Paraunitary MIMO Filters

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In §C.2, we generalized the allpass property $1=\left\vert H(e^{j\omega})\right\vert^2=H(e^{j\omega})H(e^{-j\omega})$ to the entire complex plane as

$\displaystyle {\tilde H}(z) H(z) = 1,$

where ${\tilde H}$ is defined as the paraconjugate of

. In the MIMO case, the paraconjugate is the same, but including a matrix transpose operation:

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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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