Orthogonal Two-Channel Filter BanksRecall the reconstruction equation for the two-channel, critically sampled, perfect-reconstruction filter-bank:
where the above matrix, , is called the alias component matrix (or analysis modulation matrix). If
where denotes the paraconjugate of , then the alias component (AC) matrix is lossless, and the (real) filter bank is orthogonal. It turns out orthogonal filter banks give perfect reconstruction filter banks for any number of channels. Orthogonal filter banks are also called paraunitary filter banks, which we'll study in polyphase form in §11.5 below. The AC matrix is paraunitary if and only if the polyphase matrix (defined in the next section) is paraunitary .
Simple Examples of Perfect Reconstruction
Conjugate Quadrature Filters (CQF)