A fast calculation method of the head-related transfer functions for multiple source points based on the boundary element method

Transcription

1 Acoust. Sci. & Tech. 24, 5 (2003) PAPER A fast calculation method of the head-related transfer functions for multiple source points based on the boundary element method Makoto Otani and Shiro Ise Graduate School of Engineering, Kyoto University, Yoshida-Honmachi, Sakyou-ku, Kyoto, Japan ( Received 2 December 2002, Accepted for publication 27 May 2003 ) Abstract: In the binaural method, sound signals are reproduced in each of the ears of a listener by using headphones. Usually, a dummy head microphone is used to record the signal to be reproduced. However, if the sound field to be reproduced does not exist, the dummy head recording method is not usable. In this case, we can produce the virtual sound field by calculating the input signals of the headphones from the head-related transfer functions (HRTFs) and the virtual sound image. Although the HRTFs can be obtained by measuring an impulse response between a loudspeaker and a listener s ear in an anechoic chamber, it would be very useful if they could be calculated. In many researches that focus on predicting HRTFs by calculation, the boundary element method (BEM), which calculates the HRTFs by solving the wave equation using a computer model of the head, is rather prominent. However, one of the drawbacks of the BEM in obtaining the HRTFs is the considerable amount of calculation time that is required. In this study, we suggest a new method for HRTF calculation which enables significantly enhanced speed by pre-processing an inverse of the coefficient matrix of the BEM. Keywords: Head-related transfer functions, Boundary element method, Sound field reproduction, Binaural method PACS number: Bt, Ha, Qp, Pn [DOI: /ast ] 1. INTRODUCTION Generally, humans obtain spatial information through binaural listening, which is one of the functions of phonoreception. Particularly, it is known that humans perceive the direction and distance of a sound source through interaural level differences (ILD), interaural phase differences (IPD), interaural time differences (ITD) and spectral cues, which are characteristics of a sound signal related with a direction of a sound image [1]. These physical values are very important for sound image localization and they are contained in the head-related transfer functions (HRTFs), which are acoustical transfer functions between a sound source and a listener s ears. Therefore, HRTFs are essential for methods such as the binaural technique to realize sound field reproduction precisely by synthesizing input signals at both of the ears. And because the HRTFs are acoustical transfer functions between a sound source and both ears, they can be measured. In fact, the HRTFs of a listener and those of a dummy head have been previously measured (e.g. [2,3]). otani@ae-gate1.archi.kyoto-u.ac.jp Commonly, the HRTFs can be measured in an anechoic chamber. However, such measurement requires significant equipment as well as a substantial amount of time. Furthermore, the HRTFs depend not only on direction but also on the distance between a sound source and a listener s ear [4]. Therefore, it would be virtually impossible to measure the HRTFs for every direction and distance. As a result, many researches have tried to predict the HRTFs by calculation. For example, an interpolation from the measurement data [5] or an analysis that assumes the head to be a rigid sphere model [6] or a spheroid model [7] have been used for HRTF calculation. As for the method using the rigid sphere model, it is known that the HRTFs can be simulated at a frequency range less than about 5 khz, however the influence of the ear pinna is ignored because the entire head including the ear pinna is assumed to be a sphere. The same is true for the spheroid model. On the other hand, if we solve the wave equation with the correct boundary condition of the head including the ear pinna, we can obtain the HRTFs in the high frequencies as well. 259

2 Acoust. Sci. & Tech. 24, 5 (2003) In order to predict the HRTFs, in this study we tried to solve Helmholtz integral equations as the exterior problem whose boundary is the 3D geometry of a dummy head measured by 3D scanner using the boundary element method (BEM). Weinrich was the first to investigate the deformation of a sound field caused by a manikin [8] and to suggest the BEM using a computer model of the head in order to analyze a sound field around the head region. Recently, researches on a numerical simulation with the BEM and a computer model of the head generated using a 3D scanner have been conducted [9 12]. Katz suggested using a 3D scanner in order to obtain geometric data of the head for the HRTF calculation. He measured the geometry of a human head by using a 3D scanner and created a precise computer model of the head region. Using the BEM, he subsequently