CODA -- COmputerizeD Auralization MARJAN SIKORA, B. Sc., Faculty of Engineering and Computing, Zagreb, Croatia HRVOJE DOMITROVIĆ, Mr. Sc., Faculty of Engineering and Computing, Zagreb, Croatia CODA (COmputerizeD Auralization) is a new auralization software for the simulation of indoor and outdoor acoustic fields. Based on the complete mirror image modeling aided by other methods for the improvement of accuracy, this software is used for acoustic design and evaluation. The simulated acoustic field can be presented both visually and acoustically -- through postprocessing data, which can then be convolved to create a binaural signal. 0 INTRODUCTION This paper introduces a new software for computerized auralization named CODA. CODA is the first part of the auralization system -- it calculates the room impulse response for one point in space. It can also perform an area scan for the given frequency range. The second and the third part of auralization convolution and aural presentation -- is still in the process of development. For that purpose there is a variety of commercial software available. CODA is written in pure C language. Also, it is fully incorporated in the CAD software for modern graphical environment. Therefore it combines the performance and the ease of use. This paper presents theoretical foundations, the realization and prospects of further development of CODA. 1 THEORY The most important part of the auralization is the calculation of room impulse response (RIR). Errors made in the first stage of the auralization process cannot be corrected later. So
it is of uttermost importance to make the calculation of RIR as accurate as possible. Since the sound is a traveling wave by its nature, it is necessary to incorporate algorithms that calculate the influence of all wave related phenomena. Further will be discussed algorithms for the calculation of the propagation, reflection, interference, diffraction and diffusion of the sound implemented in CODA. 1.1 PROPAGATION OF SOUND Regardless of the sound origin, ever since the oscillations of sound pressure have begun, the sound is propagating. The result of the propagation is the change of the amplitude and phase. The phase of the sound is in direct connection with the wavelength and its distance from the origin of sound (2.1). ϕ = 2π r (2.1) λ Wavelength depends on the frequency and velocity of the sound. The frequency is usually given, and velocity can be calculated from a simplified formula (2.2). It gives the relation between the velocity of the sound and temperature. c 3314. + 0. 6ϑ (2.2) the propagation of the sound causes a change in the amplitude of the sound. There are two reasons for this change. The first is that the intensity of the sound decreases with distance between the source and the receiver. The increase of distance form the source causes the enlargement of the area through which the energy radiates. Therefore, the intensity of the sound decreases (2.6). I P = (2.3) A I I 1 2 A1 = = A 2 4r 2 1 2 2 4r π π (2.4) p = Iρ 0 c (2.5)
p1 p 2 r1 = (2.6) r 2 The second reason for the decrease of the amplitude of sound is the absorption of sound in air. Cause for that absorption is the interaction between molecules of oxygen and steam. The absorption depends on frequency and humidity: it increases with frequency and decreases with humidity. 1.2 REFLECTION There are several methods for calculating the reflections. In CODA the mirror-image method has been used. It was done so because it is simple, accurate and requires less calculation than other methods. This method has its disadvantages: it does not take into account the wave-related phenomena, such as scattering and diffraction. These problems have been solved using other methods, which will be described later. The mirror-image method calculates reflections by mirroring the source across the wall. Sound that gets to the receiver seems to come from that virtual source (Fig. 1). The same algorithm applies to the second and third order reflections. The source is first mirrored across the first wall, then the virtual source of the first-order reflection is mirrored across the second wall and the process continues. When the program has determined the paths of valid reflections, it has to calculate the influence that the reflection will have on the amplitude and phase of the sound. When the sound encounters an obstacle, part of it is reflected, and part is absorbed. One part is also transmitted through the wall, but in this case it is included in the absorption. The absorption of the sound is defined by the absorption coefficient (2.7). α = E E abs tot (2.7) The phase of the sound is also changed. Ideally, when the sound reflects from the solid surface, the reflection coefficient must be -1 so that the superposition of the incident and reflected velocity waves equals zero. Because of that the phase of the reflected wave increases by 180 degrees.
