[music-dsp] Re: Revisiting C++ Filtering Classes

[Vinnie]

> From: "Martin Eisenberg" <martin.eisenberg at udo.edu>
> Trouble is that the complex division in BilinearTransform()
> can still yield a nonzero imaginary part even if the input is
> real.

UGH! I just figured out the implications of this. I calculate the poles in the s-plane first and then do the transformation. So I cannot be sure if a singleton in the s plane will remain so after the transform.

I have one list of complex conjugate pairs, and another list of complex singletons, is there a one to one mapping after the bilinear transformation of the pairs to a new set of conjugate pairs? Or do they lose the conjugate property? Do singletons become pairs? They certainly can take on an imaginary component...

Should I just give up on the 'optimization' of not calculating some of the poles? It is turning out to be more trouble than it is worth. I don't relish the thought of resampling the poles in a different order just to get the conjugates to land at the 'end'. And plus, if I do this, it will place an extra burden on anyone who wants to design their own filter.