Next  |  Prev  |  Up  |  Top  |  Index  |  JOS Index  |  JOS Pubs  |  JOS Home  |  Search

MIMO Paraconjugate



Definition: The paraconjugate of $ \mathbf{H}(z)$ is defined as

$\displaystyle {\tilde{\mathbf{H}}}(z) \isdef \mathbf{H}^\ast(z^{-1})
$

where $ \mathbf{H}^\ast(z)$ denotes transpose of $ \mathbf{H}(z)$ followed by complex-conjugation of the coefficients within $ \mathbf{H}^T(z)$ (and not the powers of $ z$ ). For example, if

$\displaystyle \mathbf{H}(z)=\left[\begin{array}{c} 1+jz^{-1} \\ [2pt] 1+z^{-2} \end{array}\right]
$

then

$\displaystyle {\tilde{\mathbf{H}}}(z)=\left[\begin{array}{cc} 1-jz & 1+z^2 \end{array}\right]
$


Next  |  Prev  |  Up  |  Top  |  Index  |  JOS Index  |  JOS Pubs  |  JOS Home  |  Search

[How to cite this work]  [Order a printed hardcopy]  [Comment on this page via email]

``Introduction to Digital Filters with Audio Applications'', by Julius O. Smith III, (September 2007 Edition).
Copyright © 2014-03-23 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA