I know this question has been asked here numerous times. But I am still unclear here :(
My book says,
A linear time-invariant system is stable if its impulse response is absolutely summable. (G. Proakis)
So that should mean that, for a stable system, the impulse response h[n] goes to zero as n approaches infinity, right? But that filter is FIR filter. So FIR filters are always stable.
So, for unstable filters, the impulse response is not absolutely summable. In another way, the impulse response never approaches zero. Again, for IIR filter, h[h] continues to go on with n i.e. never goes to zero. So, IIR filters are supposed to be unstable.
But from Z-transform, IIR filters have poles and FIR filters don't, correct? And if the poles are inside unit circle, i.e. if their value is below one, then that filter is stable.
So, what's happening here? If IIR filters have impulse response which is not absolutely summable, how come they are stable when their poles are within unit circle? Their impulse response goes on like forever, right? Their output gets feedback. So why they can be stable depending on pole's location or value?
Thanks in advance :)