Error analysis of sound source directivity interpolation based on spherical harmonics

Adam Szwajcowski, Daniel Krause, Anna Snakowska

Research output: Contribution to journalArticleScientificpeer-review

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Precise measurement of the sound source directivity not only requires special equipment, but also is time-consuming. Alternatively, one can reduce the number of measurement points and apply spatial interpolation to retrieve a high-resolution approximation of directivity function. This paper discusses the interpolation error for different algorithms with emphasis on the one based on spherical harmonics. The analysis is performed on raw directivity data for two loudspeaker systems. The directivity was measured using sampling schemes of different densities and point distributions (equiangular and equiareal). Then, the results were interpolated and compared with these obtained on the standard 5° regular grid. The application of the spherical harmonic approximation to sparse measurement data yields a mean error of less than 1 dB with the number of measurement points being reduced by 89%. The impact of the sparse grid type on the retrieval error is also discussed. The presented results facilitate optimal sampling grid choice for low-resolution directivity measurements.

Original languageEnglish
Article number10
Pages (from-to)95-104
Number of pages10
Issue number1
Publication statusPublished - 2021
Publication typeA1 Journal article-refereed


  • Interpolation error
  • Sound source directivity
  • Sparse measurements
  • Spherical harmonics

Publication forum classification

  • Publication forum level 1

ASJC Scopus subject areas

  • Acoustics and Ultrasonics


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