The PhISEM approach uses the results of ``off-line'' particle interaction simulations to derive statistical collision distributions.
From a numerical simulation of a maraca, statistics were collected with respect to frequency, waiting time, and sound intensity of bean collisions with the outer gourd wall.
In general, a short-term energy input produced an exponential decay in intensity of collisions.
The likelihood of a significant sound-producing collision was found to be roughly constant, until all beans were nearly at rest.
The collected statistics could then be used to control a model in which events trigger distinct overlapping, decaying signals.
However, a more efficient approach is found by noting the noise-like nature of the resulting sound from a maraca. This suggests the use of decaying noise to represent collision events and a single second-order digital filter to model the gourd resonance.
Because the sum of exponentially decaying random noise is equal to a single noise source multiplied by a decaying value, only a single exponential decay and a single noise source are required to compute the total sound.
The maraca synthesis algorithm requires only two random-number calculations (for collision-event likelihood and noise sound source), two exponential decay multiplications (for net system energy and sound level), and one biquad filter, as shown in Fig. 18.