Applying local search for polynomial coefficients for alias reduction in oscillators

In the development of virtual instruments, the oscillator is responsible for generating periodic waveforms. The classical sawtooth waveform, described as an increasing slope, then a straight drop, is known for its use in music production. A trivial implementation of an oscillator that generates a sawtooth is only a few lines. It requires using a counter that increments a small amount repeatedly, then resets and starts over. However, this trivial implementation is known to alias wildly due to the round off errors in the digital world. The purpose of this research is to survey current techniques, and investigate the possibility of alias reduction by modifying polynomial coefficients in the PolyBLEP algorithm. The simplicity of the PolyBLEP is most attractive. By modifying the coefficients, the alias reduction levels can be improved. Using JUCE, a framework for creating audio applications, the development of the virtual instrument BabySynth is discussed.