I found this transfer function online and for the most part I understand it. But what is tripping me up, is that they are replacing the traditional $\frac{1}{s}$ form of the integral with a sum. I understand the reasoning -- an integral is just an infinite sum, so a discrete version is a finite sum -- but I didn't realize that was allowed. Is this acceptable, and if so, are there any rules or concerns to consider?
Aside:
I should also note that the document doesn't say which method they used to convert to the discrete domain, I'm just assuming it's a laplace transform because the derivative term comes out as a multiplicand, and I don't think that happens in a fourier transform. These are the only 2 discrete transforms I'm aware of, so maybe that's my confusion.
