characterization it follows that the filters H1(z) and G1(z) are completely specified by H0(z) and G0(z), respectively. Therefore, we need to design H0(x) and G0(z) which have desired frequency responses and satisfy the polyphase-domain conditions. There are different mapping technique that can be used to get above result. Filter-bank design in the frequency domain When perfect reconstruction is not needed, the design problem can be simplified by working in frequency domain instead of using FIR filters. Note that the frequency domain method is not limited to the design of nonsubsampled filter banks (read ). Direct frequency-domain optimization Many of the existing methods for designing 2-channel filter banks are based on transformation of variable technique. For example, McClellan transform can be used to design 1-D 2-channel filter banks. Though the 2-D filter banks have many similar properties with the 1-D prototype, but it is difficult to extend to more than 2-channel cases. In Nguyen, the authors talk about the design of multidimensional filter banks by direct optimization in the frequency domain. The method proposed here is mainly focused on the M-channel 2D filter banks design. The method is flexible towards frequency support configurations. 2D filter banks designed by optimization in the frequency domain has been used in Wei and Lu. In Nguyen's paper, the proposed method is not limited to two-channel 2D filter banks design; the approach is generalized to M-channel filter banks with any critical subsampling matrix. According to the implementation in the paper, it can be used to achieve up to 8-channel 2D filter banks design. (6)Reverse Jacket Matrix In Lee's 1999 paper, the authors talk about the multidimensional filter bank design using a reverse jacket matrix. Let H be a Hadamard matrix of order n, the transpose of H is closely related to its inverse. The correct formula is: , where In is the n×n identity matrix and HT is the transpose of H. In the 1999 paper, the authors generalize the reverse jacket matrix [RJ]N using Hadamard matrices and weighted Hadamard matrices. In this paper, the authors proposed that the FIR filter with 128 taps be used as a basic filter, and decimation factor is computed for RJ matrices. They did simulations based on different parameters and achieve a good quality performances in low decimation factor. Directional filter banks Bamberger and Smith proposed a 2D directional filter bank (DFB). The DFB is efficiently implemented via an l-level