/ Application of Wave Field Synthesis in the composition of electronic music
number of small sources, whose waves will together form the next wavefront (figure 1). Based on this principle, Berkhout (1988) introduced the wave field synthesis principle in acoustics. By using a discrete, linear array of loudspeakers (figure 2), one can synthesize correct wavefronts in the horizontal plane (Berkhout, De Vries and Vogel 1993). For a complete mathematical treatment is referred to Berkhout (1988, 1993) and various other papers and theses from the TU Delft3. Figure 2. The Wave Field Synthesis Principle An interesting feature is that it is also possible to synthesize a sound source in front of the speakers (Jansen 1997), which is not possible with other techniques. Comparisons between measured wave fields and wave fields reconstructed with WFS have shown that the differences between the two are small (Bourdillat 2001); most faults in the WFS reproduction were due to reflections in the reproduction room. Perceptual experiments and practical experience have shown that with WFS one can achieve a large listening area, where the sound source is perceived correctly at the specified location (Vogel 1993, Verheijen 1998). Malham's (2001) comments that WFS cannot achieve a perfect sound image on all locations are true, but perceptually not so relevant that it makes the technique not worth considering for application in spatialisation of electronic music. 2.1 Synthesizing moving sound sources Jansen (1997) derived mathematical formulae for synthesising moving sound sources. He took into account the Doppler effect and showed that for its application one would need to have continuously time-varying delays. He also showed that for slowly 3 Sound Control Group, TU Delft, http://www.soundcontrol.tudelft.nl moving sources the Doppler effect is negligible and one can resort to updating locations and calculating filters for each location and changing those in time. This approach was chosen in this project. Additionally, in order to avoid clicks in playback, an option was built in to fade between two locations to make the movement sound smoother. 3 System setup at the TU Berlin The prototype system in Berlin was created with the specific aim to make a system for the use in electronic music (Weske 2001). The system consists of a LINUX PC, driving 24 loudspeakers with an RME Hammerfall Soundcard. The loudspeaker signals are calculated in real time with the program BruteFIR by Torger4. This program is capable of making convolutions with long filters in realtime. The filter coefficients can be calculated with the interface software described in this paper. The current system is capable of playing maximal 9 sound sources with different locations in realtime, even when the sources are moving. This is the maximum amount of sources; the exact amount of sources that can be used in a piece depend on the maximum distance range5 of each source and the amount of reflections added. Both of these aspects influence the total filter length and the filter length determines the amount of calculation power needed. In table 1 an overview is given of the capability of the system in Berlin (running on a Dual Pentium III). The filter lengths are indicated in samples. The distances are based on the assumption that the sample frequency is 44.1 kHz. The numbers indicated in the table are the real time index calculated by BruteFIR and are a measure for the processor load; to have BruteFIR run stable while sources are moving, it is best not to let the real time index go above 0.80. It can be seen that the maximum filter length and thus the distance range, within which a source can move, can become quite large. On the other hand, the larger the filter length, the larger the I/O delay6 will be and the time step after which one can change filter coefficients (important for the movement of sources). In some cases, using several partitions of a smaller filter length can diminish the I/O delay. 4 Torger, A., BruteFIR, huttj://www.udduth.setorer/brutfirhtl 5 During calculation, the smallest delay, considering all path points and all speakers, is subtracted from all delays, so that only delay differences between speakers remain. Thus the filter lengths are based on the largest distance between points on a path. 6 The I/O-delay is twice as large as the filter length.
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