The Theory Of Frequency Estimation Based On Low Complexity Filter Bank

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.