Re: Partial Fraction Decomposition in c++

dilpreet06 wrote:

Hi Andor, sorry for the confusion,

What i meant to say was :

I have the polynomial of the transfer function including its roots. From
the roots Ive calculated the frequencies Omega(i) of the (i)th pole, i.e.
where the poles lie.

I want to calculate the magnitude of the transfer function at that pole by
calculating the residuum of the transfer function at the pole.

Let's say you have the transfer function H(z) of a stable system. It
has poles (the roots of the denominator), but they are not on the unit
circle (otherwise the system wouldn't be stable). Let's further say the
poles are called p_k. Now of course the magnitude at the poles is
|H(p_k)| = infinity, that's why the are called poles. You know that
without computing the residues.

Or are you interested in the magnitude of the transfer function at the
pole _frequency_? Ie. if

p_k = r_k exp(+/- j w_k), 0 < r_k =/= 1,

you want to know | H(exp(i w_k) |? This is straight forward complex
math, no residues required. Just replace z with exp(j w_k) in the
rational expression and compute the magnitude of the complex number.

Did that answer your question?

Regards,
Andor

.

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