Filter banks for time-recursive implementation of transforms

A generalized filter-bank structure is developed and used to implement an arbitrary transform in a time-recursive manner. It is based on the N×N basis matrix of the transform, and for the general case, has a complexity of O(N² ); however, its complexity reduces considerably, to approximately 4N-5N, for the case of trigonometric transforms such as the discrete Fourier, cosine, and sine transforms (DFT, DCT, and DST). Hardware complexity is similar to that of frequency sampling structures, but unlike them, the filter bank 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