The Design of Multistage Separable Planar Filters
The Design of Multistage Separable Planar Filters
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DOI：
10.1109/tge.1971.271457
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发表时间：
1971
影响因子：
8.2
通讯作者：
S. Treitel;J. Shanks
中科院分区：
文献类型：
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作者：
S. Treitel;J. Shanks
二维或平面数字滤波器可以根据其平面响应函数来描述，其形式为加权系数矩阵或滤波器阵列。在许多情况下，这些矩阵的维度如此之大，以至于它们作为普通平面卷积滤波器的实现在计算上变得效率低下。可以将给定的系数矩阵展开为有限且收敛的矩阵值级和。每一级可以无误差地分离成m长度的列向量乘以n长行向量的乘积，其中m是原始滤波器阵列的行数，n是原始滤波器阵列的列数。如果给定的滤光器阵列可以通过扩展的前几个阶段以可容忍的小误差表示，则计算机存储和速度方面的显著节省。由于每个组成阶段由两个向量值因子组成，如果由这些向量描述的一维序列又被一维递归滤波近似，则会产生更多的计算经济。选择了两个地球物理实例来说明如何将目前的设计技术简化为实践。
A two-dimensional, or planar, digital filter can be described in terms of its planar response function, which is in the form of a matrix of weighting coefficients, or filter array. In many instances the dimensions of these matrices are so large that their implementation as ordinary planar convolutional filters becomes computationally inefficient. It is possible to expand the given coefficient matrix into a finite and convergent sum of matrix-valued stages. Each stage can be separated with no error into the product of an m-length column vector multiplied into an n-length row vector, where m is the number of rows and n is the number of columns of the original filter array. Substantial savings in computer storage and speed result if the given filter array can be represented with a tolerably small error by the first few stages of the expansion. Since each constituent stage consists of two vector-valued factors, further computational economies accrue if the one-dimensional sequences described by these vectors are in turn approximated by one-dimensional recursive filters. Two geophysical examples have been selected to illustrate how the present design techniques may be reduced to practice.