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A second-order Hadamard matrix may be defined by
with higher order Hadamard matrices defined by recursive embedding, e.g.,
When
is a power of
, the Hadamard matrix
of that
order requires no multiplies in fixed-point arithmetic. An
Hadamard matrix has the maximum possible determinant of any
complex matrix containing elements which are bounded by
in magnitude. This can be seen as an optimal mixing and
scattering property of the matrix.
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 [219].
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