Filter-Based Oscillator Algorithms for Virtual Analog Synthesis ; Suodattimiin perustuvat oskillaattorialgoritmit virtuaalianalogisynteesissä

Aalto University, P.O. Box 11000, FI-00076 Aalto www.aalto.fi Author Jussi Pekonen Name of the doctoral dissertation Filter-Based Oscillator Algorithms for Virtual Analog Synthesis Publisher School of Electrical Engineering Unit Department of Signal Processing and Acoustics Series Aalto University publication series DOCTORAL DISSERTATIONS 26/2014 Field of research audio signal processing Manuscript submitted 9 September 2013 Date of the defence 4 April 2014 Permission to publish granted (date) 20 December 2013 Language English Monograph Article dissertation (summary + original articles) Abstract This thesis deals with virtual analog synthesis, i.e., the digital modeling of subtractive synthesis principle used in analog synthesizers. In subtractive synthesis, a spectrally rich oscillator signal is modified with a time-varying filter. However, the trivial implementation of the oscillator waveforms typically used in this synthesis method suffers from disturbing aliasing distortion. Filter-based algorithms that produce these waveforms with reduced aliasing are studied in this thesis. An efficient antialiasing oscillator technique expresses the waveform as a bandlimited impulse train or a sum of time-shifted bandlimited step functions. This thesis proposes new polynomial bandlimited function generators and introduces optimized look-up table and polynomial-based functions for these algorithms. A new technique for generating nonlinearphase bandlimited functions is also presented. In addition to the aforementioned technique, the research focus in oscillator algorithms is on ad-hoc approaches that either post-process the output of the trivial oscillator algorithm or produce signals that look similar to the classical waveforms. Linear post-processing algorithms that suppress aliasing of the waveform generated, in principle, by any oscillator algorithm are introduced in this thesis. Perceptual aspects of the audibility of aliasing are also addressed in this thesis. The results of a listening test that studied the audibility of aliasing distortion in a trivially sampled sawtooth signal are shown. Based on the test results, design criteria for digital oscillator algorithms are obtained and the usability of previously used computational measures for the evaluation of aliasing audibility is analyzed. In addition, modeling of analog synthesizer oscillator outputs is addressed in this thesis. Two separate models for the sawtooth signal generated by the oscillator circuitry of the MiniMoog Voyager analog synthesizer are developed. The first model uses phase distortion to generate sawtooth waveforms that resemble that of the MiniMoog. The second model filters the output of a digital oscillator algorithm with a fundamental frequency dependent post-processing filter. The techniques described in this thesis can be used in the development of alias-free oscillator algorithms for virtual analog synthesis. Also, the output of this oscillator can be processed to sound and look like the respective waveform of any analog synthesizer using the methods proposed here.This thesis deals with virtual analog synthesis, i.e., the digital modeling of subtractive synthesis principle used in analog synthesizers. In subtractive synthesis, a spectrally rich oscillator signal is modified with a time-varying filter. However, the trivial implementation of the oscillator waveforms typically used in this synthesis method suffers from disturbing aliasing distortion. Filter-based algorithms that produce these waveforms with reduced aliasing are studied in this thesis. An efficient antialiasing oscillator technique expresses the waveform as a bandlimited impulse train or a sum of time-shifted bandlimited step functions. This thesis proposes new polynomial bandlimited function generators and introduces optimized look-up table and polynomial-based functions for these algorithms. A new technique for generating nonlinearphase bandlimited functions is also presented. In addition to the aforementioned technique, the research focus in oscillator algorithms is on ad-hoc approaches that either post-process the output of the trivial oscillator algorithm or produce signals that look similar to the classical waveforms. Linear post-processing algorithms that suppress aliasing of the waveform generated, in principle, by any oscillator algorithm are introduced in this thesis. Perceptual aspects of the audibility of aliasing are also addressed in this thesis. The results of a listening test that studied the audibility of aliasing distortion in a trivially sampled sawtooth signal are shown. Based on the test results, design criteria for digital oscillator algorithms are obtained and the usability of previously used computational measures for the evaluation of aliasing audibility is analyzed. In addition, modeling of analog synthesizer oscillator outputs is addressed in this thesis. Two separate models for the sawtooth signal generated by the oscillator circuitry of the MiniMoog Voyager analog synthesizer are developed. The first model uses phase distortion to generate sawtooth waveforms that resemble that of the MiniMoog. The second model filters the output of a digital oscillator algorithm with a fundamental frequency dependent post-processing filter. The techniques described in this thesis can be used in the development of alias-free oscillator algorithms for virtual analog synthesis. Also, the output of this oscillator can be processed to sound and look like the respective waveform of any analog synthesizer using the methods proposed here.