稀疏FIR滤波器设计算法的研究

发布时间：2018-10-13 10:00

【摘要】：FIR数字滤波器因其非递归型结构具有内禀稳定性并且在其具体设计中容易实现线性相位,所以在现代通信和信号处理过程中经常使用。然而,若要设计一个性能较好的FIR滤波器,往往需要较高的滤波器阶数,较高的滤波器阶数则意味着较高的设计复杂度以及较大的运算量。在具体硬件电路实现时,如果FIR滤波器阶数较高,则需要较多的存储单元和运算单元,这会导致在实现过程中功耗大、成本高、效率低等一系列问题。本文主要通过研究稀疏FIR滤波器设计算法来解决上述存在的问题。稀疏FIR滤波器设计旨在通过一定的优化设计算法,在满足约束条件的情况下,尽可能减少非零值滤波器系数的数目。稀疏FIR滤波器设计问题可以用满足一定约束条件的最小0范数模型进行描述。最小0范数问题是一个不易求解的NP-hard问题。在对数字滤波器及其设计的基本概念,以及压缩采样中的稀疏重构算法等进行简要介绍之后,本文对稀疏FIR滤波器的设计算法进行了研究,主要工作如下:(1)基于迭代重加权最小1范数算法和二分搜索法,提出一种线性相位稀疏FIR滤波器设计算法。首先用迭代重加权最小1范数算法设计一个滤波器,其滤波器系数中可能包含多个零值或接近零值的滤波器系数。然后在满足幅值响应约束条件下用二分搜索法查找哪些较小的非零值滤波器系数可以被强制为零。(2)在实际应用中,FIR滤波器可能并不需要具有严格线性相位,只要求满足近似线性相位即可。又因为在滤波器阶数和幅值误差相同时,近似线性相位条件下设计的滤波器系数比线性相位条件下设计的滤波器系数更稀疏。因此,本文提出一种频率响应误差约束下近似线性相位稀疏FIR滤波器设计算法。(3)频率响应误差约束下近似稀疏FIR滤波器设计算法设计的滤波器,其相位误差可能偏大。为了解决此问题,本文又提出一种可以分别对滤波器幅值误差和相位误差进行控制的近似线性相位稀疏FIR滤波器设计算法。
[Abstract]:FIR digital filter is often used in modern communication and signal processing because of its intrinsic stability and easy to realize linear phase in its specific design. However, in order to design a FIR filter with better performance, a higher filter order is often required, and a higher filter order means a higher design complexity and a large amount of computation. If the order of FIR filter is high, more memory cells and operation units are needed, which will lead to a series of problems, such as high power consumption, high cost, low efficiency and so on. In this paper, we study the sparse FIR filter design algorithm to solve the above problems. Sparse FIR filter design is designed to reduce the number of non-zero filter coefficients as much as possible under the condition of satisfying the constraint conditions through a certain optimal design algorithm. The sparse FIR filter design problem can be described by a minimum 0-norm model satisfying certain constraints. The minimum 0 norm problem is a difficult NP-hard problem. After a brief introduction of the basic concept of digital filter and its design, and the sparse reconstruction algorithm in compressed sampling, the design algorithm of sparse FIR filter is studied in this paper. The main work is as follows: (1) based on iterative reweighted minimum 1-norm algorithm and binary search algorithm, a linear phase sparse FIR filter design algorithm is proposed. First, a filter is designed using iterative reweighted minimum 1-norm algorithm, whose filter coefficients may contain multiple zero values or near zero values. Then the binary search method is used to find out which non-zero filter coefficients can be forced to zero under the constraint of amplitude response. (2) in practical applications, the FIR filter may not need to have a strict linear phase. Only approximate linear phase is required. Moreover, when the order and amplitude error of the filter are the same, the filter coefficients designed under the condition of approximate linear phase are more sparse than those designed under the condition of linear phase. Therefore, an approximate linear phase sparse FIR filter design algorithm with frequency response error constraints is proposed. (3) the phase error of the approximate sparse FIR filter design algorithm with frequency response error constraints may be too large. In order to solve this problem, an approximate linear phase sparse FIR filter design algorithm is proposed, which can control the filter amplitude error and phase error respectively.
【学位授予单位】：杭州电子科技大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：TN713

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