Peak-Error-Constrained Sparse FIR Filter Design Using Iterative SOCP
Peak-Error-Constrained Sparse FIR Filter Design Using Iterative SOCP
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DOI：
10.1109/tsp.2012.2199316
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发表时间：
2012-08
影响因子：
5.4
通讯作者：
A. Jiang;H. Kwan;Yanping Zhu
中科院分区：
文献类型：
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作者：
A. Jiang;H. Kwan;Yanping Zhu
本文提出了一种新的稀疏FIR滤波器设计算法。众所周知，由于滤波系数向量在其目标函数中的-范数的存在，该设计问题是高度非凸的。为了解决这一困难，开发了一种迭代程序来搜索潜在的稀疏模式，然后使用该模式通过求解一个凸优化问题来计算最终解。在每个迭代步骤中，将原来的稀疏滤波器设计问题逐次转化为一个更简单的子问题。证明了在较弱的条件下，这些子问题的全局最优解可以通过求解它们的对偶问题来得到。在这种情况下，整个迭代过程收敛到原始设计问题的局部最优解。上述设计过程可以重复多次，以进一步提高设计结果的稀疏性。前一阶段的输出可以作为后续设计的起点。通过两组设计实例对该算法的性能进行了评估，并与其他稀疏FIR滤波器设计算法进行了比较。
In this paper, a novel algorithm is proposed to design sparse FIR filters. It is known that this design problem is highly nonconvex due to the existence of -norm of a filter coefficient vector in its objective function. To tackle this difficulty, an iterative procedure is developed to search a potential sparsity pattern, which is then used to compute the final solution by solving a convex optimization problem. In each iterative step, the original sparse filter design problem is successively transformed to a simpler subproblem. It can be proved that under a weak condition, globally optimal solutions of these subproblems can be attained by solving their dual problems. In this case, the overall iterative procedure converges to a locally optimal solution of the original design problem. The design procedure described above can be repeated for several times to further improve the sparsity of design results. The output of the previous stage can be used as the initial point of the subsequent design. The performance of the proposed algorithm is evaluated by two sets of design examples, and compared to other sparse FIR filter design algorithms.