
2017-10-24Full publication date if available
- Authors
-
C Sandeep Reddy, Rajesh M. HegdeList of authors in order
- Landing page
-
https://arxiv.org/abs/1710.08633Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/1710.08633Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/pdf/1710.08633Direct OA link when available
- Concepts
-
Loudspeaker, Sampling (signal processing), Computer science, Representation (politics), Algorithm, Optimization problem, Set (abstract data type), Mathematical optimization, Matrix (chemical analysis), Harmonic, Condition number, Mathematics, Acoustics, Computer vision, Programming language, Composite material, Quantum mechanics, Filter (signal processing), Political science, Politics, Materials science, Law, Physics, Eigenvalues and eigenvectorsTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
2Total citation count in OpenAlex
- Citations by year (recent)
-
2022: 2Per-year citation counts (last 5 years)
- References (count)
-
20Number of works referenced by this work
- Related works (count)
-
10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.also | 267 |
| abstract_inverted_index.been | 31, 103, 150, 180, 195 |
| abstract_inverted_index.each | 210 |
| abstract_inverted_index.etc. | 52 |
| abstract_inverted_index.find | 255 |
| abstract_inverted_index.from | 128, 238 |
| abstract_inverted_index.have | 179, 194 |
| abstract_inverted_index.like | 38, 220 |
| abstract_inverted_index.made | 104 |
| abstract_inverted_index.that | 80, 140, 248, 259 |
| abstract_inverted_index.this | 1, 98 |
| abstract_inverted_index.used | 18, 33, 196, 228 |
| abstract_inverted_index.with | 214 |
| abstract_inverted_index.SHM's | 29 |
| abstract_inverted_index.above | 112 |
| abstract_inverted_index.audio | 36 |
| abstract_inverted_index.based | 116 |
| abstract_inverted_index.order | 23 |
| abstract_inverted_index.solve | 106 |
| abstract_inverted_index.sound | 27, 40, 162 |
| abstract_inverted_index.space | 79 |
| abstract_inverted_index.study | 6, 230 |
| abstract_inverted_index.task. | 96 |
| abstract_inverted_index.using | 42, 114 |
| abstract_inverted_index.which | 15 |
| abstract_inverted_index.work, | 99 |
| abstract_inverted_index.(SHM), | 14 |
| abstract_inverted_index.Matrix | 13 |
| abstract_inverted_index.better | 263 |
| abstract_inverted_index.chosen | 64 |
| abstract_inverted_index.highly | 94 |
| abstract_inverted_index.method | 148 |
| abstract_inverted_index.number | 88, 144 |
| abstract_inverted_index.paper, | 2 |
| abstract_inverted_index.points | 74, 91, 127, 258 |
| abstract_inverted_index.space, | 139 |
| abstract_inverted_index.space. | 68 |
| abstract_inverted_index.widely | 17, 32 |
| abstract_inverted_index.(HRTFs) | 51 |
| abstract_inverted_index.Related | 48 |
| abstract_inverted_index.attempt | 4, 101 |
| abstract_inverted_index.densely | 133 |
| abstract_inverted_index.depends | 59 |
| abstract_inverted_index.fields. | 28 |
| abstract_inverted_index.limited | 22 |
| abstract_inverted_index.number, | 222 |
| abstract_inverted_index.optimal | 72, 125 |
| abstract_inverted_index.problem | 113, 120 |
| abstract_inverted_index.results | 81, 260 |
| abstract_inverted_index.sampled | 134 |
| abstract_inverted_index.solvers | 193 |
| abstract_inverted_index.solving | 198 |
| abstract_inverted_index.spatial | 39, 161, 169 |
| abstract_inverted_index.version | 109 |
| abstract_inverted_index.Harmonic | 12 |
| abstract_inverted_index.Recently | 189 |
| abstract_inverted_index.Transfer | 49 |
| abstract_inverted_index.compared | 213 |
| abstract_inverted_index.discrete | 108, 119, 130 |
| abstract_inverted_index.existing | 216, 243 |
| abstract_inverted_index.geometry | 156 |
| abstract_inverted_index.identify | 123 |
| abstract_inverted_index.measures | 219 |
| abstract_inverted_index.methods. | 244 |
| abstract_inverted_index.observed | 247 |
| abstract_inverted_index.obtained | 206 |
| abstract_inverted_index.position | 208 |
| abstract_inverted_index.problem. | 188, 201 |
| abstract_inverted_index.proposed | 240, 250 |
| abstract_inverted_index.sampling | 62, 73, 90, 126, 170, 207, 235, 257 |
| abstract_inverted_index.solution | 251 |
| abstract_inverted_index.specific | 177, 272 |
| abstract_inverted_index.spectral | 225 |
| abstract_inverted_index.utilized | 152 |
| abstract_inverted_index.Functions | 50 |
| abstract_inverted_index.Objective | 218 |
| abstract_inverted_index.Spherical | 11 |
| abstract_inverted_index.behaviour | 55 |
| abstract_inverted_index.condition | 143, 221 |
| abstract_inverted_index.developed | 190 |
| abstract_inverted_index.discrete, | 21 |
| abstract_inverted_index.maintains | 268 |
| abstract_inverted_index.minimizes | 141 |
| abstract_inverted_index.positions | 63, 135 |
| abstract_inverted_index.resulting | 237 |
| abstract_inverted_index.selection | 167 |
| abstract_inverted_index.D-measure, | 223 |
| abstract_inverted_index.additional | 183 |
| abstract_inverted_index.continuous | 77 |
| abstract_inverted_index.distortion | 226 |
| abstract_inverted_index.formulated | 181, 200 |
| abstract_inverted_index.orthogonal | 24, 44 |
| abstract_inverted_index.application | 176, 211, 271 |
| abstract_inverted_index.challenging | 95 |
| abstract_inverted_index.conditioned | 264 |
| abstract_inverted_index.constraints | 184 |
| abstract_inverted_index.identifying | 154 |
| abstract_inverted_index.performance | 203, 232 |
| abstract_inverted_index.techniques. | 117 |
| abstract_inverted_index.applications | 37 |
| abstract_inverted_index.conditioning | 8, 54 |
| abstract_inverted_index.loudspeakers | 158 |
| abstract_inverted_index.measurement. | 174 |
| abstract_inverted_index.optimization | 115, 187, 192 |
| abstract_inverted_index.reproduction | 41 |
| abstract_inverted_index.requirements | 178 |
| abstract_inverted_index.subsequently | 151 |
| abstract_inverted_index.loudspeakers, | 43 |
| abstract_inverted_index.mixed-integer | 191 |
| abstract_inverted_index.reproduction, | 163 |
| abstract_inverted_index.requirements. | 273 |
| abstract_inverted_index.Identification | 69 |
| abstract_inverted_index.configurations | 171, 236 |
| abstract_inverted_index.representation | 25, 45 |
| abstract_inverted_index.configurations. | 217 |
| abstract_inverted_index.well-conditioned | 84 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 2 |
| citation_normalized_percentile |