Excitation Factoring

As another refinement, it is typically more efficient to implement the highest Q resonances of the soundboard and piano enclosure using actual digital filters (see Appendix S). By factoring these out, the impulse response is shortened and thus the required excitable length is reduced. This provides a classical computation vs. memory trade-off which can be optimized as needed in a given implementation. For lack of a better name, let us refer to such a resonator bank as an ``equalizer'' since it can be conveniently implemented using parametric equalizer sections, one per high-Q resonance.

A possible placement of the comb filter and equalizer is shown in Fig. 5.10. However, since all elements are linear and time invariant, they may be ordered arbitrarily. For example they could both appear before the string. Having the equalizer at the end, however, is convenient for defining multiple outputs having different spectral characteristics. Similarly, placing a multi-tap comb filter output can be used to create a variety of differently comb-filtered outputs.