Abstract: 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.

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-McClellan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。