{𝐡k,k=0,...,N−1}\{\mathbf{h}_k,k=0,...,N-1\} are OBV if ⟨𝐡k,𝐡l⟩=δk,l={1k=l0k≠l\langle \mathbf{h}_k,\mathbf{h}_l \rangle =\delta_{k,l} =\begin{cases} 1 & k=l\\ 0 & k \neq l\end{cases}
with OBV ⟨𝐡l,𝐟⟩=⟨𝐡l,∑k=0N−1t(k)𝐡k⟩=t(l)=𝐡lH𝐟𝐭=[𝐡0H𝐡1H⋮𝐡N−1H]𝐁−1=𝐁H or 𝐁=𝐁𝐁H=𝐈\begin{align*} \langle \mathbf{h}_l, \mathbf{f} \rangle = \langle \mathbf{h}_l, \sum_{k=0}^{N-1} t(k) \mathbf{h}_k \rangle=t(l)=\mathbf{h}_l^H \mathbf{f} \\ \mathbf{t}=\begin{bmatrix} \mathbf{h}_0^H \\ \mathbf{h}_1^H\\ \vdots \\ \mathbf{h}_{N-1}^H \end{bmatrix} \\ \mathbf{B}^{-1}=\mathbf{B}^H \textrm{ or } \mathbf{B} = \mathbf{B} \mathbf{B}^H = \mathbf{I} \end{align*} where 𝐁\mathbf{B} is unitary.
See Orthonormal basis