Low peak amplitudes for group additive synthesis

The peak amplitude of a waveform for a particular spectrum depends on the phases of its harmonic components, and lower peak amplitudes give better signal-to-noise ratios. Most previous work on peak amplitude reduction has only considered individual spectra, but applications such as wavetable synthesis require multiple wavetables. A recent study compared various phase selection methods for multiple wavetable synthesis and found that genetic algorithm (GA) optimization gave peak amplitude results 10-25\% lower than other methods. Various phase selection methods are compared with regard to group additive synthesis, a special case of multiple wavetable synthesis, where each wavetable contains a distinct subset of the harmonics. The results show that GA and simulated annealing optimization are consistently good, and usually outperform random phase selection, Schroeder's method, van den Bos's method, and Pumplin's method with one or two wavetables. The GA runs several times faster than simulated annealing and strikes the best balance between efficiency and effectiveness. With three or more wavetables, the random, van den Bos, Pumplin, GA, and simulated annealing methods give about the same results. Group additive synthesis peak factors are up to 30\% worse than their wavetable synthesis counterparts, unless wavetable matching and peak-factor optimization are integrated. While multiple wavetable synthesis allows lower peak factors and relative spectral errors than group additive synthesis, group additive synthesis has the advantage that it allows better and more intuitive control than multiple wavetable synthesis. The GA and simulated annealing low-peak methods help get the best performance out of both multiple wavetable synthesis and group additive synthesis