[hprotagonist]

> In any case, I've seen so many engineers insist in the time to frequency explanation that it must somehow be easier to understand for people.

Fourier may have used his eponymous transform for working on the heat equation, but for many generations now the primary engineering applications of it have been in electric circuit theory and acoustics, both of which live in constant need for time <-> frequency conversions.

Effectively all the literature in fourier analysis in engineering is written by or for someone whose background is in either electronics or acoustics.

e.g., the bible for many engineers is Oppenheim, Willsky and Nawab, “Signals and Systems”; all three authors are primarily EE (Nawab is BME, but trained by EEs)