Additive Inputs

Instead of initial conditions, ongoing input signals can be defined analogously. For example, feeding an input signal $u_n$ into the FDTD via

$$y_{n,m-1} = y_{n,m-1} + u_{n-1}$$

$$y_{n,m} = y_{n,m} + 2u_n$$

$$y_{n,m+1} = y_{n,m+1} + u_{n-1} \protect$$ (24)

corresponds to physically driving a single sample of string displacement at position $m$. This is the spatially distributed alternative to the temporally distributed solution of feeding an input to a single displacement sample via the filter $H(z)=1-z^{-2}$ as discussed in [13].