TBH, what made me understand the whole "frequency domain to time domain, and back again" thing was actually the F transform. When I hear that expression, I go "

TBH, what made me understand the whole "frequency domain to time domain, and back again" thing was actually the F transform. When I hear that expression, I go "oh yeah, Fourier transform". Honestly, for me, the sine curve + sine curve + sine curve + ... explanation was perfectly good even on an intuitive level. Perhaps that's because I've spent some of my adolescence in front of a computer doing tons of visualizations and graph plots, and because at the same time I was doing quite a bit of electronics (radio frequency and so on) and audio synthesis. At some point, you just go "yeah, I see it". Fun anecdote: A square wave is made entirely of odd harmonics (3, 5, 7, ...). There are no even harmonics in it. When you can see why intuitively, you've understood Fourier.