Paraunitary MIMO Filters

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

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

where ${\tilde H}$ is defined as the paraconjugate of $H$ . In the MIMO case, the paraconjugate is the same, but including a matrix transpose operation: