Infinite frequency from a single frequency sine wave.

[FreddieChopin]

I have a bit of brain experiment. If everything in our world (electric things) is all in all moving single electrons then sine wave can be approximated by rising square waves of passing single electrons, right? (Like picture below).
If you have a square wave then when square wave switches from high to low there is a high frequency. With highpass filter you can get only higher frequency from signal. So if there would be an electronic filter that works beyond single electrons (other smaller particles, quarks? gluons?) then it would be possible to do nano-level DSP, right?

[T3sl4co1l]

What?

...You seem to be working under the assumption that charge moves discretely, i.e., that an electron flow is a superposition of square waves?

This is not in fact physically true, in most cases; and even if it were, the statistics are not simply some square wave of fixed amplitude distributed evenly, but noise statistics follow what's appropriate for the situation.  Most importantly of which, full shot noise is Poissonian.  Many noise sources can be sub-Poissonian, due to the continuous freedom of movement that charges have, within say, a conductor; full shot noise only occurs when a sufficiently large (irreversable?) barrier is crossed by the charge (like a reverse-biased semiconductor junction).

You can still produce square wave transforms of ordinary signals; the resulting function or series is not necessarily very useful for signal processing purposes.  The Hadamard transform is such an example.

Regarding DSP, it might be handy to have a conversion between the traditional Fourier transform, and the Hadamard transform or such.  AFAIK, while they give similar results, converting between the two still takes equivalent effort, so you probably don't stand to save much by devising an algorithm that uses this as a shortcut.

Tim

[Kilrah]

If everything in our world (electric things) is all in all moving single electrons then sine wave can be approximated by rising square waves of passing single electrons, right? (Like picture below).

No. Moving electrons yes, jumping electrons no. They can be moving at any speed. Your assumption would assume quantization (and the effect you describe, if it existed would be a quantization error and not an actual phenomenon), but the world is analog...

[FreddieChopin]

If everything in our world (electric things) is all in all moving single electrons then sine wave can be approximated by rising square waves of passing single electrons, right? (Like picture below).

No. Moving electrons yes, jumping electrons no. They can be moving at any speed. Your assumption would assume quantization (and the effect you describe, if it existed would be a quantization error and not an actual phenomenon), but the world is analog...

Yes, I know that world is analog but just like in Minecraft - there are singular block of matter (think sub-atom particles) and you move with floating number position - looks smooth but in reality it's still changing in discrete values.

[Kilrah]

Minecraft is a computer program, so however small the position resolution is it is still finite, so you do jump from one to another. In nature the resolution is infinite, no discrete values. You can always make a "step" that is smaller than another one yet still non-zero, forever.