Signal processing is a discipline dedicated to the engineering-end of stochastic process inference and prediction, especially linear time series. The main innovation, AFAICT, is that signal processing doesn’t just consider IID driving noise, but might try to identify general deterministic or stochastic processes through the time series under observation.
There are various translation difficulties for statisticians; “Testing”=”Detection”, “Linear Filters”=”ARIMA”, estimation of parameters is system identification, estimation of hidden states is state filtering and so on.
This is a very general note to mention that the field exists. Most useful information is under sub-fields, e.g. machine listening, for some signal processing tricks for listening, or feedback systems, for some models particularly appropriate to systems that accept their own output as input etc.
See also orthogonal decompositions. There are close connections to optimal control.
Anyway, I don’t need to explain that here; there are so many software engineers involved with it. the internet is full of interactive diagrammy textbooks to fill that niche.
But here are some notes on some nuggets of interest that I wasn’t sure where else to file.