If a step signal (sudden signal change, square waves etc.) is recorded onto a vinyl record, what would be the resulting waveform actually captured on the final disk?
From my experience as a vinyl cutting engineer, the phase response makes it look more triangular in shape, but it sounds very similar.
Thing is that such a signal only exist in theory - practically this signal will be made up of a number of sine waves with varying frequency and amplitude.
The generator or the sample rate format determines the upper frequency limit (i.e. how "sharp" that seemingly discontinuous signal edge will be a the corner/peaks). This alone will transform your step signal in a similar way to how it will react to later filtering at the vinyl factory (notice the smoothing of the corners below in the red line).
It is thinkable that you have an analog square wave generator that operates in true DC offsets, but even so at some point you have to record that thing, and then you start to hit the "real world" of preamp frequency ranges, AD converter sample rates and/or analog tape frequency range limitations. Long DC spans are likely to get filtered out by DC coupling capacitors (DC removal)
At the factory they will probably filter it even further using high and low passes. If the stereo image is too wide for fast changing low frequency material, they will also reduce the width in lower region.
Guys who master vinyl will tell you something like this: -
A pure step signal has an infinite spectrum and, considering you can't hear above 20kHz (a lot less as you get older) there's no point doing what you suggest.
You may then say "oh please do it" and the vinyl mastering guy might say "OK we'll give it a go" and then completely ignore your request because you won't be able to tell the difference i.e. the mastering guy will apply the normal low pass filtering to a "tape" to prevent too much high frequency rubbish being put on the vinyl.
The basic problem is that a step change cannot be put onto vinyl or any other type of media (including CD, MP3) because the basic media cannot support an infinite bandwidth, so it is limited to whatever bandwidth the media supports. Common sense really.