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.
is the three-port scattering junction.
is a time-varying allpass filter.
is the modified integrator that integrates the incoming initial hammer velocity impulse signal, , taking into account the wave decomposition and the nonlinear effects of the hammer felt.
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.
is a look-up table for the stiffness coefficient, , indexed by felt compression.
computes the time-varying wave impedance of the hammer system from .
when the hammer is not touching the string and as well, so the string equations are then not affected by the hammer system.