一种设计M通道双正交过采样图滤波器组的新算法

A Novel Method for Designing M-channel Biorthogonal Oversampled Graph Filter Banks

针对现有的M通道过采样图滤波器组整体性能较差的问题,该文提出一种过采样图滤波器组设计的新算法。在新算法中,分两步来设计图滤波器组。首先,从频谱特性方面考虑来设计分析滤波器,以分析滤波器的通带波纹和阻带能量为目标函数,以3 d B约束为约束条件,通过半正定规划求解出频谱选择性较好的分析滤波器;然后,从完全重构特性方面考虑来设计综合滤波器,以综合滤波器的阻带能量为目标函数,以完全重构条件为约束函数。上述两个约束优化问题都是半正定规划问题,都可有效地求解。新算法综合考虑了滤波器组的重构特性和频率特性,因此可以设计得到整体性能良好的M通道双正交过采样的图滤波器组。仿真对比表明,与已有的设计算法相比,新算法设计所得的图滤波器组具备更小的重构误差。

This paper presents an efficient algorithm to design M-channel oversampled graph filter banks with better overall performance. In the new algorithm, a two-step scheme is exploited to tackle the design task. Firstly, for controlling the spectral selectivity, the analysis filter is designed by solving a constraint optimization problem that minimizes the passband ripple and stopband energy subject to 3 dB constraint; secondly, by taking the Perfect Reconstruction （PR） condition into account, the design problem of synthesis filters is formulated into an optimization problem that minimizes the stopband energy subject to PR constraint. Both the optimization problems are Semi-Definite Programming （SDP）, which can be efficiently solved. Since the proposed method fully considerate the spectral characteristic and PR condition, M-channel biorthogonal oversampled graph filter banks with better performance can be obtained. Numerical examples and comparison show that compared with the existing methods, the proposed method can lead to graph filter banks with smaller reconstruction error.