[music-dsp] Vectorising IIR Filters

[Thomas Young]

Does anyone have any thoughts on vectorising IIR filters?

I can't see how an IIR filter implementation can be broken down into parallelisable pieces when there is feedback involved, and I guess that more broadly applies to any effect where feeding back is required. 

For example and perhaps to clarify, if we take a transfer function and put it into direct form 1, then we will end up with the coefficients in our denominator relying on previous outputs. Naively a vectorised implementation would process n outputs concurrently, for example using a 4 float vector and vector intrinsics to process the filter 4 samples at a time, however this obviously does not work when each ouput requires the previous output to have been already calculated.

Tom Young