Hadamard Matrix
A second-order Hadamard matrix may be defined by
![$\displaystyle \mathbf{H}_2 \isdef
\frac{1}{\sqrt{2}}
\left[\begin{array}{rr}
1 & 1\\
-1 & 1
\end{array}\right],
$](http://www.dsprelated.com/josimages_new/pasp/img748.png)
![$\displaystyle \mathbf{H}_4 \isdef
\frac{1}{\sqrt{2}}
\left[\begin{array}{rr}
\...
...}{rrrr}
1& 1& 1&1\\
-1& 1&-1&1\\
-1&-1& 1&1\\
1&-1&-1&1
\end{array}\right].
$](http://www.dsprelated.com/josimages_new/pasp/img749.png)
![$ n$](http://www.dsprelated.com/josimages_new/pasp/img146.png)
![$ 4$](http://www.dsprelated.com/josimages_new/pasp/img750.png)
![$ \mathbf{H}_n$](http://www.dsprelated.com/josimages_new/pasp/img751.png)
![$ n\times
n$](http://www.dsprelated.com/josimages_new/pasp/img752.png)
![$ n\times
n$](http://www.dsprelated.com/josimages_new/pasp/img752.png)
![$ 1$](http://www.dsprelated.com/josimages_new/pasp/img138.png)
As of version 0.9.30, Faust's math.lib4.12contains a function called hadamard(n) for generating an
Hadamard matrix, where
must be a power of
. A
Hadamard feedback matrix is used in the programming example
reverb_designer.dsp (a configurable FDN reverberator)
distributed with Faust.
A Hadamard feedback matrix is said to be used in the IRCAM Spatialisateur [218].
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