Design of Two-dimensional Modified DFT Modulated Filter Banks Based on Lagrange Multiplier Method
ZHOU Fang①② SHUI Penglang① JIANG Junzheng③
①(National Laboratory of Radar Signal Processing, Xidian University, Xi’an 710071, China) ②(School of Life and Environmental Sciences, Guilin University of Electronic Technology, Guilin 541004, China) ③(School of Information and Communication, Guilin University of Electronic Technology, Guilin 541004, China)
Base on Lagrange multiplier method, an iterative algorithm is proposed to design the two-dimensional modified Discrete Fourier Transform (DFT) modulated filter bank. In each iteration, the design problem is described as a Quadratically Constrained Quadratic Program (QCQP). The Lagrange multiplier method is then employed to transform the constrained problem into an unconstrained one, the solution of which is obtained by solving a set of linear equations. By analyzing the coefficient matrix, block LU factorization is applied to considerably reduce the computational complexity. Numerical results and comparison with the existing methods demonstrate the improved performance of the proposed scheme, including the reconstruction error and stopband attenuation.
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