Integer-Based Wavetable Synthesis for Low-Computational Embedded Systems Ben Wright and Somsak Sukittanon University of Tennessee at Martin Department of Engineering Martin, TN USA
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[email protected] Abstract— The evolution of digital music synthesis spans from discussed. Section B will discuss the mathematics explaining tried-and-true frequency modulation to string modeling with the components of the wavetables. Part II will examine the neural networks. This project begins from a wavetable basis. music theory used to derive the wavetables and the software The audio waveform was modeled as a superposition of formant implementation. Part III will cover the applied results. sinusoids at various frequencies relative to the fundamental frequency. Piano sounds were reverse-engineered to derive a B. Mathematics and Music Theory basis for the final formant structure, and used to create a Many periodic signals can be represented by a wavetable. The quality of reproduction hangs in a trade-off superposition of sinusoids, conventionally called Fourier between rich notes and sampling frequency. For low- series. Eigenfunction expansions, a superset of these, can computational systems, this calls for an approach that avoids represent solutions to partial differential equations (PDE) burdensome floating-point calculations. To speed up where Fourier series cannot. In these expansions, the calculations while preserving resolution, floating-point math was frequency of each wave (here called a formant) in the avoided entirely--all numbers involved are integral. The method was built into the Laser Piano. Along its 12-foot length are 24 superposition is a function of the properties of the string. This “keys,” each consisting of a laser aligned with a photoresistive is said merely to emphasize that the response of a plucked sensor connected to 8-bit MCU.