Localization, in computer music, is the sound effect generated by a certain algorithm that, given a sound source and its locat

Huang-Jung Chang

13207260

Final Project

LOCALIZATION

Localization, in computer music, is the sound effect generated by a certain algorithm that, given a sound source and its location, will create several virtual locations for the source and make the source sound stereo. The purpose of developing the stereo sound effect is because we humans have two ears and the environment we live on is a 3 dimensional space. The distances from the sound source to the two ears are somewhat different unless the sound source is located straight away from the center point of the two ears, or usually called the central axis of the brain, in 2 certain dimensions (The idea will be further discussed in the later section). If stereo sound effect does not apply, the source sound would be heard from one of the points mentioned above and would lose its realness comparing to the sounds we hear regularly in our daily life. Therefore, localization is an important aspect in the purpose of simulating the realness of sound signal in computer music.

First of all, we should clarify ourselves with the proper names for each of the 3 planes in the 3-dimensional environment we live on. Using the X-Y-Z axis in space, we can easily specify a plane with any two of the three axes. If we specified the horizontal axis that we face as the Y axis and the other horizontal axis, the axis we would face if we turn our heads 90 degrees to the left or right, as the X axis, then the vertical axis would be specified as the Z axis. Given any of the two axes at a time, we could specified the X-Y plane as the horizontal plane, the X-Z plane as the frontal plane, and the Y-Z plane as the median plane.

In the horizontal plane, two important factors are presented due to the natural existence of two ears in human. One is the Interaural Time Difference, the ITD, which is the difference in arrival time of the signal at our different ears due to the location of the sound source at an horizontal angle other than 90 degrees or directly straight to the front, and 270 degrees or directly straight to the back. The other factor is the Interaural Intensity Difference, which refers to the difference in intensity of the level of the signal at our different ears. Due to the fact amplitude of a sound source behaves inversely to the distance of the sound source from us, the sound source, if not directly in front or on the back of the central axis, should reach the two ears in different time with different intensity. Therefore, calculating the ITD and the IID is necessarily in simulating virtual locations in computer music.

However, calculating only the ITD and the IID is not sufficient enough to judge the location of the sound source. When the source is located on the median plane along the central axis of the brain, some useful information of the location, such as the elevation and the direction of the sound source, cannot be determined by calculations of ITD and IID since both would than be zero in the ideal case. As a result, head-related transfer functions, a set of impulse responses that correspond to the filtering effects of the pinnae from different locations, is applied to help determine the location of the sound source in addition to the ITD and IID.

The purpose of my final project is to calculate the factors and the parameters needed in simulating a virtual sound source in a multi-loudspeaker system. In general, positioning a virtual sound source in space is complicated and difficult to achieve in the case of huge crowds as listeners due to the complexity of reverberation on the sound source itself inside a room. Therefore, the system is restricted to the assumption that only a very restricted portion of the audience area where optimal listening conditions are met. This restricted area is called sweet spot. The sweet spot is always referred to the center point of the system with position (0, 0) on the horizontal plane within this project. In addition, this system is restricted to simulations on the horizontal plane.

The name of the system is generally called Distance Vector Panning System. It takes place on the horizontal plane with N loudspeakers placed in a circumference of radius R to the center position, which is the origin of the X-Y axes. In this project, the number of loudspeakers, N, is assigned to 4 and the radius equals 0.5, for four loudspeakers with each equal distance to the listener positioned at the origin. Therefore, the speakers are generally staying on a circle with radius 0.5 to the listener at the sweet spot. Given the information of the desired virtual location in space, the strength of this virtual signal can be calculated to simulate this virtual location. This could be done by first calculating the gain factor of each loudspeaker in the system because, after all, the virtual location is made possible by applying different intensity levels to each speaker in the system. Finally, the angle q on the horizontal plane can be calculated to specify the direction of the virtual sound source to the listener at origin. A figure of the setup is shown below.

In order to achieve this simulation, the desired virtual location of the sound source must be known. Therefore, the input parameters must include both the X and Y values of the location according to the coordinate axes applied. In addition, different calculations performed at source frequency above and below 700 Hz, each separately. At frequencies below 700Hz, the strength of the sound source at the virtual location would be given in velocity vectors, while energy vectors are given for frequencies above 700Hz to be effective. As a result, frequency of the sound source should also be an input parameter in addition to the information location-wise.

The amplitude gains for each speaker are calculated next. The formula is given below:

Ai = 1-Sqr(di), i = 1, 2, 3, 4

Where di is the distance from the virtual sound source position P to each loudspeaker. This is done by calculating the differences in X and Y values for the location and each loudspeakers. After the amplitude levels for each speaker is known, the velocity vector for the virtual sound source less than 700 Hz can be calculated according to the following definition:

summation (Ai*Vi), i = 1 to N

Rv = ------------------------------------ = (Rvx, Rvy)

summation (Ai), i = 1 to N

whereas the energy vector for the virtual sound source less than 700Hz can be calculated according to the following definition:

summation (Sqr(Ai)*Vi), i = 1 to N

Re = ------------------------------------ ------- = (Rex, Rey)

summation (Sqr(Ai)), i = 1 to N

where Vi is the unitary vector pointing to the ith loudspeaker from the origin. The angle q to determine the direction of the virtual sound source is given by:

q = atan (Rvy/Rvx) for velocity vector or q = atan (Rey/Rex) for energy vector

the energy vector or the velocity vector along with the q angle and the gains of each loudspeaker are outputs of the program.

In conclusion, this program does not generate the sound effect in virtual location itself, as it does not take a signal and output the effect like a Max/Msp object does. However, it gives sufficient information, such as the azimuth angle, the q angle on the horizontal plane, and the distance of the virtual sound source and the gains of each speaker. The information can be distributed further to make the performance of virtual location possible.

Setup Diagram for the System

Sources

· Multi-loudspeaker Reverberation System, http://www.cps.unizar.es/~fbeltran

· Gardner, W.G., Reverberation Algorithms, chapter 3 in Kahrs, M. and Brandenburg, K. editors Applications of Digital Signal Processing to Audio and Acoustics, Kluwer Academic Publishers, Boston, 1998.

· M.A. Guerzon, “General Metatheory of Auditory Localisation”, presented at the 92 nd Convention of the Audio Engineering Society, preprint 3306, Viena 1992.

· Pulkki, V. "Virtual Sound Source Positioning Using Vector Base Amplitude Panning", J. Audio Engineering Society, Vol. 45, No. 6, pp. 456-466, 1997.

· Pernaux, J.M., Boussard, P., Jot, J.M. “Virtual SoundSource Positioning and Mixing in 5.1 Implementation on the Real-Time System Genesis”, Proc. Workshop on Digital Audio Effects (DAFx-98), Barcelona, Spain, pp. 76-80, 1998.