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Hadamard Feedback Matrix

A second-order Hadamard matrix:

$\displaystyle \mathbf{H}_2 \mathrel{\stackrel{\mathrm{\Delta}}{=}}
\frac{1}{\sqrt{2}}\left[\begin{array}{rr}
1 & 1\\
-1 & 1
\end{array}\right],
$

Higher order Hadamard matrices defined by recursive embedding:

$\displaystyle \mathbf{H}_4 \mathrel{\stackrel{\mathrm{\Delta}}{=}}
\frac{1}{\sqrt{2}}\left[\begin{array}{rr}
\mathbf{H}_2 & \mathbf{H}_2\\
-\mathbf{H}_2 & \mathbf{H}_2
\end{array}\right].
$


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``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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