DSP is all about when you can approximate discrete-time systems with continuous ones and vice versa. Here are some details on this time-honoured form of coarse graining.
Sampling theorems. Nyquist rates, etc. Neat tricks with SDEs; relationship to classic state filter inference. The classic connection here is difference equations versus differential equations, because of some nice Markov properties. There are other possible relations, though, with actual time-delay equations.
I assume regular discretisation here, (uniform sampling, if you are taking measurements) but there is also stuff at nonuniform sampling.
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