中文摘要：

针对大规模的离散傅里叶变换（DFT）调制滤波器组设计算法复杂度高的问题，该文提出一种基于无约束优化的快速设计算法。该算法将两个原型滤波器的设计问题归结为一个无约束优化问题，将滤波器组的传递失真，混叠失真以及原型滤波器阻带能量的加权和作为目标函数。进而，采用双迭代机制来求解该优化问题。在单步迭代中，运用矩阵求逆的等效条件和Toeplitz矩阵求逆的快速算法，显著地降低了迭代的计算代价。仿真对比表明，与已有的设计算法相比，新算法计算代价低，可以得到整体性能更好的滤波器组，并且可以快速设计大规模的滤波器组。

英文摘要：

This paper presents an efficient algorithm to design high-complexity Discrete Fourier Transform （DFT） modulated filter bank with double-prototype. The algorithm is based on unconstrained optimization, where the design problem is formulated into an unconstrained optimization problem, whose objective function is the weighted sum of the transfer distortion, the aliasing distortion of the filter bank, and the stopband energy of the Prototype Filters （PFs）. The optimization problem can be efficiently solved by utilizing the bi-iterative scheme. The matrix inverse identity and the fast algorithm for Toeplitz matrix inversion are employed to dramatically reduce the computational cost of the iterative procedure. Numerical examples and compared tests to show that compared with the existing methods, the proposed method possesses much lower computational cost and can be used to design large-scale filter bank with better overall performance.