Limitations of Digital Filter Design

Digital filter design works best for linear, time-invariant elements.

• What about nonlinear systems?
  (Example: clarinet mouthpiece)
• What if physical parameters are changing over time?
  (Example: stopped violin string with vibrato)
• What if two different systems collide?
  (Example: piano hammer striking a string)

Approaches for nonlinear, time-varying systems:

• Filter coefficient interpolation
• Filter switching
  (usually filter state must be modified as well)
• Filters having a precise physical interpretation
  (true ``explicit finite difference schemes'')

Both the digital waveguide and wave digital modeling frameworks have precise physical interpretations. They both therefore classify as physically meaningful explicit finite difference schemes.