Efficient Sound Synthesis by Recursive Digital Filters in Parallel Form: Virtual Musical Instruments and Artificial Reverberation

Participants: Esteban Maestre, Gary P. Scavone

Collaborators: Julius O. Smith, Jonathan S. Abel

Period: 2014 - ongoing

Recursive digital filters in parallel form offer a number of advantages. Besides their suitability for parallel implementation, improved numerical precision and parametric control are some of their attractive features. This project explores frequency-domain optimization techniques to design high-order recursive parallel filters suited for the efficient simulation of musical instruments and reverberation via modal synthesis.

* Maestre, E., Scavone, G., and Smith, J.O. (2016). "Design of Recursive Digital Filters in Parallel Form by Linearly Constrained Pole Optimization" IEEE Signal Processing Letters, Vol. 23, No. 11, pp. 1547-1550.

A first research pursuit engages in the development of novel methods to render musical instrument sound by combining the digital waveguide and modal synthesis frameworks. Through a modal analysis technique based on constrained optimization of parallel filter coefficients, measured resonator immitances are faithfully reproduced via an efficient modal formulation that allows their realization as lumped elements within a digital waveguide model.

* Maestre, E., Scavone, G., and Smith, J.O. (2017). "Joint Modeling of Bridge Admittance and Body Radiativity for Efficient Synthesis of String Instrument Sound by Digital Waveguides" IEEE Transactions on Audio, Speech, and Language Processing, Vol. 25, No. 5, pp. 1128-1139.

* Maestre, E., Scavone, G., and Smith, J.O. (2018). "Joint Modeling of Impedance and Radiation as a Recursive Parallel Filter Structure for Efficient Synthesis of Wind Instrument Sound" 21st International Conference on Digital Audio Effects, Aveiro, Portugal, 4-8 September 2018

In a related problem, the challenge of designing a modal reverberator to match a measured room impulse response is considered. The modal reverberator architecture expresses a room impulse response as a parallel combination of resonant filters, with the pole locations determined by the room resonances and decay rates, and the zeros by the source and listener positions. Our objective is to first estimate the pole positions in an iterative process involving a series of constrained pole position optimizations in overlapping frequency bands; then, with the pole locations in hand, the zeros are fit to the measured impulse response using least squares.

* Maestre, E., Abel, J., Smith, J. and Scavone, G. (2017) "Constrained Pole Optimization for Modal Reverberation." Proceedings of the 2017 International Conference on Digital Audio Effects, Edinburgh, UK, 5-9 September 2017.