camsr wrote:mystran wrote:camsr wrote:I suppose I am looking for the most "natural" way to develop a sine with the least sideband and fastest response.
You can't have it, because the sidebands and the fast response are the exact same thing just viewed in two different domains.
So a sine wave is only a resultant behavior of some other kind of energy input then.
A sine wave is an infinite [no starting point or ending point, just infinite steady-state both ways], like any finite-bandwidth signal. You can never have a signal that is finite in time and bandwidth at the same time. Any finite-length (time-limited) signal has theoretically unlimited bandwidth. What you can increase the spectral roll-off for the side-bands by smoothing the time-domain signal, but whatever "resolution" you gain in one domain, you lose in the other domain.
It sucks, but that's the way it works.