You really aren't. That assertion is like commenting that elementary arithmetics is discrete signal analysis because 1+1=2, which happens to match the amplitude of a resonance of a normalized vibration mode.

It isn't. It's a cherry picked example. A broken clock which coincides with the current time.

> It isn't. It's a cherry picked example. A broken clock which coincides with the current time.

No. It really is. Look at the example.

Nobody can convince you if you are already set up against that idea, but look at what happens when you multiply two polyomials P(z)Q(z). You obtain a polynomial whose coefficients are the convolution of those of P and Q. Now, a decimal number is "just" a polynomial evaluated on z=10. And a vibrating string is "just" a polynomial evaluated at z=exp(it). The algebra of convolutions and products is exactly the same in all three cases.