An interesting third (nonlinear) input possibility is to add the input
to the *instantaneous magnitude* of . This mode is useful
for ``restriking'' a decaying filter oscillation in a
*phase-preserving* manner. The result is that the amplitude of a
decaying oscillation can be jumped without altering its phase at all.

Adding a real signal to the magnitude of is equivalent to scaling by , where , to get

Waiting for phase 0 to scale the state by some gain factor is equivalent to adding an input impulse with amplitude to at that time. Therefore, another approach to achieving smooth filter restriking is to delay them until the next positive-going zero-crossing in the output signal .

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