There may be some benefit even for LR4, but the main difference is for LR8. You only need 2xSVF4pole instead of 5xSVF2pole, so you save one SVF2Pole worth of computation. The internal computation of the solution has more terms for the SVF4Pole and appears to be more parallel in nature, but I've not done any rigorous profiling to see if this would make it more efficient.Z1202 wrote:The question would be, is there any benefit of this higher-order SVF (I believe also referred to as canonical controllable form of a state-space system) compared to simply cascading multiple 2nd-order ones. Especially if the 2nd-order coefficients are already known and there is even no need to factor th polynomials. Particularly, IIRC some people reported precision/noise issues being worse with higher-order SVFs, not unlikely the direct forms.
Edit: ok, if they are modulated, you can save a division, since there is only one feedback path. But besides that?
Edit2: actually instead of dividing twice in the case of representing a 4th order filter as a product of two 2nd order ones, you could reciprocate the product of the denominators and multiply back by each of them in turn
I was mainly interesting in the SVF4Pole for an analog filter prototype I was considering for a eurorack module. I thought it would be cool to have a 4 pole SVF that you could use either as a regular resonant filter, but also a voltage controlled x-over