【作者】 刘航；

【导师】 王开；

【作者基本信息】 东南大学 ， 信号与信息处理， 2017， 硕士

【摘要】 频率估计是现代数字信号处理的重要内容,广泛应用于军用雷达探测、生物设别、语音处理、地震监测等各个领域,受到众多学者的关注和重视,成为当下的研究热门,研究频率估计具有重要的理论意义和应用价值。本文围绕基于低复杂滤波器组的频率估计进行研究,开展了如下工作:本文首先研究了频率估计的数学模型,这是频率估计的理论基础,在此理论基础上的以DFT为例分析其用于频率估计产生频谱泄露问题,并对频率估计算法的性能作了研究,衡量指标主要包括估计偏差和均方误差(MSE),再从概率论的角度对参数估计的理论下限(CRB)进行了推导,给出了实信号和复信号二者的频率估计CRB,同等条件下复信号能够得到比实信号更为精准的频率估计效果,然后从最大似然估计的角度分别对实信号和复信号的频率估计算法进行了推导,二者等效于周期图方法。接着,研究了四种经典的频率估计算法,主要包括基于频域方法的Rife和SINE-ODD以及基于时域方法的Prony和SVD,其中还包括对Rife频率细分增加其DFT点数的RF-Rife算法和频移半根谱线增强抗噪性能的IRife算法,以及对SVD增加全局最小二乘的SVD-TLS算法。给出了上述算法的理论分析、公式推导和性能分析,单频信号频率估计中SINE-ODD在超过阈值信噪比后最能够逼近CRB,基于时域的SVD、SVD-TLS、Prony算法在多频信号频率估计中依然保持优良性能。然后,对多相结构的余弦调制滤波器组(CMFB)进行了研究,DCT调制比DFT调制的优势在于调制滤波器系数为实系数,可以有效减少运算量,同时CMFB的2M倍降采样可以使得系统运算量大大降低。对前人提出的三种低复杂度设计原型滤波器方法做了对比研究,主要包括基于FISTA迭代的系数稀疏法(CP)、基于SOCP的二次外插法(EIR)以及基于SOCP优化频罩法(FRM),对比CP-CMFB、EIR-CMFB、FRM-CMFB三种低复杂度滤波器组的各自对应结构和设计性能,从通带波纹、阻带衰减、过渡带带宽、设计参数个数和系统复杂度等做出了比较。最后,对基于低复杂滤波器组的频率估计做了综合研究,滤波器组能够运用于802.1 1ac的多载波通信和数字信道化,引入SDFT技术可以有效改善滤波器组通道输出信号信噪比恶化问题,基于此可以完成基于滤波器组的频率粗估计,确定信号频率的有效范围。对结合时域算法SVD、SVD-TLS、Prony和CMFB设计方法以及SDFT改进通过仿真给出性能分析,基于CMFB可以有效降低系统复杂度同时提高频率分辨率。结合低频和高频两种应用场景对本文提出的低复杂度滤波器组方法仿真实现,仿真结果表明本文采用的三种低复杂度方法可以较好的实现基于滤波器组的频率估计。更多还原

【Abstract】 Frequency estimation is an important part of modern digital signal processing.It is widely used in military radar detection,biological setting,voice processing,earthquake monitoring and other fields,which has attracted the attention of many scholars and become the most popular research.This paper focuses on the frequency estimation based on low complexity filter banks and the following work is carried out:Firstly,we study the mathematical model of frequency estimation,which is the theoretical basis of frequency estimation.On this basis,DFT is used to analyze the frequency spectrum estimation problem,and the performance of frequency estimation algorithm is studied.The measurement index mainly includes the estimation of deviation and mean square error(MSE),and then the theoretical lower limit(CRB)of the parameter estimation is deduced from the perspective of probability theory.The frequency estimation CRB of both the real signal and the complex signal is given.Under the same condition,the complex signal can obtain more accurate frequency estimation than the real signal.And then the frequency estimation algorithm of real signal and complex signal is deduced from the perspective of maximum likelihood estimation,which is equivalent to the periodic graph method.Secondly,four classical frequency estimation algorithms are studied,including Rife and SINE-ODD based on frequency domain method,and,Prony and SVD based on time domain method,which also includes RF-Rife for Rife frequency subdivision to increase its DFT points.And the IRife algorithm for frequency-enhanced anti-noise performance,and the SVD-TLS algorithm for increasing the globalleast squares of SVD.The theoretical analysis,formula derivation and performance analysis of the above algorithm are given.SINE-ODD in the frequency estimation of the single-frequency signal is most close to the CRB after exceeding the threshold SNR.Based on the time domain SVD,SVD-TLS,Prony algorithm in the multi-frequency signal frequency estimation still maintain excellent performance.Thirdly,the CMFB of the multiphase structure is studied.The advantage of DCT modulation over DFT modulation is that the modulation filter coefficients are real coefficients and can effectively reduce the amount of computation.At the same time,the 2M times sampling of CMFB can make the system greatly reducing the amount of computation.This paper presents a comparative study of three low-complexity prototyping filters proposed by predecessors,including CP based on FISTA iteration,secondary EIR based on SOCP,and FRM based on SOCP,the corresponding structure and design performance of the three low-complexity filter banks of CP-CMFB,EIR-CMFB and FRM-CMFB are compared,such as passband ripple,stopband attenuation,transition band bandwidth,design parameter number and system complexity.Last but not least,the frequency estimation based on low complexity filter banks is studied synthetically.The filter banks can be applied to multi-carrier communication and digital channelization of 802.11ac.The introduction of SDFT technique can effectively improve the SNR deterioration of the output signal of the filter bank channel.Based on this,the frequency coarse estimation based on the filter bank can be completed to determine the effective range of the signal frequency.Based on the CMFB which can effectively reduce the system complexity and improve the frequency resolution.Combining the application scenarios of low frequency and high frequency,this paper presents a low complexity filter group method simulation,The simulation results show that the three low complexity methods used in this paper can realize the frequency estimation based on filter banks in a good performance.更多还原