Yet another meaning for is [20, p. 326]
where the resonator is freely decaying (unexcited).
To analyze this, let's again consider a one-pole resonator as in §E.7.1. Then the impulse response is given by
The total stored energy at time is given by the total energy of the remaining response at time :
The energy dissipated in the first period is , where
Assuming as before, so that
Assuming further that , we have so that
as claimed. Note that this rule of thumb requires , while the one of the previous section only required .