Physical signals are not band limited except by the bandwidth of the medium on which they are carried. In order for Analogue to Digital converters to work properley, the signal must be low pass filtered before conversion, to band limit it to less than 1/2 the sampling rate.
I missed the redaction of my post, I was intending to say “composed by single added frequencies” which in practice means that physical signals are always sums of analytical functions. This configure the Hilbert orthogonal basis on Fourier analysis.
When using all of the basis, you have the space of all continuous functions defined on a compact domain, as fundamental Fourier theorem proves.
In nature, is totally unlikely to find non differentiable signals or even non analytical signals, because this will imply infinite values of momentum, acceleration or forces. Even in quantum mechanics, all should be “smooth”
In practical the limitation bandwidth creates a subspace on the Hilbert space, which dimensions are specified with the range of frequencies, so the only region of interest is this subset.
This is the simplest element on the proof to Nyquist theorem that Monty explains when he says “there is only one signal with limited bandwidth that can pass trough the samples”
Any other signal will be a function outside of the subspace of all Hilbert vectors that are linear combinations of the limited chosen basis.
Is a very nice theorem, I had s good time this morning reading the demonstration and it clarified totally to me the influence of bit depth and sample rate on audio digitalization.
Thanks for recommending Shanon-Nyquist!
Still have a lot more doubts, but don’t want to abuse of your time.
I will try to dissociate my learning process form my setup, it cost me a lot in relationship with my salary, and perhaps the experiments I do are perturbing my emotional relationship with music and stressing a little bit when I try to listen and relax.
Always trying to listen defaults instead of enjoying, perhaps this happens to many new audiophiles
