Design of 2D linear phase DFT modulated filter banks using bi-iterative second-order cone program

In this paper, the recent bi-iterative second-order cone program (BI-SOCP) to design one-dimensional (1D) DFT modulated filter banks is extended to the 2D case to design two-dimensional (2D) linear phase nonseparable DFT modulated filter banks. Some essential properties of 2D DFT modulated filter banks are presented and a permissibility of the configuration of filter banks is given. The design problem is formulated into a non-convex optimization, which minimizes the maximal amplitude of the transfer function distortion and aliasing transfer functions of the filter bank subject to predefined bounds on the stopband energy, the transition-band energy, and a passband flatness measure of the prototype filters (PFs). The optimization problem is solved by the BI-SOCP algorithm, where 2D linear phase analysis and synthesis PFs are alternately optimized via second-order cone programs (SOCPs). Numerical examples are included to show that the BI-SOCP can yield 2D linear phase nonseparable DFT modulated filter banks with good overall performance.