Seonglae ChoStable system (bounded-input, bounded-output)
LTI system is BIBO stable iff is absolutely summable (finite). Finite-duration impuse response (FIR Filter) is always stable
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BIBO Stability and the convergence of the frequency
There are cases in which the Fourier transform doesn't converge uniformly, but it does converge in some other sense if it is square-summable (i.e. it has finite energy). In these cases, the transform converges to a discontinuous function. If the Fourier transform is not continuous, then you know that its inverse is not in the sequence space. So one can judge the stability of a system by looking at the continuity of its transfer function. (Main reason is that the Delta function has internal paradox as a function with integral)
그래서 필요충분 조건이 아니라 필요조건임
BIBO Stability and the convergence of the frequency response of a system
It is my understanding that an LTI system is BIBO stable if and only if its impulse response $h(t)$ is absolutely integrable. This also happens to be one of the Dirichlet conditions for the converg...
https://dsp.stackexchange.com/questions/47387/bibo-stability-and-the-convergence-of-the-frequency-response-of-a-system
BIBO stability
In signal processing, specifically control theory, bounded-input, bounded-output (BIBO) stability is a form of stability for signals and systems that take inputs. If a system is BIBO stable, then the output will be bounded for every input to the system that is bounded.
https://en.wikipedia.org/wiki/BIBO_stability