WLS Design of Sparse FIR Digital Filters
WLS Design of Sparse FIR Digital Filters
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DOI：
10.1109/tcsi.2012.2215742
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
A. Jiang;H. Kwan
中科院分区：
文献类型：
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作者：
A. Jiang;H. Kwan
本文提出了一种稀疏有限冲激响应（FIR）滤波器设计的新算法。本文考虑的稀疏数字滤波器设计问题的目标是减少非零值滤波器系数的数量，受到加权最小二乘（WLS）逼近误差约束施加在频域上。所提出的设计方法的灵感来自迭代收缩/阈值（IST）算法，这是用于稀疏和冗余表示的信号。所提出的设计算法的基本思想是连续的原始非凸问题转化为一系列的约束子问题在一个更简单的形式。尽管他们的非凸性，这些子问题可以有效地和可靠地解决在每一个迭代步骤，本文开发的数值方法。此外，它可以证明，所获得的解决方案基本上是最优的各自的子问题。由于其主要部分只涉及标量运算，所提出的算法是计算效率。本文给出了三组数值例子来说明所提出的设计算法的有效性。
In this paper, we propose a novel algorithm for sparse finite impulse response (FIR) filter designs. The objective of the sparse digital filter design problem considered in this paper is to reduce the number of nonzero-valued filter coefficients, subject to a weighted least-squares (WLS) approximation error constraint imposed on the frequency domain. The proposed design method is inspired by the iterative shrinkage/thresholding (IST) algorithms, which are used in sparse and redundant representation for signals. The basic idea of the proposed design algorithm is to successively transform the original nonconvex problem to a series of constrained subproblems in a simpler form. Despite of their nonconvexity, these subproblems can be efficiently and reliably solved in each iterative step by a numerical approach developed in this paper. Furthermore, it can be demonstrated that the obtained solutions are essentially optimal to their respective subproblems. Since its major part only involves scalar operations, the proposed algorithm is computationally efficient. Three sets of numerical examples are presented in this paper to illustrate the effectiveness of the proposed design algorithm.