Wave voxel: A multimodal volumetric representation of three dimensional lookup tables for sound synthesis Anis Haron, George Legrady Media Arts & Technology Program University of California Santa Barbara, USA anisharon@mat.ucsb.edu, legrady@mat.ucsb.edu Abstract Our research presents an extension to current implementations of table lookup techniques for sound synthesis. In this paper, we present methods for generating volumetric representations of data as three dimensional lookup tables for sound synthesis. Keywords 3D lookup tables, wave voxels, three-variable functions. Introduction Table lookup techniques are widely used in many sound syn- thesis applications today as an efficient technique for signal generators (Roads 1996). In this paper, we propose meth- ods to generate volumetric representations of data as three di- mensional lookup tables for sound synthesis, based on previ- ous research and experiments in sound synthesis by means of two-variable functions (Mitsuhashi 1982) (Aldo Borgonovo 1986). We introduce the term wave voxels 1 to denote three dimensional lookup tables for sound synthesis. An overview of 1D and 2D table lookup techniques in sound synthesis. A one dimensional lookup table of length N is represented graphically in two dimensions as illustrated in figure 1a, where amplitude values (y-axis) changes through time (x- axis). x-axis spans from 0 to N - 1, while y-axis stores the appropriate amplitude at location n of x-axis. A one dimen- sional lookup table with amplitude values for one cycle of an arbitrary wave is called a wavetable (Horner 1997) (Roads 1996). Indexing operations for a one dimensional lookup ta- ble occurs in one axis. For the purpose sound synthesis, con- sider a lookup table of length N containing amplitude values for one cycle of a sine wave. To produce a sine wave of fre- quency 1hz, we continuously traverse from index 0 to N - 1 using modulo arithmetic, at a rate of 0 to N - 1 in 1 second. Traversing twice as fast (0 to N - 1 in 0.5 seconds) generates a 2hz sine wave. An extension to the wavetable was formally introduced in (Mitsuhashi 1982) as an alternative to frequency modula- tion (FM) synthesis. This method extends a one dimensional lookup table into two dimensions. 1 Voxel is a portmanteau for volume and pixel. (a) a wavetable (b) a wave terrain Figure 1: An example of a 1D (a) and 2D (b) lookup table for sound synthesis. Another technique employing two dimensional lookup ta- bles is Scanned Synthesis, introduced by Bill Verplank, Max Mathews and Rob Shaw at Interval Research between 1998 and 2000 (Bill Verplank 1999). Two dimensional lookup ta- bles are graphically represented in three dimensions. In a 2D wavetable of size N x by N y , location on x-axis (loc x ) spans from 0 to N x and location on y-axis (loc y ) spans from 0 to N y . z-axis stores amplitude values at coordinate (loc x , loc y ). A graphical representation of a two dimensional lookup ta- ble is possible using a three dimensional mesh surface where the height of a vertex at coordinate (loc x , loc y ) represents amplitude on z-axis. Alternatively, it could be visualized as a two dimensional plot where a color at coordinate (loc x , loc y ) represents amplitude on z-axis, as illustrated in figure 1b. A two dimensional lookup table is called a wave terrain in com- puter music terminology (John Bischoff 1978)(Roads 1996). For two dimensional surfaces, both x and y axes are used for indexing operations. Trajectory of an indexing operation used to read amplitude values in a wave terrain is called an orbit (Aldo Borgonovo 1986). There are many implementations for generating wave ter- rains. Y.Mitsuhashi, A.Borgonovo and R.Golds implementa- tion focussed on trigonometric polynomials for terrain gen- eration (Mitsuhashi 1982) (Aldo Borgonovo 1986), A. Di Scipio experimented with functional iterations (Scipio 2002), H.Mikelson uses the Julia set as terrains (Mikelson 1999), D.Overholt fabricated a hardware interface for generation of user defined terrains (Overholt 2002), while R.Dannenberg and T. Neuendorffer uses real-time video images (Roger