Design of linear-phase variable 2-D digital filters using matrix-array decomposition
Design of linear-phase variable 2-D digital filters using matrix-array decomposition
复制标题
使用矩阵阵列分解设计线性相位可变二维数字滤波器
DOI：
10.1109/tcsii.2003.812913
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发表时间：
2003
期刊：
影响因子：
--
通讯作者：
T. Deng
中科院分区：
文献类型：
--
作者：
T. Deng
提出了一种基于实值多维阵列矩阵-阵列分解的线性相位可变二维数字滤波器设计方法。利用该方法，可以将期望的变幅度二维响应分解为普通零相位常数二维滤波器的实值频响指标和多维多项式的近似指标。因此，近似期望的可变二维幅度响应问题可以分解为涉及零相位常数二维滤波器设计和多维多项式近似的子问题。一旦获得零相位常数二维滤波器和多维多项式，将它们互连就得到了零相位变量二维数字滤波器。最后，通过移动滤波器系数，简单地将零相位常数二维滤波器（非因果）修改为线性相位滤波器（因果），可以很容易地获得线性相位变量二维数字滤波器。由于子问题比直接逼近给定的可变二维量级规范要容易得多，因此这种基于mad的设计方法非常有效和直接。在设计零相位常数二维滤波器和逼近多维多项式时，我们还提出了一种新的客观准则来选择合适的滤波器阶数和多项式度。此外，我们还证明了所得到的线性相位可变二维滤波器具有高度并行结构和模块化，适用于高速多维信号处理。给出了两个数值算例，验证了基于mad的设计方法的有效性。
A novel approach for designing linear-phase variable two-dimensional (2-D) digital filters is described, which is based on the matrix-array decomposition (MAD) of real-valued multidimensional arrays. By using the MAD, the desired variable 2-D magnitude response can be decomposed into the real-valued frequency response specifications of the normal zero-phase constant 2-D filters and the approximation specifications of multidimensional polynomials. Consequently, the problem of approximating the desired variable 2-D magnitude response can be decomposed into sub-problems that involve the design of zero-phase constant 2-D filters and the approximation of multidimensional polynomials. Once the zero-phase constant 2-D filters and the multidimensional polynomials are obtained, interconnecting them yields a zero-phase variable 2-D digital filter. Finally, a linear-phase variable 2-D digital filter can be easily obtained by simply modifying the zero-phase constant 2-D filters (noncausal) to linear-phase ones (causal) through shifting the filter coefficients. Since the sub-problems are much easier to solve than the direct approximation of the given variable 2-D magnitude specification, this MAD-based design approach is extremely efficient and straightforward. In designing zero-phase constant 2-D filters and approximating multidimensional polynomials, we also propose a new objective criterion for selecting appropriate filter orders and polynomial degrees. Furthermore, we also show that the resulting linear-phase variable 2-D filters have highly parallel structures and modularity, which are suitable for high-speed multidimensional signal processing. Two numerical examples are given to demonstrate the effectiveness of the MAD-based design approach.