Listening to the String

• Chaigne and Askenfelt compute string displacement at every node on the string, at each time step. This is useful for visualizations, etc.

• For sound synthesis, we need only ``listen'' to the string at the ``bridge''. The bridge is where most of the string vibrational energy couples to the piano soundboard.

• Let's define the output as
  $$y_{out}={\bf C_1}{\bf y}_{n}$$
  where ${\bf C_1}$ is some constant row vector. A typical choice of ${\bf C_1}$ might be ${\bf C_1}=[0,\ldots,0,1]$ , which picks out the last sample of string dispacement nearest the bridge.

• More generally, we could take any linear combination of string displacement samples as the output.