Paraunitary filter banks form an interesting subset of perfect reconstruction (PR) filter banks. We saw above that we get a PR filter bank whenever the synthesis polyphase matrix times the analysis polyphase matrix is the identity matrix , i.e., when
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Paraconjugation is the generalization of the complex conjugate transpose operation from the unit circle to the entire plane. A paraunitary filter bank is therefore a generalization of an orthogonal filter bank. Recall that an orthogonal filter bank is one in which is an orthogonal (or unitary) matrix, to within a constant scale factor, and is its transpose (or Hermitian transpose).