Set of Perfect Reconstruction Non-uniform Filter Banks via a Tree Structure

In this paper, we propose a novel method to test if a non-uniform filter bank can achieve perfect reconstruction via a tree structure. The set of decimators is first sorted in an ascending order. A non-uniform filter bank can achieve perfect reconstruction via a tree structure if and only if some or all of the channels corresponding to the maximum decimation ratio can be grouped into one channel, and the procedure can be repeated until all the channels are grouped together.

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