CAJ | 학술논문

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。
침대대규모적리산부리협변환(DFT)조제려파기조설계산법복잡도고적문제，해문제출일충기우무약속우화적쾌속설계산법。해산법장량개원형려파기적설계문제귀결위일개무약속우화문제，장려파기조적전체실진，혼첩실진이급원형려파기조대능량적가권화작위목표함수。진이，채용쌍질대궤제래구해해우화문제。재단보질대중，운용구진구역적등효조건화Toeplitz구진구역적쾌속산법，현저지강저료질대적계산대개。방진대비표명，여이유적설계산법상비，신산법계산대개저，가이득도정체성능경호적려파기조，병차가이쾌속설계대규모적려파기조。
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.