New answers tagged digital-filters
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(This should have been a comment if I had enough reputation.)
In the comment to Matt's comprehensive answer, as well as in the original question, @Slev1n has asked about the relation suggesting $\alpha = -e^{\frac{-T}{\tau}}$, while Matt has arrived at the formula $1 - e^{\frac{-T}{\tau}}.$
While it is impossible to have $\alpha = -e^{\frac{-T}{\tau}}$ as $...
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A few points first
Since you are using digital filters, you should be using residuez() not residue()
Matlab's residuez() is not particularly well implemented: in case of higher order or steep filters, you can get a lot of numerically noise or results that are just totally wrong. Always check the result against your original target.
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