关键词: 离散傅里叶变换, 调制滤波器组, 原型滤波器, 双迭代算法, 无约束优化

Abstract:

A design algorithm is proposed based on the bi-iterative scheme, due to the difficulty of designing the discrete Fourier transform (DFT) modulated filter bank. The design of the filter bank is formulated as an unconstrained optimization whose objective function is the weighted sum of the transfer distortion and the stopband energy of the prototype filters(PFs). Since the objective function is a bi-quadratic function of analysis and synthesis PFs, the optimization problem can be efficiently solved by using the bi-iterative scheme. At each iteration, one of the PFs is fixed and the other can be solved analytically. Numerical examples show that the computational cost of the proposed method is lower than that of the traditional method. Furthermore the transfer distortion of the filter bank obtained by the proposed method is approximately 16dB lower than that of the filter bank designed by the traditional method and the improvement on the reconstruction error is about 1dB.

Key words: discrete Fourier transform, modulated filter bank, prototype filter, bi-iterative method, unconstrained optimization