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

or

as claimed. Note that this rule of thumb requires , while the one of the previous section only required .

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