compared this computer model with a model that lacked a ear pinna and a rigid sphere model [9], and incorporated the acoustic properties of human skin and hair into the BEM calculation [10]. Kahana et al. meanwhile created a computer model of the KEMAR in order to construct an HRTF database [11]. Although the BEM can be used to calculate HRTFs accurately, the time required for such calculation is extremely long compared with conventional calculation methods. And although the computational capacity/resources available to man are constantly becoming more powerful, it still remains a difficult computational task to calculate the HRTFs using the conventional BEM. There are two solutions to avoid increased calculation time caused by calculating the HRTFs for many source positions. One is a frequently used method which calculates the results all at once for multiple source positions previously defined in the pre-process. This method is realized by applying LU factorization to the coefficient matrix and solving the simultaneous equations sequentially, while changing the term dependent on source position. The drawback to this method is that we cannot obtain results for source position undefined in the pre-process. The other method is one that utilizes the principle of reciprocity which enables the conversion between a source point and a receiver point. Katz and Kahana et al. utilized the principle of reciprocity in order to eliminate extreme increases in calculation time caused by calculating the HRTF for many source positions [9,11]. Theoretically, the principle of reciprocity is guaranteed to hold true for the Helmholtz integral equation. Numerically, however, the results obtained by the principle of reciprocity are different from those obtained by the normal method and the accuracy of the reciprocity method decreases compared with the normal method. Thus, it is necessary to investigate the effects caused by the principle of reciprocity with the BEM. In this paper, we describe the method of calculating the HRTFs using the BEM. In order to minimize the error factor caused by the non-uniqueness problem of the exterior integral equation at eigen-frequencies inside a boundary, the CHIEF method is incorporated into the use of the BEM [13]. Furthermore, we suggest a new calculation method which enables significantly enhanced speed for HRTF calculation by using an inverse of the coefficient matrix of the BEM. By using the new method proposed in this paper, it is possible to define truely arbitrary source positions in the post-process and obtain the same results as those in conventional precise methods. This method is realized by multiplying an inverse of the coefficient matrix and a vector which are independent on the source position and preserving the resulting vector on the disk, while the simultaneous equations are solved in order to obtain acoustic pressures on the surface elements in conventional method. In the numerical study, these methods are compared and are discussed. 2. HRTF CALCULATION WITH THE BEM The BEM used to calculate the HRTFs is categorized as an exterior problem of the Helmholtz integral equation. As the boundary condition, the boundary surface is given by the shape of the dummy head. By solving the integral equation, we obtain the acoustic pressure at the ears when a sound source is located at a particular position Calculation of the Acoustic Pressure within the Volume Based on the BEM, the acoustic pressure within the volume V (pðs 2 VÞ) can be written as where pðsþ ¼g s A j!g s V ðg ns þ j!g s YÞ ^P; g s ¼½Gðr 0 k jsþš 2 CN ; 2 3 ZZ 6 7 G s ¼ 4 Gðr j jsþds5 2 C M ; s j 2 ZZ 6 G ns ¼ 4 s j 3 7 ds5 2 C M ; A ¼½q 1 ; q 2 ; q 3 ; ; q N Š T 2 C N ; V ¼ ½vðr 1 Þ; vðr 2 Þ; vðr 3 Þ; ; vðr M ÞŠ T 2 C M ; Y ¼ diagðy n ðr 1 Þ; y n ðr 2 Þ; y n ðr 3 Þ; ; y n ðr M ÞÞ 2 C MM ; ð1þ 260

3 M. OTANI and S. ISE: FAST CALCULATION METHOD OF HRTF BASED ON THE BEM S j : the j-th surface element ðj ¼ 1...MÞ, r 0 k : point source position ðk ¼ 1...NÞ, r j : center of S j, p : acoustic pressure, G : the Green function, q k : volume velocity of the source k,! : angular frequency, : air density, n : normal vector, v : particle velocity in the normal direction, y n : acoustic admittance in the normal direction. ^P represents the acoustic pressures on the surface elements given by solving the following equation, 1 2 I M þ G n þ j!gy P ¼ ga j!gv; ð2þ where 2 3 ZZ 6 7 G n ¼ 4 Gðrjr i ÞdS5 2 C MM ; S j 2 ZZ 6 G ¼ 4 S i 3 7 ds5 2 C MM ; g ¼ Gðr 0 k jr iþ 2 C MN : ð3þ 2.2. Calculation of the HRTFs It is known that the entrance of the ear canal is the optimal point for HRTF measurements and binaural recordings using for both a dummy head and a real head, because a transmission between the entrance (or a few millimeters outside the entrance) of the ear canal and the ear drum does not depend on the source direction [14]. Reference [14] describes that practical HRTFs are able to be measured at 6 millimeters