Implementation

Let $h_{ij}(n) =$ impulse response from source $j$ to ear $i$. Then the output is given by six convolutions:

$$\begin{eqnarray*} y_1(n) &=& (s_1 \ast h_{11})(n) + (s_2 \ast h_{12})(n) + (s_3 ... ..._1 \ast h_{21})(n) + (s_2 \ast h_{22})(n) + (s_3 \ast h_{23})(n) \end{eqnarray*}$$

• For small $n$, filters $h_{ij}(n)$ are sparse
• Tapped Delay Line (TDL) a natural choice

Transfer-function matrix:

$$\left[\begin{array}{c} Y_1(z) \\ [2pt] Y_2(z) \end{array}\right] ... ...left[\begin{array}{c} S_1(z) \\ [2pt] S_2(z) \\ [2pt] S_3(z)\end{array}\right]$$