[cbondurant]

This feels like a very indirect way of saying "yes the fourier transform of a signal is a breakdown of its component frequencies, but depending on the kind of signal you are trying to characterize for it might not be what you actually need."

Its not that unintuitive to imagine that if all of your signals are pulses, something like the wavelet transform might do a better job at giving you meaningful insights into a signal than the fourier transform might.

[adornKey]

The thinking that sinus are basic building blocks and own frequencies is part of the problem. Fourier is a breakdown into frequencies of "sinus" waves. Sinus are fundamental in physics of some idealistic conditions, but using Sinus is just a choice, mathematically you could just as good use other bases. A triangle has mathematically the same right to own a frequency as a sinus.

Reality is often different from ideal and not that linear. So basic wave-forms often aren't really sinus. But people usually only know sinus, so they'll use this hammer on every nail. Some guys into electrical engineering maybe know about rectangles, but there's, not yet, enough deeper understanding out there for playing with the mathematical tools correctly.

[badlibrarian]

Physics didn’t pick sinusoids because it “only knows about sinuses.” Physics picked them because the math forces them on you.

Actual engineers:

  - use sinusoids because LTI systems respond, uh... linearly to them
  - use square waves for digital logic
  - use triangle waves for modulation
  - use wavelets for compression or time/frequency localization
  - use Hilbert transforms (and actually know what "orthonormal" means)
  - use STFT, CWT, FFTs... and know exactly why Fourier works and when it breaks