Implementation

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

$$\begin{eqnarray*} y_1(n) &=& (s_1 \ast h_{11})(n) + (s_2 \ast h_{12})(n) + (s_3 \ast h_{13})(n)\\ y_2(n) &=& (s_1 \ast h_{21})(n) + (s_2 \ast h_{22})(n) + (s_3 \ast h_{23})(n) \end{eqnarray*}$$

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

Transfer-function matrix:

$$\left[\begin{array}{c} Y_1(z) \\ [2pt] Y_2(z) \end{array}\right] = \left[\begin{array}{ccc} H_{11}(z) & H_{12}(z) & H_{13}(z)\\ [5pt] H_{21}(z) & H_{22}(z) & H_{23}(z) \end{array}\right] \left[\begin{array}{c} S_1(z) \\ [2pt] S_2(z) \\ [2pt] S_3(z)\end{array}\right]$$