Spherical correlation as a similarity measure for 3-D radiation patterns of musical instruments
We investigate the use of spherical cross-correlation as a similarity measure of sound radiation patterns, with potential applications for their study, organization, and manipulation. This work is motivated by the application of corpus-based synthesis techniques to spatial projection based on the ra...
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| Format: | Article |
| Language: | English |
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EDP Sciences
2023-01-01
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| Series: | Acta Acustica |
| Subjects: | |
| Online Access: | https://acta-acustica.edpsciences.org/articles/aacus/full_html/2023/01/aacus220100/aacus220100.html |
| _version_ | 1797740312591859712 |
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| author | Carpentier Thibaut Einbond Aaron |
| author_facet | Carpentier Thibaut Einbond Aaron |
| author_sort | Carpentier Thibaut |
| collection | DOAJ |
| description | We investigate the use of spherical cross-correlation as a similarity measure of sound radiation patterns, with potential applications for their study, organization, and manipulation. This work is motivated by the application of corpus-based synthesis techniques to spatial projection based on the radiation patterns of orchestral instruments. To this end, we wish to derive spatial descriptors to complement other audio features available for the organization of the sample corpus. Considering two directivity functions on the sphere, their spherical correlation can be computed from their spherical harmonic coefficients. In addition, one can search for the 3-D rotation matrix which maximizes the cross-correlation, i.e. which offers the optimal spherical shape matching. The mathematical foundations of these tools are well established in the literature; however, their practical use in the field of acoustics remains relatively limited and challenging. As a proof of concept, we apply these techniques both to simulated radiation data and to measurements derived from an existing database of 3-D directivity patterns of orchestral instruments. Using these examples we present several test cases to compare the results of spherical correlation to mathematical and acoustical expectations. A range of visualization methods are applied to analyze the test cases, including multi-dimensional scaling, employed as an efficient technique for data reduction and navigation. This article is an extended version of a study previously published in [Carpentier and Einbond. 16th Congrès Français d’Acoustique (CFA), Marseille, France, April 2022, pp. 1–6. https://openaccess.city.ac.uk/id/eprint/28202/]. |
| first_indexed | 2024-03-12T14:10:39Z |
| format | Article |
| id | doaj.art-5eac4d5f897a47439af76f120003c6ec |
| institution | Directory Open Access Journal |
| issn | 2681-4617 |
| language | English |
| last_indexed | 2024-03-12T14:10:39Z |
| publishDate | 2023-01-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | Acta Acustica |
| spelling | doaj.art-5eac4d5f897a47439af76f120003c6ec2023-08-21T08:59:05ZengEDP SciencesActa Acustica2681-46172023-01-0174010.1051/aacus/2023033aacus220100Spherical correlation as a similarity measure for 3-D radiation patterns of musical instrumentsCarpentier Thibaut0Einbond Aaron1https://orcid.org/0000-0003-1734-6641STMS Lab – IRCAM, CNRS, Sorbonne Université, Ministère de la CultureCity, University of LondonWe investigate the use of spherical cross-correlation as a similarity measure of sound radiation patterns, with potential applications for their study, organization, and manipulation. This work is motivated by the application of corpus-based synthesis techniques to spatial projection based on the radiation patterns of orchestral instruments. To this end, we wish to derive spatial descriptors to complement other audio features available for the organization of the sample corpus. Considering two directivity functions on the sphere, their spherical correlation can be computed from their spherical harmonic coefficients. In addition, one can search for the 3-D rotation matrix which maximizes the cross-correlation, i.e. which offers the optimal spherical shape matching. The mathematical foundations of these tools are well established in the literature; however, their practical use in the field of acoustics remains relatively limited and challenging. As a proof of concept, we apply these techniques both to simulated radiation data and to measurements derived from an existing database of 3-D directivity patterns of orchestral instruments. Using these examples we present several test cases to compare the results of spherical correlation to mathematical and acoustical expectations. A range of visualization methods are applied to analyze the test cases, including multi-dimensional scaling, employed as an efficient technique for data reduction and navigation. This article is an extended version of a study previously published in [Carpentier and Einbond. 16th Congrès Français d’Acoustique (CFA), Marseille, France, April 2022, pp. 1–6. https://openaccess.city.ac.uk/id/eprint/28202/].https://acta-acustica.edpsciences.org/articles/aacus/full_html/2023/01/aacus220100/aacus220100.htmlradiation patternsspherical acousticsrotational matching |
| spellingShingle | Carpentier Thibaut Einbond Aaron Spherical correlation as a similarity measure for 3-D radiation patterns of musical instruments Acta Acustica radiation patterns spherical acoustics rotational matching |
| title | Spherical correlation as a similarity measure for 3-D radiation patterns of musical instruments |
| title_full | Spherical correlation as a similarity measure for 3-D radiation patterns of musical instruments |
| title_fullStr | Spherical correlation as a similarity measure for 3-D radiation patterns of musical instruments |
| title_full_unstemmed | Spherical correlation as a similarity measure for 3-D radiation patterns of musical instruments |
| title_short | Spherical correlation as a similarity measure for 3-D radiation patterns of musical instruments |
| title_sort | spherical correlation as a similarity measure for 3 d radiation patterns of musical instruments |
| topic | radiation patterns spherical acoustics rotational matching |
| url | https://acta-acustica.edpsciences.org/articles/aacus/full_html/2023/01/aacus220100/aacus220100.html |
| work_keys_str_mv | AT carpentierthibaut sphericalcorrelationasasimilaritymeasurefor3dradiationpatternsofmusicalinstruments AT einbondaaron sphericalcorrelationasasimilaritymeasurefor3dradiationpatternsofmusicalinstruments |