中文摘要：

二维滤波器组通常用于图像处理中,而图像子带编码希望滤波器组同时也具有线性相位（LP）特性。提出了一种基于一类新余弦调制系统的二维线性相位-近似完全重构（LP-NPR）滤波器组的设计方法,设计过程分为两个步骤：首先采用Parks-Mc-Clellan算法来计原型滤波器,再经过余弦调制能到一系列的线性相位分析和综合滤波器,从而可以构造一维LP-NPR滤波器组;然后利用树状结构来结合两个一维LP-NPR滤波器组,并运用单位模变换,可以得到二维不可分离LP-NPR滤波器组。实验结果表明此方法是可行的,所设计的滤波器组可达到令人满意的重构精度。

英文摘要：

Two dimensional filter banks are usually applied to image processing.Linear Phase （LP） property of filter banks is also desired in sub-band image coding.In this paper,a design method of two dimensional Linear Phase Nearly Perfect Reconstruction （LP-NPR） filter banks based on a new class of cosine modulation systems is presented,which can be described as follow： firstly,the Parks-McClellan algorithm is adopted for designing the prototype filter,then by employing cosine modulation,a series of analysis and synthesis filters can be obtained,accordingly a one-dimensional LP-NPR filter banks can be constructed;Secondly, cascading two one-dimensional LP-NPR filter banks in the form of tree structure and using the unimodular transformation,a two dimensional nonseparable LP-NPR filter banks can be obtained.Experimental results indicate the proposed method is feasible,and the designed filter banks can obtain the satisfying reconstructive precision.