>Matt Timmermans wrote:
>> There is a limit to how concentrated a signal can be in both time and
>> frequency. In quantum mechanics, this implies Heisenberg's uncertainty
>> principle, which is such a catchy name that a lot of people apply it to this
>> time-frequency compactness limit in all circumstances.
>I'll try to come at this point another way. As R.B-J. pointed out, a
>narrow notch can be made by subtracting a sharp peak from the original
>signal ("short wire"). It doesn't matter how the notch is made; it
>behaves like what it is. When an impulse excites a sharp peak, all the
>energy comes out, but only at the peak's frequency. It follows that it
>comes out over an extended period. Think about the impulse of a hammer
>on a sharply tuned structure (say, a bell or a piano string) as you
>think about what "ringing" means.
>Sharp resonances -- high Qs -- have steep sides. Low Q resonances have
>broader bases for the same height. When the slope is low enough to
>approximate critical damping, there's no ringing at all.
Thanks for the additional perspective.
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