The Lossless Digital Model

• The resulting system of equations can be combined as shown in the block diagram of Fig. 14.

  Figure 14: The wave digital hammer block diagram.

  

• $S$ is the three-port scattering junction.

• $H$ is a time-varying allpass filter.

• $G$ is the modified integrator that integrates the incoming initial hammer velocity impulse signal, $v_{I}[n]$, taking into account the wave decomposition and the nonlinear effects of the hammer felt.

• $X$ computes the actual felt compression, taking advantage of the fact that the force of compression on the felt is instantaneously proportional to the felt compression.

• $K$ is a look-up table for the stiffness coefficient, $a_{0}[n]$, indexed by felt compression.

• $R$ computes the time-varying wave impedance of the hammer system from $a_{0}$.

• $R_{h}[n] = 0$ when the hammer is not touching the string and $k(x_{k}) = 0$ as well, so the string equations are then not affected by the hammer system.