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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*}

Transfer-function matrix:

$\displaystyle \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]
$


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Download Reverb.pdf
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Download Reverb_4up.pdf

``Artificial Reverberation and Spatialization'', by Julius O. Smith III, (From Lecture Overheads, Music 420).
Copyright © 2014-03-24 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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