This sounds like a useful complement to our existing residue/residuez functions. For consistency with our other ZPK functions, a name like residue_zpk would fit better than residues. Eric On Tue, Oct 10, 2017 at 8:24 AM, Leonhard Neuhaus < neuhaus@spectro.jussieu.fr> wrote:

Hi all,

I have written a function residues() which does the same as scipy.signal.residue, but that accepts an input in the form (zeros, poles, k) - k is the global prefactor - instead of the usual (b, a)-Polynomial form of the transfer function to transform. This was necessary since I wanted to do the partial fraction expansion of an transfer function of roughly 10th order (given in the zero-pole-form) and numerical imprecision issues prevented me from passing through the (b, a)-form. The partial fraction expansion was necessary in my case to decompose the transfer function into parallel biquads (opposed to the more common serial biquad decomposition). The way I implemented the transformation can be found here:

https://github.com/lneuhaus/pyrpl/blob/55cb112a50e221f11eb28 f106ba11272890c3b7f/pyrpl/hardware_modules/iir/iir_theory.py#L145

This implementation does not suffer from the typical numerical imprecision issues associated with higher-order polynomials since the coefficients (i.e. the prefactors of x^n in the numerator/denominator of the transfer function) are never explicitly calculated.

I would be happy to prepare a proper pull-request that extends the residue function with the (zero, pole, k)-input option if this is desired. Please let me know and I will get to work.

Cheers, Leo

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