一种降维空域滤波矩阵的设计方法

摘要

为解决降维滤波矩阵设计存在的维数与滤波性能之间的矛盾,提出了一种结合K-L变换(Karhunen-Loeve Transform)降维空域滤波矩阵的设计方法.该文首先推导出了滤波矩阵较大特征值的数量取决于滤波矩阵通带带宽的规律,并利用阻带衰减给出了区分大小特征值的门限,进而通过向大特征值对应的特征向量矩阵投影的方法,获得最终的降维空域滤波矩阵.仿真实验证明,由该方法获得的降维矩阵具有与降维前接近的空域滤波能力.%The performance of spatial filter matrix degrades sharply in the presence of matrix dimension reduction.To solve the problem,a method using K-L (Karhunen-Loeve) Trans-form to reduce the matrix dimension is proposed.Theoretical derivation show the eigenvalues of the spatial-filter matrix and its conjugate transpose matrix product,has two characteristics.Firstly,there exists some eigenvalues that are much greater than the other eigenvalues.Secondly,the number of greater eigenvalues depends on the bandwidth of filter matrix pass-band.Based on those characteristics,K-L Trans-form was used to realize matrix dimension reduction through abandoning the eigenvectors corresponding to small eigenvalues.The proposed reduction dimension filter matrix has the advantage of orthogonality.Simulation results show the proposed reduction matrix and matrix with maximum dimension have similar filter capability.