Paraunitary filter banks and wavelet packets

Binary tree-structured filter banks have been employed in the past to generate wavelet bases. The equivalence between binary paraunitary tree-structures and orthonormal wavelet bases is proven. It is known that a binary tree with paraunitary filters on each level generates a discrete time orthonormal wavelet basis. It is shown that every discrete-time orthonormal wavelet basis can be generated using paraunitary binary trees. Next, this analysis is extended to arbitrary tree structures such as those used for generating wavelet packets. It is shown that an arbitrary tree with paraunitary filers gives an orthonormal basis of wavelet packets. The strict converse is not true, but a weaker result is presented