数字滤波器参数化设计与高效实现研究

发布时间：2018-08-20 20:24

【摘要】：数字信号处理作为一个科学与工程交叉的学科,是现代科技发展最重要的基石之一,已经被广泛应用于科学研究和生产实践的各个领域。作为数字信号处理系统的核心部分之一:数字滤波器,其设计与实现方法一直是该学科重要的研究领域。基于系统的状态空间理论,对于一个给定传输函数的数字滤波器,存在着许多种等价的实现结构。数字滤波器的无限精度设计注重找到可行解的效率和系统的稳定性;有限精度设计还要进一步考虑实现结构的低复杂度和减少有限字长(finite word length-FWL)效应。另一方面,数字滤波器可以用两种方法实现,当采用计算机软件实现时,特别注重算法的高吞吐率;当采用专用或通用集成电路等硬件方法实现时,则更注重综合结果的高速率和低成本。本文以如何提高数字系统性能为背景,基于系统结构理论研究数字滤波器的参数化设计方法与高效实现问题,主要工作和成果如下:1.基基于JSS结结构的IIR数数字滤波器参数化方法:设计无限冲激响应(infinite impulse response-IIR)数字滤波器的代价函数一般是高度非线性的,而且还与滤波器的稳定性有关。由于模拟滤波器的JSS结构对于一个N阶滤波器,只含有2N+1个参数,且具有l2-scaling特性,本文基于JSS结构和广义双线性变换,提出一种设计IIR滤波器的参数化方法,该方法是完备和紧凸的,具有较好的收敛性能,同时优化模型建立为成熟的无约束非线性规划问题。该方法能更高效地设计稳定的IIR滤波器,且通带波动、阻带衰减、群迟延等性能更好。2.基基于遗传算法的格型结构参数离散化设计:分子注入式和分子抽头式相结合的格型滤波器结构具有自由度,可以对节点信号功率比等FWL性能进行优化,且该结构只有2N+1个乘法器,参数灵敏度很低,特别适用于IIR滤波器离散化设计。但传统的梯度优化方法已经不再适用,且参数的搜索空间较大,穷举法也并非为有效方法。本文利用基于格雷码的遗传算法解决该非线性优化问题,在滤波器低阶时采用全局优化,高阶时采用分步优化,有效解决了IIR滤波器参数离散化问题中效率和性能的矛盾,有利于IIR滤波器的实用化。3.并并行计算的全通数字滤波器结构:输入平衡实现具有低参数敏感度和很小的舍入噪声增益。基于一类输入平衡海森伯格实现和归一化格型结构,提出两类并行计算的全通数字滤波器结构。基于状态空间分析方法论述并行处理原理,并推导了舍入噪声增益的表达式,对于一个N阶全通滤波器,其舍入噪声增益仅为4N。所提结构由于具备并行处理能力,更加适合低复杂度高吞吐率的数字系统实现。4.基基于集成电路的低成本FIR数数字滤波器实现:子项空间技术利用有限冲激响应(finite impulse response-FIR)数字滤波器系数之间的子项共享可以有效减少实现时加法器的个数;外推补偿技术利用FIR滤波器冲激响应的准周期特性可以有效降低多常系数乘法的复杂度。基于这两种技术,利用硬件描述语言编程在集成电路上对FIR滤波器进行了实现,并结合集成电路综合特点,通过硬件结构的改进得到高速率低成本FIR滤波器的实现方法,有利于进一步推动FIR滤波器的实用化。
[Abstract]:As an interdisciplinary subject of science and engineering, digital signal processing is one of the most important cornerstones of the development of modern science and technology, and has been widely used in various fields of scientific research and production practice. Fields. Based on the state space theory of systems, there are many equivalent implementation structures for a digital filter with a given transfer function. Infinite precision design of digital filters focuses on the efficiency of finding feasible solutions and the stability of the system. Finite precision design also considers the low complexity and the limited reduction of the implementation structure. On the other hand, digital filters can be implemented in two ways, with special emphasis on the high throughput of algorithms when implemented by computer software, and with more emphasis on the high speed and low cost of synthesis results when implemented by hardware methods such as special purpose or general purpose integrated circuits. The main work and achievements are as follows: 1. Based on the JSS junction structure, the IIR number digital filter parameterization method: The cost function of designing infinite impulse response-IIR digital filter is generally used. Because the JSS structure of an analog filter contains only 2N+1 parameters for a N-order filter and has l2-scaling property, a parametric method for designing IIR filters is proposed based on the JSS structure and generalized bilinear transform. The method is complete, compact and convex, and has the property of l2-scaling. This method can design stable IIR filters more efficiently, and has better performances such as passband fluctuation, stopband attenuation, group delay and so on. 2. Based on genetic algorithm, the discrete design of lattice structure parameters: the combination of molecular injection and molecular tapping The lattice filter structure has the degree of freedom and can optimize the FWL performance such as node signal power ratio. The structure has only 2N+1 multiplier, and the parameter sensitivity is very low. It is especially suitable for the discrete design of IIR filter. In this paper, the genetic algorithm based on Gray code is used to solve the nonlinear optimization problem. The global optimization is used in the low-order filter, and the step-by-step optimization is used in the high-order filter. The contradiction between efficiency and performance in the discretization of IIR filter parameters is effectively solved, which is conducive to the practicality of IIR filter. 3. All-pass digital filter with parallel computation is used. Structure: Input balancing implements low parametric sensitivity and low rounding noise gain. Based on a class of Heisenberg implementations and normalized lattice structures, two types of all-pass digital filters for parallel computation are proposed. Parallel processing principle is discussed based on state space analysis method, and rounding noise gain expression is derived. For a N-order all-pass filter, the rounding noise gain is only 4N. The proposed architecture is more suitable for low-complexity and high-throughput digital systems because of its parallel processing capability. 4. Low-cost FIR digital filter implementation based on integrated circuits: subspace technology uses finite impulse response-FI R) Subitem sharing among the coefficients of digital filters can effectively reduce the number of adders for implementation; extrapolation compensation technique can effectively reduce the complexity of multiplication of multiple constant coefficients by utilizing the quasi-periodic characteristics of impulse response of FIR filters. Based on these two techniques, FIR filters are programmed on integrated circuits using hardware description language. Combining with the integrated circuit characteristics, the implementation method of high-speed and low-cost FIR filter is obtained by improving the hardware structure, which is helpful to further promote the practicality of FIR filter.
【学位授予单位】：浙江工业大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TN713.7

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