Specifying String State

The complete state of the string is given at time $n$ by

• $\{y(t_n,x_m), {\dot y}(t_n,x_m)\}_{m=0}^{N-1}$ (typical in acoustics)
• $\{y(t_n,x_m), y(t_{n-1},x_m)\}_{m=0}^{N-1}$ (typical in acoustic simulations)
• $\{y^{+}(n-m), y^{-}(n+m)\}_{m=0}^{N-1}$ (what we did)
• $\{y'^{+}(n-m), y'^{-}(n+m)\}_{m=0}^{N-1}$ (today)
• $\{v^{+}(n-m), v^{-}(n+m)\}_{m=0}^{N-1}$ (today)
• Any two linearly independent variables
  (either physical variables or wave variables)

• All traveling-wave variables can be computed from any others, as long as string state is specified

• Wave variable conversions requiring differentiation or integration are relatively expensive since a large-order digital filter is necessary to do it right