I used to think that the frequencies obtained by a Fourier Series or Transform from a signal in the 'time domain' were simply a consequence of our mathematical system. In other words, it is a consequence of the fact that sinusoids are used to recreate or synthesize the signal. It's just an approximation technique using an orthogonal set; and could've been done through another orthogonal set. Since I viewed it as a consequence of our mathematical system, I did not see time signals having actual frequencies in nature. This seemed evident to me as well in terms of a simple square signal. Due to the inverse relationship between bandwidth and time duration, a 'larger rectangle' had smaller frequency than a 'smaller rectangle.' But clearly both rectangles have NO frequency...they're just boxes! Now that I am studying modulation, specifically amplitude modulation, I see that signals are analyzed via their Fourier Transforms and that actual filters (say a low-pass filter) are used to extract the signals again in demodulation. This contradicts my original thoughts and so something is wrong. Frequency is being used here in practice, so there must be some link between a frequency spectra and the signal in reality. If someone could please clarify this I would be very appreciative. Thank you.