A New Separable Two-dimensional Finite Impulse Response Filter Design With Sparse Coefficients
A New Separable Two-dimensional Finite Impulse Response Filter Design With Sparse Coefficients
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DOI：
10.1109/tcsi.2015.2486079
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发表时间：
2015-10
期刊：
影响因子：
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通讯作者：
Hao Wang
中科院分区：
文献类型：
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作者：
Hao Wang
可分离二维有限冲激响应滤波器可以降低传统二维有限冲激响应滤波器的实现复杂度。提出了一种新的可分离二维FIR滤波器设计方法。所提出的设计处理的原型2-D FIR滤波器系数矩阵的子矩阵，其中包含的所有信息的滤波器系数矩阵。它的基本思想是利用子矩阵本身的列向量来分解子矩阵。在所提出的滤波器中存在零值和/或一值系数。在滤波器实现中，这些零值系数不需要乘法器或加法器。而且，这些单值系数不需要乘法器。此外，一般可分离的2-D FIR滤波器的最小-最大意义上的频域最小二乘意义上的最优设计提供了一个统一的框架，为第一次。最后，通过与其他可分离结构二维FIR滤波器设计的比较，以及与其他非可分离结构低复杂度二维FIR滤波器设计的比较，验证了该方法的优越性。
The separable two-dimensional (2-D) finite impulse response (FIR) filter can be utilized to decrease the implementation complexity of the traditional 2-D FIR filter. A novel separable 2-D FIR filter design is proposed in this paper. The proposed design deals with a submatrix of the prototype 2-D FIR filter coefficient matrix, which contains all the information of the filter coefficient matrix. And, its basic idea is to try to utilize some column vectors of the submatrix itself to decompose this submatrix. There are zero-valued and/or one-valued coefficients in the proposed filter. In the filter implementation, these zero-valued coefficients do not require multipliers or adders. And, these one-valued coefficients do not require multipliers. Additionally, an optimal design of the general separable 2-D FIR filter in the mini-max sense and the least-square sense in the frequency domain is provided in a uniform framework, for the first time. Finally, the experimental comparison of the proposed separable 2-D FIR filter design with other separable 2-D FIR filter designs, and the comparison with other non-separable-structure low-complexity 2-D FIR filter designs are provided to validate the superiority of the proposed method.