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My $G(s)=1-e^{-s/\tau}$, $\tau$ is very small, say of order $10^{-4}$.

I need to compute a $H(z)$ (a digital filter) such that $H(z)$ has the inverse response of $G(s)$. Is ok even if $G(z)$ has the inverse response just for $f$<20k.

I don't not also zero and pole go $G(s)$.

I'm able to have an proximation of $H(z)$, but I found it with an iterative algorithm set $H(z)=\dfrac{\alpha}{1 -\beta z^{-1}}$.

I prefer a formal solution.

Phonon
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mattia settin
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  • Are you sure that your $s$-domain transfer function looks like that? That's a strange form; rational Laplace domain transfer functions would be much more common. I think your TF would correspond to an impulse response of $h(t) = \delta(t) - \delta(t-\frac{1}{\tau})$. – Jason R Jan 29 '14 at 21:32
  • @JasonR, it's an analog LTI system with some delay. perhaps SAW (surface acoustic wave) or a long transmission line. – robert bristow-johnson Jan 30 '14 at 02:43
  • @robertbristow-johnson: Sounds like reasonable examples. – Jason R Jan 30 '14 at 03:17
  • To the OP: Note that $G(s)=0$ for $s=0$ (it has a highpass response). Therefore, you won't be able to exactly invert it for $f < 20000\text{ Hz}$, whether you're in the analog or digital domain. – Jason R Jan 30 '14 at 03:19

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