[SciPy-User] [signal] zpk -> s domain?

[Fabrice Silva]

El ven., 11-02-2011 a las 11:23 -0500, Neal Becker escribió:
> 
> I have a digital filter design, which is specified as poles and zeros
> in the z-transform domain (zpk).
> 
> k (z-z0)(z-z1)...
> -----------------
> (z-p0)(z-p1)...
> 
> I want it expressed in the s domain (laplace transform), in a form
> such as:
> 
> (s-a)(s-b)...
> -----------
> (s-c)(s-d)...
> It is true that z=e^(sT), but simply making this substitution doesn't
> seem very useful.

Yes it is! For each pole pn, you have to solve pn=exp(sn Ts) which have
an infinity of solutions (due to aliasing when sampling)
sn = Fs( log(abs(pn)) + 1.j*(angle(pn)+2*k*pi)), k being integer
Choose for each pn the one that is in the frequency bandwidth of
interest [-Fs/2, Fs/2] or [0,Fs]..

The same for the zeros. It then remains to identify the gain, a mere
scalar...

-- 
Fabrice