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Algorithm

To start the separation algorithm, $ \mbox{${\bm \gamma}$}$$ _0$ is initialized to the zero-shifted impulse response data $ {\mathbf{h}}\cdot$diag$ (z^{\tau_i})$, ignoring the tails of the base-leakage they may contain. Then $ \mbox{${\bm \alpha}$}$$ _0$ is estimated as the mean of $ {\mathbf{h}}-$$ \mbox{${\bm \gamma}$}$$ _0$diag$ (z^{-\tau_i})$. This mean is then subtracted from $ {\mathbf{h}}$ to produce $ {\mathbf{b}}_1 = ({\mathbf{h}}-$   $ \mbox{${\bm \alpha}$}$$ _0)$diag$ (z^{-\tau_i})$ which is then then converted to $ \mbox{${\bm \gamma}$}$$ _1 = {\mathbf{g}}_1 \cdot {\mathbf{w}}_1$ by a truncated SVD. A revised base-leakage estimate $ \mbox{${\bm \alpha}$}$$ _1$ is then formed as $ {\mathbf{h}}-$$ \mbox{${\bm \gamma}$}$$ _1$diag$ (z^{-\tau_i})$, and so on, until convergence is achieved.


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``Doppler Simulation and the Leslie'', by Julius O. Smith III, Stefania Serafin, Jonathan Abel, David P. Berners, Music 421 Handout, Spring 2002 .
Copyright © 2006-03-30 by Julius O. Smith III, Stefania Serafin, Jonathan Abel, David P. Berners
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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