Research On Design Of A Special Type Of DFT Modulated Filter Banks

Multirate filter banks have been widely used in the coding, compression, recognition and transmission of image and speech signal. As a special kind of multirate filter banks, modulated filter banks have been paid more and more attention because of their simple designs. The complex modulated filter banks and cosine modulated filter banks are two main types of modulated filter banks. The complex modulated filter banks are also called Discrete Fourier Transform (DFT) modulated filter banks, which are easy in design due to that only one or two prototype filters (PFs) need to be designed.As a special class of DFT modulated filter banks, two-dimensional (2D) DFT modulated filter banks possess many good properties, for instance, good directional selectivity and frequency tiling, which are desired in image processing. In view of this point, we focus on the design of 2D DFT modulated filter banks in this paper. A class of 2D double-prototype DFT modulated filter banks with redundancy ratio two is constructed. By means of the polyphase decomposition of the PFs, the perfect-reconstruction (PR) condition for the filter bank is derived. With the condition, two algorithms are proposed to design the PFs. On one hand, a method based on the lifting structure is presented. The PR condition is parameterized as expressions with respect to lifting filters. The stopband energy of the PFs is minimized by optimizing the lifting filters. As a result, PR filter bank with fine frequency selectivity is obtained. On the other hand, an algorithm based on unconstrained optimization is given to design the 2D linear phase DFT modulated filter banks. The design problem is formulated as an unconstrained optimization with respect to the polyphase components of the PFs. Since the PFs are linear phase, their polyphase components are related, which simplifies the design problem. The numerical result suggests that the second algorithm is efficient. And the generated filter bank has very small reconstruction error and good frequency property, which basically meets the requirement of the practical applications.