outside of the entrance of the ear canal. In this study, the HRTFs are defined as the acoustical transfer functions between a point source located in a free field and a point near the entrance of the ear canal Fast Calculation Method of the HRTFs The computational process which solves the simultaneous equations and obtains the surface pressures ^P accounts for a considerable amount of the calculation time required in the BEM. Furthermore, because ^P depends on the position of the point source, changing the position of this point source results in recalculation of ^P and additional computation time. As a result, the total time necessary for calculation becomes quite enormous. Considering the Eqs. (1) and (2), (I M =2 þ G n þ j!gy) and (G ns þ j!g s Y) do not depend on the source position. Therefore, if we calculate 1 1 Q ¼ðG ns þ j!g s YÞ 2 I M þ G n þ j!gy ; ð4þ we can reuse Q when another source position needs to be recalculated. The acoustic pressure within the volume pðsþ is written as pðsþ ¼g s A j!g s V QðgA j!gvþ; ð5þ where Q is independent regarding the source position on which ^P depends. The other terms in the right side of Eq. (5) are dependent on the source position. Hence, by calculating the inverse matrix (I M =2 þ G n þ j!gyþ 1 and, consequently, Q once for all, it is possible to calculate the acoustic pressure pðsþ for an arbitrary source position without recalculating Q. Once Q is calculated and stored on computer disk, we don t have to calculate Q any more in this method, whereas in the conventional BEM it is necessary to calculate ^P repeatedly for all source positions which takes an enormous amount of time. Therefore, by using this method, it is possible to greatly reduce the total time required for calculation and realize fast calculation of the HRTFs since calculating pðsþ in Eq. (5) takes only a few seconds using a PC. If the inverse matrix ði M =2 þ G n þ j!gyþ 1 can be stored on disk, the receiving position as well as the source position can be changed in the recalculation. In this case, however, we need a storage size M-th times as much as Q, where M is the number of elements. Therefore, we adopt the method to store Q. 3. COMPUTER SIMULATION 3.1. Boundary Condition of Head Shape We prepared a triangular elements group for the shape of the surface of the dummy head. First, the 3D coordinate data was measured using a 3D scanner (Cyberware 3030RGB/I). This system can measure geometric and color data of a 3D object all around in a noncontact method, and features an accuracy of 512 points for circumference and 450 points for height, within a 20 cm vertical region. Because the HATS (Head and Torso Simulator) is 69.5 cm in vertical height, we measured it four times and synthesized each data portion post-measurement to obtain an overall model of the HATS. Next, the triangle mesh data was calculated using the triangle mesh generator [15]. Although the measured coordinate data of the dummy head surface included the body of the head torso simulator, we used only the head part of the data in this study. Generally it is suggested that the element size should be less than 1/4 to 1/6 of the wavelength in order to achieve accurate calculation in the BEM. Therefore, we created an upper limit of the element size when the surface was 261

4 divided into the triangular elements. This upper limit of the element size was not set too stringent and the approximate planar surfaces were roughly divided by triangular elements. In contrast, surfaces with complicated shapes were divided finely so as to be precisely shaped. In this study, approximate planar surfaces correspond to the cheeks and forehead. Surfaces with complicated shapes meanwhile correspond to the ear pinnas. Ideally, all of the surfaces should be divided finely for the BEM calculation. However, it is considered to be reasonable to divide the cheeks and forehead in a more rough fashion than the ear pinnas. This is because the cheeks and forehead have approximate planar surfaces far from the ear canal, while the ear pinnas feature a complicated shape in the region close to the ear canal. If the frequency becomes higher and higher in the BEM calculation, higher mesh resolution of the ear pinnas is needed, however the mesh resolution of the cheeks and forehead becomes less significant. This is because the cheeks and forehead have less effect on sound pressures at the ear canal at higher frequencies. For accurate calculation it might not be ideal to roughly divide the cheeks and forehead, however, from the viewpoint of computational cost, it is reasonable. After determining these conditions, the boundary elements were created as shown in Figs. 1, 2 and 3. The number of triangular elements in these models were 5,014, 7,654 and 10,000, respectively. The 7,654 triangular-element model had a higher resolution than the 5,014 triangular-element model. And the 10,000 triangularelement model had even a higher resolution. The average size of the elements was approx. 