摘要
传统的2维大规模滤波器组的设计方法具有复杂度高的缺点。该文提出一种设计2维双原型滤波器组的快速方法,该方法利用近似完全重构的条件,并采用完全过采样的离散傅里叶变换(DFT)调制滤波器组来设计。新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,其中目标函数为滤波器组的总体失真(传递失真和混叠失真)与原型滤波器阻带能量的加权和,利用目标函数的梯度向量,通过双迭代机制求解该优化问题。单步迭代中,利用矩阵求逆的等效条件和块Toeplitz矩阵求逆的快速算法,显著地降低了计算复杂度。理论分析和数值实验表明,新算法可以得到整体性能更好的滤波器组,计算复杂度大幅度降低,故可以快速设计大规模的2维滤波器组。
Traditional design methods of two-dimensional large-scale filter banks suffer from high-complexity. This paper presents an algorithm to design two-dimensional double-prototype fully oversampled Discrete Fourier Transform （DFT） modulated filter bank with Nearly Perfect Reconstruction （NPR）. The algorithm is based on bi-iterative scheme, where the design issue is formulated into an unconstrained optimization issue whose objective function is the weighted sum of the transfer distortion and the aliasing distortion of the filter bank, and the stopband energy of the Prototype Filters （PFs）. By exploiting the gradient information, the optimization problem can be efficiently solved by utilizing the bi-iterative scheme. The matrix inverse identity and the fast algorithm for Toeplitz-block Toeplitz matrix inversion are employed to dramatically reduce the computational cost of the iterative procedure. The theoretical analysis and numerical experiments are carried out to show that compared with the existing methods, the new algorithm possesses much lower computational cost and can be used to design large-scale two-dimensional filter bank with better overall performance.
出处
《电子与信息学报》
EI
CSCD
北大核心
2016年第11期2753-2759,共7页
Journal of Electronics & Information Technology
基金
国家自然科学基金(61261032
61371186)
广西区自然科学基金(2013GXNSFBA019264)
关键词
2维离散傅里叶变换
无约束优化
完全过采样
块Toeplitz矩阵求逆
双迭代算法
Two-dimensional Discrete Fourier Transform （DFT）
Unconstrained optimization
Fully oversampled
Toeplitz-block Toeplitz matrix inversion
Bi-iterative scheme
