Sound Field Analysis along a Circle and Its Applications to HRTF Interpolation

The sampling and interpolation of a sound field in two and three dimensions along a circle is discussed. The Fourier domain representation of the sound field is used, and an angular sampling theorem is developed for the sampling of the sound field along a circle. Based on these results, HRTF sampling and interpolation are discussed. This method achieves very precise interpolation in terms of mean square error. However, these results are only possible if very finely spaced HRTF measurements are available. A method is proposed to improve interpolation results when the HRTF measurements are more coarsely spaced than dictated by the angular Nyquist theorem. The proposed method interpolates the HRTFs in a subband domain. In subbands where small angular aliasing occurs, the previous method is applied. In the other subbands, interpolation is carried out in a complex temporal envelope domain to avoid aliasing. Simulations with models and measured data show that the proposed algorithm performs significantly better than previous methods in a mean square error sense.

[1]  Flemming Christensen,et al.  Interpolating Between Head-Related Transfer Functions Measured with Low-Directional Resolution , 1999 .

[2]  R. Kress,et al.  Inverse Acoustic and Electromagnetic Scattering Theory , 1992 .

[3]  F. Wightman,et al.  A model of head-related transfer functions based on principal components analysis and minimum-phase reconstruction. , 1992, The Journal of the Acoustical Society of America.

[4]  Ramani Duraiswami,et al.  INTERPOLATION AND RANGE EXTRAPOLATION OF HRTFS , 2004 .

[5]  Gregory H. Wakefield,et al.  A comparison of head related transfer function interpolation methods , 1995, Proceedings of 1995 Workshop on Applications of Signal Processing to Audio and Accoustics.

[6]  T. Ajdler.  The plenacoustic function and its applications , 2006 .

[7]  R. Duda,et al.  Range dependence of the response of a spherical head model , 1998 .

[8]  Swen Müller,et al.  Transfer-Function Measurement with Sweeps , 2001 .

[9]  H. Colburn,et al.  On the minimum-phase approximation of head-related transfer functions , 1995, Proceedings of 1995 Workshop on Applications of Signal Processing to Audio and Accoustics.

[10]  Rodney A. Kennedy,et al.  On dimensionality of multipath fields: Spatial extent and richness , 2002, 2002 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[11]  Neil Gershenfeld,et al.  MIT-Media Lab , 1991, ICMC.

[12]  Gregory H. Wakefield,et al.  Pole-zero approximations for head-related transfer functions using a logarithmic error criterion , 1997, IEEE Trans. Speech Audio Process..

[13]  Sascha Spors,et al.  Spatial Aliasing Artifacts Produced by Linear and Circular Loudspeaker Arrays used for Wave Field Synthesis , 2006 .

[14]  Stephen A. Dyer,et al.  Digital signal processing , 2018, 8th International Multitopic Conference, 2004. Proceedings of INMIC 2004..

[15]  H. Jones.  On multipath spatial diversity in wireless multiuser communications , 2001 .

[16]  Jean-Marc Jot,et al.  Study and Comparison of Efficient Methods for 3-D Audio Spatialization Based on Linear Decomposition of HRTF Data , 2000 .

[17]  Diemer de Vries,et al.  Parameterization and Reproduction of Concert Hall Acoustics Measured with a Circular Microphone Array , 2002 .

[18]  Martin Vetterli,et al.  Plenacoustic function on the circle with application to HRTF interpolation , 2005, Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005..

[19]  M. H. Heycock,et al.  Papers , 1971, BMJ : British Medical Journal.

[20]  Constantine A. Balanis,et al.  Antenna Theory: Analysis and Design , 1982 .

[21]  Minh N. Do,et al.  On the bandlimitedness of the plenoptic function , 2005, IEEE International Conference on Image Processing 2005.

[22]  Diemer de Vries,et al.  Improved microphone array configurations for auralization of sound fields by Wave Field Synthesis. , 2002 .

[23]  R. Duraiswami,et al.  Fast Multipole Methods for the Helmholtz Equation in Three Dimensions , 2005 .

[24]  Mark A. Poletti,et al.  A Unified Theory of Horizontal Holographic Sound Systems , 2000 .

[25]  S. Robeson.  Spherical Methods for Spatial Interpolation: Review and Evaluation , 1997 .

[26]  Don H. Johnson,et al.  Array Signal Processing: Concepts and Techniques , 1993 .

[27]  Diemer de Vries,et al.  Circular Microphone Array for Discrete Multichannel Audio Recording. , 2003 .

[28]  Bill Gardner,et al.  HRTF Measurements of a KEMAR Dummy-Head Microphone , 1994 .

[29]  Klaus Hartung,et al.  Comparison of Different Methods for the Interpolation of Head-Related Transfer Functions , 1999 .

[30]  Christof Faller,et al.  Interpolation of Head Related Transfer Functions Considering Acoustics , 2005 .

[31]  Mark A. Poletti,et al.  Effect of Noise and Transducer Variability on the Performance of Circular Microphone Arrays , 2005 .

[32]  Flemming Christensen,et al.  Directional resolution of head-related transfer functions required in binaural synthesis , 2005 .

[33]  B. V. Van Veen,et al.  A spatial feature extraction and regularization model for the head-related transfer function. , 1995, The Journal of the Acoustical Society of America.

[34]  Durand R. Begault,et al.  3-D Sound for Virtual Reality and Multimedia Cambridge , 1994 .

[35]  Abhijit Kulkarni,et al.  Infinite-impulse-response models of the head-related transfer function. , 1995, The Journal of the Acoustical Society of America.

[36]  V. Ralph Algazi,et al.  Motion-Tracked Binaural Sound , 2004 .

[37]  T. Ajdler,et al.  The Plenacoustic Function and Its Sampling , 2006, IEEE Transactions on Signal Processing.

[38]  Sascha Spors,et al.  Simulation and Visualization of Room Compensation for Wave Field Synthesis with the Functional Transformation Method , 2005 .

[39]  P. K. Chaturvedi,et al.  Communication Systems , 2002, IFIP — The International Federation for Information Processing.