1.3 INTERFERENCE Interference occurs when two coherent sources of the same frequency are emitting within the same space. Because CODA can work with multiple sound sources, interference has to be taken into account. After the amplitude and phase of direct and reflected sounds have been calculated in the location of the receiver, the sounds are added. They are added as complex numbers, so as to take their phase into account. This is the reason why interference occurs (Fig. 2). 1.4 DIFFUSION The mirror-image method does not imply diffusion. For this reason it is necessary to use ome other method, because diffusion is a crucial part of auralization. Why is diffusion so important? It is important because diffusive objects can be found in almost all listening environments, especially in studios. Diffusers are an important tool in acoustic design, and it is necessary to include them adequately into calculations. The most general situation occurs when both specular and diffuse surfaces coexist. In that case four possible reflection combinations coexists (Fig. 3). The usage of the mirror-image method covers only specular to specular reflections. Therefore, to cover other three combinations -- specular-diffuse, diffuse-specular, and diffuse-diffuse it was necessary to include new algorithms. The principle of the calculation of the diffuse reflection is shown in Fig. 4. The position of diffuse reflection theoretically can be anywhere on the wall, but those closer to the specular reflection (which is the shortest way between the source and the receiver) are more likely to occur. The probability of the occurrence of the diffuse reflection is governed by a normal distribution. After the calculation every valid diffuse reflection gets its virtual source. It is further treated as any other reflection. If that reflection hits another diffuse wall, the procedure is repeated. The diffusion of the wall is defined by three parameters: diffusion coefficient, frequency range, and directivity characteristics. The diffusion coefficient determines the amount of the diffused energy in total sound energy of the sound (2.8).
δ = E diff E tot (2.8) Thus the total sound energy consists of three parts: absorbed energy, speculary reflected energy, and diffusely reflected energy (2.9). 1= α + ( 1 α )( 1 δ ) + ( 1 α ) δ (2.9) The frequency range in which a diffuse reflection can occur is determined by the dimension of surface elements. In order to achieve greater accuracy, the user has to input a directivity characteristic for each diffuse wall. 1.5 DIFFRACTION Diffraction, like diffusion, is not part of the mirror-image method. That problem is solved in a similar way as diffusion in the points where diffraction occurs new virtual sources are defined. These sources are a supplement that corrects the sound field. Each source has its directivity characteristic depending on the type of diffraction. Once this source is defined, it is included in further calculations like any other source. 2 REALISATION CODA is written for IBM PC compatible computers, based on 80486 processor or higher. It requires the minimum of 4 MB of RAM. Since auralization is closely linked with architecture, CODA has been integrated in CAD software. The choice fell on AutoCAD for Windows because of its popularity, and because the use of AutoCAD import and export formats has been recommended for auralization software. Programming of CODA was started in LISP language, because its interpreter is part of AutoCAD software package. Very soon it became too slow for complex and ever growing calculations involved in auralization. So CODA was translated to AutoCAD Development System (ADS) which is in its essence a library of AutoCAD functions for C language. Even after that, calculations were not carried out quickly enough. Therefore, for all calculations proprietary procedures had to be written.
For the time being the only ADS procedures used in CODA are those for screen input/output. In this way it was possible to combine the performance of C language with the ease of use, which makes this CAD software package widely accepted. There are two ways of entering the room geometry. The first one is to load it from an existing CAD drawing, and the second one is to draw it manually. All objects in the room, such as sources, receivers, walls, etc., are defined as blocks (Fig. 5). Each block has its geometrical data (position, orientation in space...) as well as its acoustic-related data. Sources and receivers are defined by their directivity characteristics (Fig. 6). Walls are defined by their absorption and diffusion properties. CODA can analyze the room acoustics in two ways. It can analyze sound in the location of the particular listener, which is defined by its directivity characteristics. It can also produce an area scan. The frequency resolution for the first type of calculation can be adjusted by the user. It can vary from 1/3 of the octave to 1/100 of the hearing range. The user can also decide which reflections are to be taken into account during the calculation. After the calculation has been completed, results are displayed in three windows. The first one represents the drawing of the simulated room, including all direct sound and reflections, which are drawn in different colors (Fig. 7). In the second window CODA displays frequency characteristics of amplitude and phase, at the position of the receiver (Fig. 8). The precision of these characteristics is limited by frequency resolution which was defined earlier. The third window contains the reflectogram time diagram of direct sound and incoming reflections (Fig. 9). This window contains information for the second part of auralization convolution. If the user chooses the second type of sound analysis area scan of the test room CODA calculates the sound for every point in the room. The resolution of this area scan is variable, and the user can adjust it. The calculation done, CODA draws the test room and displays results in different colors (Fig. 10). This form of analysis usually refers to one frequency, but it is also possible to find the average value for given frequency range. Results of both types of calculation can be printed and saved on disk in both graphical and textual forms using recommended formats -- DWG and DXF formats. 3 FURTHER DEVELOPMENT
