If we are talking about BIBO stability, then this is sort of a tautology, because .. well a filter is "BIBO stable" if bounded input leads to bounded output (duh). For LTI filters this implies it eventually decays to zero (or by extension some constant term if you add one). I believe such a system is called "asymptotically stable" (all initial conditions converge to the same final state), but BIBO stability need not imply asymptotic stability if the system is non-linear. For example, a self-oscillating filter is BIBO stable (hopefully), but need not ever stop oscillating.Time-domain methods are continuous, if the functions are. Therefore a time-domain continuous filter that's also BIBO is always stable, right?
That said, it can actually sometimes be quite difficult to formally define what we mean by "stable" in any given context... and you obviously can't prove that something is "stable" unless you've formally defined the stability conditions.
Statistics: Posted by mystran — Wed Mar 27, 2024 11:25 am
