That differs a lot. In my world (drives, control, general electric engineering) it is like this:
Pulse: In TDR applications to look for discontinuities in cables.
Step: Always to check step response and stability margin in systems. Advantage is that a step signal is extremely easy to generate and that there are standardized evaluation methods.
Ramp: Not so often. Sometimes used to check that all drives in a drive system (paper machine for instance) follow with same delay so that draw between sections remains constant.
Sinus (sine for UK/US): General use when checking frequency response (gain and phase angle). Bode plot.
The unit pulse (Dirac pulse) is often used by acoustic engineers to check room properties.
Noise (white): Very useful when doing quick checks to see if a transmission component is free from resonance and has adequate band-width. I use that to check broadband transformers and such components.
Gunnar Englund
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Half full - Half empty? I don't mind. It's what in it that counts.