3 dimensional physical modelling filter.


Partial differential equations are one of the most ubiquitous industrial engineering problems, that need to be solved in applications where physical processes need to be accurately predicted, from thermal management in energy generating facilities, high speed moving vehicles, to control of fluid flow. But so far, the research done into these models has not been translated to music devices, in either analogue or digital.

Through research it was discovered that these processes could in fact be modelled very accurately and efficiently using analogue techniques, where the main building block of the circuit was the humble state variable equation. This is the circuitry that can be found in every good sine oscillator, and in many filters, but here it appears in an extended form. A three dimensional model of the wave equation, which in musical terms represents the vibration modes of a circular membrane, like a drum, is simply three SVFs in parallel with a shared feedback path. (Incidentally the wave equation in two dimensions represents a vibrating string.) The fluid flow equation simply requires one of these SVFs to be inverted, giving an easy opportunity to fit an additional mode into the circuit.

There are individual inputs to each of the filters, where the centre frequency of each can be independently adjusted, and individual outputs for LP, BP and HP are available. The outputs are a composite of all three filters inputs, as a result of how a process is modelled, and the filters cannot be split up to use seperately.

But this is not the intention of the module, anyway. One possible use is in spacial patches, and swept phase effects can be realised with stereo patching. The primary focus of the design, however, was in the complex resonant modes that are possible through the multiple feedback paths and their harmonic relations to each other.

See here:

A classic filter can superimpose a single additional resonant peak upon an input signal, but this can give several. Like the VCOs, this may take some mastery, as some settings may be unstable, unpredictable, even chaotic, but totally unique results are possible, and this to me is the true spirit of synthesis.

Ex, Why and ZZZ control the centre frequencies of the 3 parallel filters. Suppress, is the same as resonance, or peaking, but the meaning is inverted (to most accurately follow real life). The Mode switch changes the physical modelling behaviour between the wave equation and fluid flow, the latter is slightly more unstable.