Nonlinear abstract sound synthesis algorithms

Jari Kleimola

Research output: ThesisDoctoral ThesisCollection of Articles


This thesis explores abstract sound synthesis methods in digital musical instrument applications and proposes new algorithms for sound production, aliasing reduction, and efficient control of synthesis parameters. The specific focus is on nonlinear distortion and audio-rate modulation techniques, which are approached from two complementary perspectives .First, the classic view, built on closed-form mathematical expressions and computer algorithms, was seen to converge into a compound model where different abstract synthesis methods both generalize and reinforce each other. In this view, the recent phaseshaping technique was investigated as pipelined phaseshaper expressions, with applications in efficient and novel oscillator effects algorithms discovered in the thesis, such as an efficient super sawtooth simulation. In addition, a two-dimensional multi-point extension of the phase distortion method called vector phaseshaping synthesis (VPS) was proposed and demonstrated as an intuitive parametrization of the complex phase modulation technique. The method is well suited for contemporary multi-touch interaction and planar control- and audio-rate modulation. The second perspective into the nonlinear distortion and audio-rate modulation techniques, based on periodically linear time-varying filters, led to the discovery of a synthesis algorithm where the coefficients of an allpass filter chain are modulated at an audio rate. In addition, the filter approach enabled an alternative interpretation of the feedback amplitude modulation (FBAM) technique, whose first-order form was extended and a second-order form was introduced.To complement the sound production stage of digital musical instrument applications, two aliasing reduction methods were introduced, one based on scaled sinusoids and another on polynomial transition regions (PTR). The latter is currently the most efficient method for implementing alias-suppressed virtual analog oscillators. Finally, a streamlined control protocol that dramatically reduces the bandwidth of control data streams was proposed. The efficient and novel algorithms introduced in the thesis are useful for sound synthesis in resource constrained mobile platforms, web browsers, and in applications requiring a high polyphony.
Translated title of the contributionEpälineaariset abstraktit äänisynteesialgoritmit
Original languageEnglish
QualificationDoctor's degree
Awarding Institution
  • Aalto University
  • Välimäki, Vesa, Supervising Professor
  • Välimäki, Vesa, Thesis Advisor
Print ISBNs978-952-60-5015-7
Electronic ISBNs978-952-60-5016-4
Publication statusPublished - 2013
MoE publication typeG5 Doctoral dissertation (article)


  • acoustics
  • digital signal processing
  • music
  • nonlinear filters
  • sound synthesis

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