Although in the present form CODA can make analysis of room acoustics, and produce data required for convolution, there is enough room for further improvement. The existing methods for the calculation of RIR can be improved, in terms of both speed and accuracy. It is also possible to introduce other methods such as ray-tracing, hybrid method, FEM and BEM, since the calculation of some parts of RIR cannot be covered with the mirror-image method. As the majority of wave phenomena have already been taken into account, the next logical step is the addition of a third dimension. It would considerably increase the amount of calculation, and the ammount of data created by these calculations. So it would be convenient to increase the speed, and reduction and compression of data would also be of great help. And finally, it would be good to create a proprietary system for convolution and aural presentation of calculated data. In the present form CODA can export data required for convolution (which can be then convoluted externally), but the proprietary system could improve its performance. It could also be easily improved and changed simultaneously with the changes of CODA. 4 CONCLUSION In its present form CODA incorporates algorithms for nearly all relevant wave phenomena. The merging of the speed of C language and the ease of use of CAD software for Windows enables the user to define simulated rooms quickly and easily. The user gets promptly an accurate result either through a reflectogram used for later convolution and presentation, or through an area scan suitable for the analysis of room acoustics. In spite of this fact, as it was mentioned earlier, there is much space for further development. It is also possible that other software packages for auralization include the features that are not yet covered by CODA. The only reason for that is the fact that CODA has been in development for only a year and a half, and the majority of the work has been done solely by the author. So far, it has been an academic project, and its commercialization is expected to boost its development. The development of proprietary convolution software has already started, and there is an increasing interest for development of versions specialized in hydroacoustics and speech intelligibility. All new features and versions of CODA will be promptly presented.
5 REFERENCES [1] Kleiner, M., Dalenback, B.-I., Svensson, P., Auralization, J. Audio Eng. Soc., vol. 41, 1993 November. [2] Dalenback, B.-I., Kleiner, M., Svensson, P., A Macroscopic View of Diffuse Reflection, J. Audio Eng. Soc., vol. 42, 1994 October. [3] Sinclair, I. R., Audio & Hi-Fi Handbook, Butterworth-Heinemann, Oxford, 1993. [4] Crawford, F. S. jr., Waves, McGraw-Hill, New York, 1968. [5]Autodesk, Inc, AutoLISP Programer's Reference Manual, Autodesk, Inc, 1992. [6] Autodesk, Inc, AutoCAD Development System Programer's Reference Manual, Autodesk, Inc, 1992. [7] Somek, B., Electroacoustics - Technical encyclopedia, Croatian lexicographical department, Zagreb, 1983. (in Croatian language) [8] Jelaković, T., Sound, hearing and architectural acoustics, School book, Zagreb, 1978. (in Croatian language)
Fig. 1. Mirror-image method implemented in CODA. Fig. 2. Interference between two sources, positioned in the center of picture on the distance of 2λ (result of CODA calculation).
Fig. 3. Four possible reflection combinations taken into account in CODA. Fig. 4. Principle of a diffuse reflection.
Fig. 5. All objects in the room (walls, sources, receivers...) are defined as blocks. Fig. 6. Sources and receivers are defined by its directivity characteristics.
Fig. 7. Drawing of a room with paths of direct (green) and reflected sound (diffuse in red, 1. order in cyan, 2. order in blue, and 3. order in black). Fig. 8. Frequency characteristic of amplitude and phase for one point in the simulated room.
Fig. 9. Time diagram of direct sound and incoming reflections. Fig. 10. An area scan of simulated room.
Fig. 1. Mirror-image method implemented in CODA. Fig. 2. Interference between two sources, positioned in the center of picture on the distance of 2λ (result of CODA calculation).
Fig. 3. Four possible reflection combinations taken into account in CODA. Fig. 4. Principle of a diffuse reflection.
Fig. 5. All objects in the room (walls, sources, receivers...) are defined as blocks. Fig. 6. Sources and receivers are defined by its directivity characteristics.
Fig. 7. Drawing of a room with paths of direct and reflected sound. Fig. 8. Frequency characteristic of amplitude and phase for one point in the simulated room.
Fig. 9. Time diagram of direct sound and incoming reflections. Fig. 10. An area scan of simulated room.