This is an open question, just for discussion. During my years studying and working on signal processing, I have identified several factors that are relevant for understanding any type of signal. For example, PSD for analyzing frequency spectrum and distribution of fundamental frequencies, if any; envelope of the signal for "slow" signals (below lets say 1KHz), skewness and kurtosis analysis of probability distribution of the signal, and so on.
However, I have always been curious about what do other people focus on analyzing a new signal and what are the important elements that you first try to get out before starting to plan a signal processing technique and filter design.
Do you have any particular protocol or procedure that you follow when approaching a "new signal" analysis?