6.8 mm, 5.6 mm and 5.1 mm, respectively. Although the inlet to the external ear canals was closed off in these models, it can be regarded as the same as the HRTF measurement with the ear canal blocked. Reportedly, even HRTF measurement with the ear canal blocked includes spatial information [16]. Fig. 1 Fig. 2 Acoust. Sci. & Tech. 24, 5 (2003) Computer model: 5,014 elements. Computer model: 7,654 elements Numerical Condition We next were able to use three computational methods for the HRTF calculation. First is the conventional BEM. Second is the method which utilizes the pre-processing of an inverse matrix. And the third is the method which utilizes the pre-processing of an inverse matrix and the CHIEF method. The computational results obtained by utilizing the preprocessing of an inverse matrix are slightly different from those in the conventional method. This difference between the results of these methods arises from the difference in the numerical methods used, which are computing the inverse of the coefficient matrix and the solution to the simultaneous equations. However, we used the method utilizing pre-processing of an inverse matrix rather than the conventional BEM, because this slight difference is Fig. 3 Computer model: 10,000 elements. negligible for the HRTF calculation as shown in the following subsection. So in this study, two methods for calculating the HRTFs, i.e. methods which utilize the preprocessing of an inverse matrix and the pre-processing of an inverse matrix with the CHIEF method, were used for HRTF calculation. The distance we used between the point source and the center of each ear was 1.4 m. The point source was located at the same height as the ears. The interval of horizontal angle was 5 degrees. Therefore, we calculated the HRTFs 262

5 M. OTANI and S. ISE: FAST CALCULATION METHOD OF HRTF BASED ON THE BEM Fig. 4 Location of sound source. for 72 patterns of source position around the head. The entire boundary of the head was assumed to be acoustically rigid. We calculated the acoustic pressure at the entrance of each ear canal. The frequency range of calculation was 43 12,015 Hz at intervals of 43 Hz. Figure 4 shows the patterns of source position Numerical Results First, the HRTFs were calculated for 72 azimuth patterns by using the 5,014 triangular-element model. Figure 5 shows the directional transfer functions (DTF) for two azimuth patterns (30, 30 degrees), i.e. frontal source positions. On the other hand, DTFs for rear source positions are shown in Fig. 6 (120, 120 degrees). DTFs were obtained by normalizing the HRTFs by the root mean squares of the sound pressures for 72 azimuth patterns at each frequency. DTFs emphasize the component depending on the azimuth of source position. The solid line shows results without the CHIEF method and the bold solid line shows results with the CHIEF method. As mentioned in the previous subsection, there are slight differences between the results of the proposed method and those of the conventional method. In order to examine the differences of both results, the conventional method was also used to calculate the HRTF for 30-degrees pattern. As a result, the differences between the relative sound pressure level at each frequency obtained by these methods were less than db. Even when the CHIEF method was applied to both of the methods, the differences were less than db. Therefore, differences between these methods are ignored in this study. As shown in Figs. 5 and 6, the results obtained without the CHIEF method show spikes, which are peaks and dips appearing locally at certain frequencies. These spikes are thought to arise from the coarseness of the discretized Fig. 5 Calculated DTFs for two azimuth patterns (30, 30 degrees) based on the 5,014 triangular-element model. solid line: without the CHIEF method, bold solid line: with the CHIEF method. Fig. 6 Calculated DTFs for two azimuth patterns (120, 120 degrees) based on the 5,014 triangular-element model. solid line: without the CHIEF method, bold solid line: with the CHIEF method. 263

6 Acoust. Sci. & Tech. 24, 5 (2003) surface or from a non-uniqueness problem, that is, a rank deficiency or a large condition number in the coefficient matrix of the BEM, occurring at eigen-frequencies of the corresponding interior problem. A large condition number in the coefficient matrix causes the solution error due to approximations made and round-off errors [17]. As shown in Figs. 5 and 6, the use of the CHIEF method causes some of the spikes to disappear and the amplitude of the spikes becomes smaller over the whole region. We found that the condition numbers of the coefficient matrices become smaller at these frequencies. For example, by using the CHIEF method, the condition number of the coefficient matrix decreases to from 20,842.9 at 4, Hz where a spike appears in Figs. 5 and 6. Therefore, it can be said that the numerical inaccuracies are improved with the use of the CHIEF method. In addition, more spikes appears in the 30-degrees and 120-degrees patterns compared to the 30-degrees and 120-degrees patterns. This occurs when the source is located at the opposite side of the listening ear. Sound pressures calculated at such a position become smaller whereas the unwanted effect of the non-uniqueness problem remains constant. In Figs. 7 and 8, results obtained by using three computer models, which have 5,014, 7,654 and 10,000 triangular elements respectively, are compared. The CHIEF method was not used for these calculations. When using the 7,654 triangular-element model, the number of spikes decrease and the amplitude of the spikes becomes smaller than when using the 5,014 triangular-element model. When using the 10,000 triangular-element model, the number and the amplitude of the spikes are also suppressed. However, the differences between the results of the 7,654 and 10,000 triangular-element models are unremarkable in this frequency range. It is shown that the unwanted effect of the non-uniqueness problem, appearing as dips or peaks caused by inaccuracy of numerical computation, can be diminished when high resolution models are used, unless the CHIEF method is utilized Necessary CPU Time and Memory Size for Computation When computing the HRTFs using the BEM, one of the major problems is the computational cost including necessary CPU time and memory. Figure 9 shows the relation between necessary memory size and the number of elements when using the conventional BEM and the pre-processing of an inverse matrix with or without the CHIEF method, respectively. The amount of memory is proportional to the square of the number of elements. The amount of memory required for the conventional BEM and the pre-processing of an inverse Fig. 7 Calculated DTFs for two azimuth patterns (30, 30 degrees). dashed line: 5,014 elements, solid line: 7,654 elements, bold solid line: 10,000 elements. Fig. 8 Calculated DTFs for two azimuth patterns (120, 120 degrees). dashed line: 5,014 elements, solid line: 7,654 elements, bold solid line: 10,000 elements. 264

7 M. OTANI and S. ISE: FAST CALCULATION METHOD OF HRTF BASED ON THE BEM Fig. 9 Relation between the necessary memory size for BEM calculation and the number of elements. solid line with o mark: conventional BEM, broken line with o mark: conventional BEM with CHIEF method, solid line with mark: pre-processing of inverse matrix, broken line with mark: pre-processing of inverse matrix with CHIEF method. matrix is the same. The necessary memory for the CHIEF method is twice as much as that for conventional BEM, while that for preprocessing of an inverse matrix is four times as much as that for conventional BEM. Compared with the memory size for the pre-processing which is proportional to the square of M, the memory size for the post-processing is very small because it is proportional to M, where M is the number of elements. From the viewpoint of CPU time, it is apparent that the pre-processing of an inverse matrix is of great advantage to the conventional BEM. In the case of using the 5,014 triangular-element model and a Xeon 2.5 GHz machine, it takes 45 hours to calculate the HRTFs for a single source position with the conventional BEM, whereas it takes 116 hours to calculate the Q in Eq. (5) using the pre-processing of an inverse matrix. However, once the Q is calculated, the HRTFs for any other source position can be calculated in only 2 seconds. For example, if we want to calculate HRTFs for a source position undefined in the pre-process, it takes only 2 seconds with the method proposed in this paper while it takes 45 hours with the conventional BEM. Though a powerful computer is required for the preprocessing, we do not need to use such a machine for the post-processing at all. That is, we can construct the HRTF calculation system very easily once we have obtained the pre-processing data. Even when the CHIEF method is used, this advantage of the pre-processing of an inverse matrix compared to the conventional BEM is maintained. 4. CONCLUSION In this paper, we introduced the method for HRTF calculation based on the boundary element method (BEM). Computer models that are boundary surfaces of the Helmholtz integral equation were generated based on B&K HATS by using a 3D scanner and mesh generator. HRTFs based on these computer models of a head were calculated by using the conventional BEM and utilizing the CHIEF method which enables us to avoid the nonuniqueness problem and improve the accuracy of the numerical results. Furthermore, we proposed a new effective technique to speed up the HRTF calculation for many patterns of source position when using the BEM. By preserving only the factors that are independent regarding the source position, the process of recalculation of such factors can be skipped when the source position changes. This technique allows us to