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Chapters

See Also

Embedded SystemsFPGAElectronics

Introduction to Digital Filters
    Allpass Filters
       Multi-Input, Multi-Output (MIMO) Allpass Filters
          Paraunitary MIMO Filters
             MIMO Paraconjugate

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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] $

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Next: MIMO Paraunitary Condition

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About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.


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