Multi-channel filter banks associated with linear canonical transform

The linear canonical transform (LCT) has been shown to be a powerful tool for optics and signal processing. This paper investigates multi-channel filter banks associated with the LCT. First, the perfect reconstruction (PR) conditions are analyzed and design method of PR filter banks for the LCT is proposed, which demonstrates that the LCT based filter banks can inherit conventional design methods of filter banks in the Fourier domain. Then polyphase decompositions in the LCT domain are defined and polyphase realization of the LCT based filter banks is derived in terms of polyphase matrices. Furthermore, multi-channel cyclic filter banks associated with the LCT are proposed by defining circular convolution in the LCT domain. The PR design method and polyphase representation of cyclic filter banks for the LCT are derived similarly. Finally, simulations validate the proposed design methods of the LCT based filter banks and also demonstrate potential application of the LCT based cyclic filter banks in image subband decomposition.