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We already have partial fraction decomposition in SymPy. Try
If you need the decomposition to single poles,
What would you do with multiple poles, by the way? |
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Since to my current knowledge, the substitution discretizations backward_diff, bilinear and forward_diff, seem practical for usage I don‘t know how relevant the impulse invariant, step invariant, etc… discretization methods are… |
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The bilinear discretization transform for a continuous transfer function$H(s)=\frac{b_0+b_1 s+b_2 s^2+...}{a_0+b_1 s+a_2 s^2+...}$ discussed in
issue-24544 on bilinear discretization
and
pr-24558
is frequency-response-invariant and stability preserving.
https://en.wikipedia.org/wiki/Bilinear_transform
There are numerical counterparts
https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.bilinear.html
https://de.mathworks.com/help/signal/ref/bilinear.html
In digital circuit design a impulse response invariance may be preferred to a frequency-response-invariance.
https://en.wikipedia.org/wiki/Impulse_invariance
A numerical counterpart exists in
https://de.mathworks.com/help/signal/ref/impinvar.html
Here is a proposition of a symbolic impulse invariant transformation, in analogy to the bilinear discretization, based on partial fraction decomposition.
pr-24558
example
@hanspi42, what do you think of the
impinvar
function? and of the following partial fraction decomposition?One could also add the partial fraction decomposition to physics.control.lti
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