Filter Banks for Time-Recursive Implementation of Transforms

A generalized filter-bank structure is developed, to implement an arbitrary transform in a time-recursive manner. It is based on the NxN basis matrix of the transform, and for the general case, has a complexity of O(N 2); however, its complexity reduces considerably, to approximately 47V - 57V, for the case of trigonometric transforms such as the DFT, DCT, and DST. As far as hardware complexity is concerned, it is similar to frequency sampling structures, but unlike them, it has much better behavior under finite precision arithmetic; it remains stable under coefficient truncation, and also does not sustain limit cycles if magnitude truncation is applied. The linear complexity, modularity, and good finite precision behavior of the structure make it extremely suitable for implementation using VLSI circuits or digital signal processors. © 1993 IEEE