【作者】 张博；

【导师】 黄翔东；

【作者基本信息】 天津大学 ， 信息与通信工程， 2018， 硕士

【摘要】 可变分数时延(VFD,Variable Fractional Delay)技术因其灵活可变的分数时延值,在采样率转换、软件无线电、滤波器设计、雷达、图像插值、阵列信号处理和语音处理等场合中获得广泛应用。在可变分数时延滤波器设计领域最经典的滤波结构便是Farrow结构,Farrow滤波结构一旦选定,其子滤波器系数的配置便成为了核心问题。因而设计出能保证整体VFD滤波器具备优良传输性能的快速滤波器系数配置方法是急需解决的问题。本文基于全相位FIR滤波器设计法,提出了一种为Farrow结构快速配置子滤波器系数的方法,所做的主要工作就是寻求其在传输性能和设计效率两方面的统一。将全相位滤波器系数以公式化的形式解析表示是实现Farrow结构子滤波器系数快速配置的有效途径。为此,本文在消化吸收现有全相位相关文献的基础上,对全相位数字滤波器的理论属性进行深入的挖掘与探索,利用循环移位形成一种新的基于自然优化的FIR滤波器高效设计法,在该方法中不涉及任何的迭代和矩阵求逆操作。进一步在循环移位图的基础上,归纳得到了全相位滤波器的三步设计方法、推导出了相应的全相位数字滤波器的解析公式,为滤波器的高效设计、快速配置、工程应用提供了技术支撑。在全面分析全相位数字滤波器理论属性及设计方法的基础上,本文将全相位数字滤波器的解析设计、三次样条插值和泰勒级数展开这三种技术进行有机结合,推导得到一种系数快速配置程序,实现了分数时延和截止频率的同时可调。接着,分别推导出了两种不同时延状况下可变分数时延滤波器Farrow结构子滤波器系数的解析配置公式。在今后的设计中,只需要将相应的设计参数(如分数时延、滤波器长度、截止频率等)代入解析配置公式便可以立即计算得到我们所需要的子滤波器系数,从而实现了可变分数时延滤波器的高效、解析设计。最后,本文对设计得到的可变分数时延滤波器的复杂度及性能展开具体的分析,并通过一系列的实验仿真观察其幅频及相位特性曲线,将其与同步可变的WLS设计方法在时延误差及时间复杂度方面进行比较,可以得出结论:本方法是一种适用于设计具有中、低截止频率的可变分数时延滤波器的高效解析设计法。更多还原

【Abstract】 The variable fractional delay technique has been widely used in a lot of fields such as sampling rate conversion,filter design,radar,multi-carrier communication,software radio,Image interpolation,array signal processing,speech processing and so on,since it has flexible fractional delay value.The most classical filtering structure in the design of variable fractional delay filters is Farrow structure.Once the Farrow structure is selected,the subfilter’s coefficients configuration will become the key problem.Therefore,it is an urgent task to develop an efficient coefficient configurating method that can ensure an excellent transfer characteristic of the variable fractional delay filter.This paper will introduce the all-phase filter design method to implement the subfilter’s coefficients configuration of the Farrow structure.The main work focus on enhancing both filter’s transfer characteristics and design efficiency.The coefficients’ closed-form formula of the all-phase FIR filter provides a straightforward and effective way of fast subfilter’s coefficients configuration of the Farrow structure.Based on the absorption of the existing literatures,this paper deeply explored the theoretical and property of the all-phase digital filter.Further,a new efficient design method for FIR filters is proposed.This method is based on the natural optimization,and it doesn’t involved any iteration or matrix inversion operations,so the computational complexity and hardware cost is very low.What’s more,the method uses cyclic-shift technique,on the basis of cyclic shift graph,a novel three-steps design method is summarized,then the corresponding closed-form formula of all-phase FIR filter can be derived,which provides a technical support for the filter’s efficient design,fast coefficients configuration and engineering application.Based on the full analysis of theoretical properties and design methods of all-phase FIR digital filters,the all-phase FIR filter analysis design,the cubic spline interpolation and the Taylor series expansion technology are organic combined in this paper,thereby deriving a fast configuration procedure for all tap coefficients in the Farrow structure.Meanwhile,both the fractional delay and the cutoff frequency can be flexibly adjusted by this procedure.Then analytical expressions for the sub filter’s coefficients of Farrow structure under two different delay conditions are derived respectively.In the future design,once the corresponding parameters(such as fractional delay,filter length,cutoff frequency,etc.)are substituted into the analytic configuration formula,the required sub filter’s coefficients can be immediately calculated.Hence,the design of variable fractional delay filter can be realized in a efficient and analytical way.Finally,the computational complexity and transmission performance of the variable fractional delay filter are analyzed in this paper,both the amplitude-frequency curve and phase characteristic curve can be directly observed by a series of experimental simulation.Compared the delay error and time complexity of our proposed design with the simultaneously variable WLS design,It can be concluded that our proposed design is an efficient closed-form design method for designing variable fractional delay filters with medium or low cut-off frequencies.更多还原