Physically Informed Control of Modal Synthesis (PhISAM)

The “physically informed spectral additive modeling” (PhISAM) technique is based on modal synthesis with the addition of “physical” parametric controls such as “stick hardness” and “strike position”.
The approach is suitable for resonant percussion instruments characterized by impulsive excitation of a relatively few exponentially decaying, weakly coupled sinusoidal modes (i.e., marimba, vibraphone, cowbell, ...).
Frequency tracking, or mode “picking”, can be accomplished using Fourier analysis, linear predictive coding, or other all-pole filtering techniques.
Prototype excitations can be determined by recording a stick strike while damping the resonant modes of an instrument or by extracting a residual signal from an LPC or sinusoidal analysis.
Physical parametric controls, such as strike position and stick hardness, can be simulated using simple rules to control modal gains.
The analysis/resynthesis approach can be outlined as:
1. Take a recorded sound and perform high-order LPC, ARMA, or SMS sinusoidal + noise analysis:
  - Determine the highest-Q resonances or highest-amplitude FFT peaks;
  - Extract LPC residual or SMS noise envelope for resynthesis excitation or record a dry strike.
2. Derive resynthesis parametric control rules:
  - For strike position, analyze modal behavior for various strike position excitations;
  - For stick hardness and strike vigor, first choose resynthesis method (resonant filters or sinusoidal functions) and then derive rules.
3. Perform resynthesis with derived rules and include dynamics of player/performer.
A PhISAM system block diagram is shown in Fig. 8 below.

Figure 8: A PhISAM system block diagram.
$\begin{figure}\begin{center} \epsfig{file = figures/phisam.eps,width=4in} \end{center} \end{figure}$
The “stick hardness” can be simulated by varying the playback rate of the strike signal. That is, a softer strike can be simulated using a recording hard strike by reading through the sound at a slower rate. This effectively lowers the frequency content of the original sound.