A realization method of cyclic filter banks

In recent years theories on filter banks (cyclic filter banks) in cyclic LTI systems have been proposed. Not only are cyclic filter banks that use cyclic convolution suitable for processes such as picture signals (finite signals), the design of cyclic filter banks is also limited to specific discrete frequency points. Consequently, there are advantages such as greater freedom of design compared to filter banks (noncyclic filter banks) in noncyclic LTI systems which use conventional linear convolution. Definite design methods have been given which realize a two-partition construction as a cyclic filter bank with linear phase characteristics and orthogonality at the same time not possible in conventional noncyclic filter banks up to the present. Other than this, there have been no discussions on multi-partition construction utilizing, for example, a modulated structure, methods that utilize various other advantages which can obtain a cyclic LTI system, or discussions on problems which can be solved by these. Based on this, we propose one method to achieve a cyclic filter bank in this paper. We propose a configuration that uses DFT modulation. To start with, we lead with polyphase expressions of cyclic filter banks that use DFT modulation and then present complete reconstruction conditions. We subsequently mention that the complete reconstruction conditions are given as a linear equation whose synthesized coefficients are unknown parameters by means of using a resolution given beforehand. Next, we examine the essential properties of a cyclic LTI system and then describe the advantages of this configuration method obtained by means of using these properties. Finally, we provide a design example of the proposed cyclic filter bank and show that a cyclic filter bank can be configured with DFT modulation. In addition, we mention the combined effects when dividing and synthesizing image signals based on applying this method to image compression applications.