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
The energy dissipated in the first period
Assuming
as before,
so that
Assuming further that
or
as claimed. Note that this rule of thumb requires