Here's a question.
I have been reading the entries on wikipedia on signal processing and the filtering problem. It seems as both theories are conserned with the processing or estimation of some "true" or underlying signal/parameter.
How is the theory of stochastic filtering different from the theory of signal processing, and is it the case that one is a (proper) subset of the other?
How do they each compare to stochastic differential equations and forecasting?
My first impression, since the stochastic filtering theory is heavily based on measure theoretic probability, is that signal processing seems "easier", and also more applicable with it's more algorithmic focus.
For any hints, thanks in advance.