Generalized and parallelized a Trous and Mallat algorithms to design non-uniform filter-banks

Due to the attractive properties of the wavelet transform, wavelet filter banks are frequently used in areas such as signal processing and communication systems. Furthermore, the increasing computational power of microprocessors leads to a leap in the use of techniques such as parallel processing, concurrent programming, and VHDL design. However, the inherently sequential tree structure of the traditional wavelet theory does not merge efficiently with the aforementioned techniques. This work presents an algorithm to generate uniform and non-uniform filter banks in a parallel structure. This algorithm generalizes the a Trous and Mallat algorithms for parallelized filter bank design, which is efficient for parallel processing, concurrent programming, and VHDL design. The algorithm generates a set of parallelized perfect-reconstruction filter banks for an arbitrary number of end-nodes of a traditional tree structure. The algorithm encompasses both the decimated and the undecimated cases. Examples of image and speech signal applications are presented.