Overview
Signals and systems is a field that grew out of electrical engineering. It first was used to analyze a signal that is transmitted over a wire, and then transmitted over radio. As such, it could be considered as analyzing time series signals.
Later, the field developed to analyze two dimensional data structures, such as images, and two dimensional time series such as video.
The methods of signals and systems do not always use the tools of probability and statistics. Even when there is noise in the signal, the techniques that deal with the noise can sometimes be studied and utilized without going in depth in probability theory. When the topic does deal with randomness explicitly, it is often called statistical signal processing.