sence of E in the right-hand side of (5.162) implies a small time derivative of the process q(T). This ensures that substantial changes in q(T) only occur over a long period of time. Hence, the process q(t) contains a dominant low-frequency component. As outlined in section 5.6, the equation that governs the behavior of this component can be extracted by means of an averaging transformation (5.163) If we use the ideal lowpass averaging operator (5.90), then the averaged equation cor- responding to (5.162) becomes (5.164) As will be demonstrated experimentally in section 5.8.3, this averaged equation cap- tures the essence of the dynamic behavior of a (system of coupled) harmonic oscil- lator(s). Furthermore, it can be solved very efficiently using traditional (SPICE-like) simulation algorithms. Hence, it serves as a compact behavioral harmonic oscillator model. Of course, in order to be useful in practice, the right-hand side of (5.164) must be stored in a way that can be evaluated efficiently while being easy to implement in environments for system-level simulation. 5.8.1 Model extraction theory 5.8.1.5 Storing the averaged equations A first approach stores hq(q,t) as a table of precomputed values. During simulation, model evaluations are performed using table lookup and interpolation in between. As illustrated in section 5.8.3.1, this approach works fine for modeling a single harmonic oscillator's behavior. However, since the storage space increases exponentially with the dimension of the vector q, it becomes cumbersome for sets of coupled oscillators. For stable oscillators, a more elegant approach exists. Stability ensures that all am- plitudes and phase differences converge to a neighborhood of a stable operating point. It is therefore possible to construct behavioral models by approximating the averaged equations near such an operating point. In order to put this idea to practice, we partition the state vector in two major components: AQx 0] (5.165) (5.166) A first component q1 contains the amplitudes and p