In November 2013 I posted a draft of “Time Varying BIBO Stability Analysis of Trapezoidal integrated optimised SVF v2” to the music-dsp mailing list.[1] The draft applied Jean Laroche’s state-space method [2] to prove the time varying stability of the SVF filter that Andy Simper had recently derived using trapazoidal integration.[3] I didn’t quite finish the stability proof. You can read the discussion in the mailing list thread to see how close we got.

I recently learnt that Aaron Wishnick had completed the stability proof and had also published a number of useful coefficient formulas for the SVF.[4] Aaron kindly cited my partial proof. Thanks Aaron!

For future reference the maxima source file for my draft analysis is now archived on github.

[1] Bencina, R. (2013) “Time Varying BIBO Stability Analysis of Trapezoidal integrated optimised SVF v2,” music-dsp mailing list, Nov. 2013, Available at www.mail-archive.com/music-dsp@music.columbia.edu/msg02467.html

[2] Laroche, J. (2007) “On the Stability of Time-Varying Recursive Filters,” J. Audio Eng. Soc., vol. 55, no. 6, pp. 460-471, June 2007.

[3] Simper, A. (2013) “Solving the Continuous SVF equations Using Trapezoidal Integration and Equivalent Currents,” Nov. 2013, Available at www.cytomic.com/files/dsp/SvfLinearTrapOptimised2.pdf

[4] Wishnick, A. (2014) “Time-Varying Filters for Musical Applications” Proc. of the 17th Int. Conference on Digital Audio Effects (DAFx-14), Erlangen, Germany, September 1-5, 2014. Available at www.dafx14.fau.de/papers/dafx14_aaron_wishnick_time_varying_filters_fo r_.pdf