reduce the CPU time for HRTF calculation when using the BEM. This technique is realized by calculating and preserving an inverse of the coefficient matrix while the coefficient matrix is solved as simultaneous equations in the conventional BEM. Differences between the results of this pre-processing of an inverse matrix and the conventional BEM are virtually negligible, so from the viewpoint of computational cost it is very reasonable for us to use the pre-processing of an inverse matrix instead of conventional BEM. The numerical results of the pre-processing of an inverse matrix with or without the CHIEF method were compared, and the results of 5,014, 7,654 and 10,000 triangular-element models were compared as well. It was shown that the number and amplitude of spikes on the frequency response caused by the non-uniqueness problem can be decreased by using the CHIEF method or higher resolution model. REFERENCES [1] J. Blauert, Spatial Hearing (The MIT Press, London, 1997), p [2] W. Gardner and K. Martin, HRTF measurement of a KEMAR, J. Acoust. Soc. Am., 97, (1995). [3] S. Takane, D. Arai, T. Miyajima, K. Watanabe, Y. Suzuki and T. Sone, A database of head-related transfer functions in whole directions on upper hemisphere, J. Acoust. Soc. Jpn. (E), 23, (2002). [4] D. S. Brungart and W. M. Rabinowitz, Auditory localization of nearby sources. head-related transfer functions, J. Acoust. Soc. Am., 106, (1999). [5] T. Nishino, S. Kajita, K. Takeda and F. Itakura, Interpolation of the head related transfer function on the horizontal plane, J. Acoust. Soc. Jpn. (J), 55, (1999). [6] G. F. Kuhn, Model for the interaural time differences in the azimuthal plane, J. Acoust. Soc. Am., 62, (1977). [7] K. Sugiyama, T. Sakaguchi, S. Aoki and I. Kinoshita, Calculation of acoustic coefficients between two ears using spheroids, J. Acoust. Soc. Jpn. (J), 51, (1995). [8] S. Weinrich, Deformation of a sound field caused by a 265

8 Acoust. Sci. & Tech. 24, 5 (2003) manikin, J. Acoust. Soc. Am., 69, (1981). [9] B. F. G. Katz, Boundary element method calculation of individual head-related transfer function. I. Rigid model calculation, J. Acoust. Soc. Am., 110, (2001). [10] B. F. G. Katz, Boundary element method calculation of individual head-related transfer function. II. Impedance effects and comparison to real measurements, J. Acoust. Soc. Am., 110, (2001). [11] Y. Kahana, P. A. Nelson, M. Petyt and Sunghoon Choi, Boundary element simulation of HRTFs and sound fields produced by virtual acoustic imaging systems, Audio Eng. Soc. 105th Convention, pre-print 4817 (1998). [12] M. Otani and S. Ise, Numerical calculation of the head related transfer function by using the boundary element method, Proc. WESTPRAC VII, pp (2000). [13] H. A. Schenck, Improved integral formulation for acoustic radiation problems, J. Acoust. Soc. Am., 44, (1968). [14] D. Hammershøi and H. Møller, Sound transmission to and within the human ear canal, J. Acoust. Soc. Am., 100, (1996). [15] J. Schoeberl, NETGEN An advancing front 2D/3D-mesh generator based on abstract rules, Comput. Visualisation Sci., 1, (1997). [16] H. Møller, Fundamentals of binaural technology, Appl. Acoust., 36, (1992). [17] P. Juhl, A numerical study of the coefficient matrix of the boundary element method near characteristic frequencies, J. Sound Vib., 175, (1994). Makoto Otani received the B.E. and M.E. degrees in Architectural Acoustics from Kyoto University, Japan, in 1999 and 2001, respectively. He is currently a Ph.D. candidate at Graduate School of Engineering, Kyoto University. His research interests are sound localization and sound field reproduction. He is a member of Acoustical Society of Japan. Shiro Ise received the B.E. degree in Electronics and Communication Engineering from Waseda University, Japan in From 1984 to 1986 he was a development engineer at KORG Co., Ltd. He received the M.E. degree in Electrical Acoustics from Waseda University in 1988 and the Ph.D. degree in Architectural Acoustics from Tokyo University, Japan in From 1991 to 1993 he was a chief engineer at Institute of Construction Engineering. From 1993 to 1994 he was a visiting lecturer at Advanced Research Center for Sci. and Eng., Waseda University. From 1993 to 1998 he was a research associate at Acoustic Information Processing, Information Science, Nara Institute of Science and Technology, Japan. From 1996 to 1997 he was a visiting scholar at Fluid and Acoustic Lab, Engineering Department, Cambridge University, England. Since 1998 he has been an associate professor at Architectural System, Faculty of Engineering, Kyoto University, Japan. He is a member of Acoustical Society of Japan, Architectural Institute of Japan, Institute of Noise Society of Japan, Virtual Reality Society of Japan, Acoustical Society of America. His main field is active noise control and sound field reproduction, but he is increasingly interested in incorporating semiotics into acoustical psychology. 266