Download Virtual Analog Oscillator Hard Synchronisation: Fourier series and an efficient implementation
This paper investigates a number of digital methods to produce the Analog subtractive synthesis effect of ‘Hard Synchronisation.’ While the original effect is produced by an explicit waveform phase reset, other approaches are given that produce an equivalent output. In particular, based on measurements taken from a real-analog synthesizer, a comb filtering model is proposed. This description ties in with earlier work but here an explicit structure is provided. This filter-based approach is then shown to be far more computationally efficient than the synchronisation by phase reset. This efficiency is at a minor cost as it is shown that it has a minimal impact on the sonic accuracy.
Download Nonlinear-Phase Basis Functions in Quasi-Bandlimited Oscillator Algorithms
Virtual analog synthesis requires bandlimited source signal algorithms. An efficient methodology for the task expresses the traditionally used source waveforms or their time-derivatives as a sequence of bandlimited impulses or step functions. Approximations of the ideal bandlimited functions used in these quasi-bandlimited oscillator algorithms are typically linear-phase functions. In this paper, a general nonlinear-phase approach to the task is proposed. The discussed technique transforms an analog prototype filter to a digital filter using a modified impulse invariance transformation method that enables the impulse response to be sampled with arbitrary sub-sample shifts. The resulting digital filter is a set of parallel first- and/or second-order filters that are excited with short burst-like signals that depend on the offset of the waveform discontinuities. The discussed approach is exemplified with a number of design cases, illustrating different trade-offs between good alias reduction and low computational cost.