Filters - Maximizing Quality (Structures and Scaling)

Started by davidross January 18, 2006
Martin Eisenberg wrote:
> robert bristow-johnson wrote: > > Martin Eisenberg wrote: > > >> DF2 transposed halves the number of states. > > > > not for multiple cascaded biquad sections. the two output > > states of "section n-1" are the same as the input states of > > "section n". > > OK -- numerical properties aside you presume one way of constructing > programs there, and so did I when I catered to David's immediate > question but no more. Fusing the states of adjacent DF1 sections is > of course easy if you write the thing from scratch every time. If you > just want to chain modules from a library and still do it, either you > end up connecting filter objects to state buffers explicitly which > sort of defies the premise; or you abstract the fusing into another > library entity which is unconventional enough to add a fair bit of > complexity however its code actually looks, and also possibly incurs > runtime overhead.
well, i'm trying to compare apples to apples here. there are little optimized subroutines to do the DF2 with N sections, why don't TI and ADI write them as DF1 (with that state "fusing")?
> > although the DF2 won't suffer saturation if floating point is > > used, i have noted a numerical problem for DF2 if single > > precision is used (having to do with loss of precision when > > scaled states are subtracted). we've discussed this before on > > comp,dsp you might unwrap this URL and read about it: > > Are you referring to DF2 or DF2-transposed here? You didn't respond > to Nigel's pointing out in that thread that the latter is more benign > (even though it has three summing nodes, alas). Also, when the code > mostly keeps states in the extended-precision registers of the x86 > (David's target, as I learned on music-dsp) the difference between > DF1 and DF2-t might be inconsequential after all, what do you say?
i didn't try the DF2-t, so what you and Nigel say might very well be correct. but, unless you put in a couple of quantizers, the states in the DF2 transpose must be double precision. if they are not, then the DF2-t has 3 quantization noise sources instead of 1. the DF1 needs only a double precision accumulator and has only one quantization per section. r b-j