Question about a Signal's Frequency Spectra and Modulation

[Noesis]

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.

 

[Noesis]

Also..as another clarification to the above:

The definition of frequency is very clear to me: x repeating per y . I don't see anything repeating in my rectangular box voltage (gate signal) up above and just don't see how frequency has anything to do with it--except as mathematical convenience.

Thanks.

 

[rbj]

The definition of frequency is very clear to me: x repeating per y . I don't see anything repeating in my rectangular box voltage (gate signal) up above and just don't see how frequency has anything to do with it--except as mathematical convenience.

the concept of addition is really only a mathematical concept. perhaps in another universe this purely mathematical concept of addition would have nothing to do with the reality of what happens when quantities of the same kinda stuff accumulates. but in this universe, when you have X thingies in one bucket and Y thingies in another bucket, and you pour the Y thingies into the bucket with X thingies, we expect the quantity of thingies in that bucket to be X+Y. but why should physical reality (of collecting or accumulating thingies) submit itself to this mathematical model of addition? but it does. (sometimes it doesn't exactly, such as in relativistic velocity addition.)

so, even if in a square wave, you, in your anthropocentric observation, do not see evidence of a first harmonic added to a third harmonic added to a fifth harmonic, etc., but that is how a resonant circuit might look at that square wave; as a sum of sinusoids with these particularly related frequencies.