Research On High Performance Prototype Filter In Filter Bank System

Nowadays,the mobile communication network and services are developing rapidly.In order to meet the growing demand for images,video and other services,the multi-rate system and filter bank technology used for sub-band coding have been applied to the signal processing and communication systems of the fourth generation mobile communication system(4G)and the fifth generation mobile communication system(5G).The filter bank technology allocates the whole frequency band of signal into sub-bands and processes them respectively.The filter on each sub-band is the frequency domain shift of the same prototype filter,and the design of the filter bank is ultimately determined by the design of the prototype filter.At present,the prototype filter is designed based on infinite word length.But,when it is finally implemented on digital components stored in the form of finite-bit binary,the finite-length effect due to quantization may distort the filter's transmission performance.The output signal deviates from the expected value,making the designed prototype filter performance lower than expected.At present,relevant research of finite word length effect are mainly focusing on the infinite impulse response(IIR)filter.However the prototype filter in the filter bank system is the finite impulse response(FIR)filter.There is a lack of the research on this aspect,and therefore how to design a high performance FIR filter in resisting the finite word length effect is still a problem worth discussing.This paper studies the finite word length effect of FIR filter and the theoretical basis when is applied in the filter bank,which includes the following two aspects:1.The filter performance will get worse caused by the finite word length effect when the traditional shift operator is used with high-speed sampling.An optimal structure of FIR filter based on the forward-difference operator is proposed to solve the problem.By analyzing the source of roundoff noise,the modified Delta operator prevents node overflow effectively by introduced coupling parameters.First,the deduction on the expression of the roundoff noise gain and sensitivity are conducted using the polynomial parameterization method and the equivalent state space method respectively,which provide the necessary theoretical basis for the high-performance filter design by using the Delta operator.Then,compared with the existing finite word length optimization algorithms,the simulation example shows that the optimal structure has better performance in the roundoff noise gain and sensitivity.The deviation of the amplitude-frequency and phase-frequency response from the theoretical value based on the Delta operator is small when implementing with the finite word length register.The prototype filter based on the optimized structure with the forward difference operator has better finite word length properties.2.The designed high performance prototype filter is applied to the multichannel filter bank system,which needs its theoretical basis and the performance analysis of the system.There is different performance in Frequency domain for different discretization methods.In this paper,the reconstruction conditions of the multi-channel filter bank system based on the forward-difference operator are deduced corresponding to the classical filter bank theory.First,the basic components and the perfect reconstruction conditions of the filter bank are derived from the frequency domain using the traditional shift operator and the forward difference operator respectively.According to the theory of filter bank,the roundoff noise gain and sensitivity performance of the multi-channel filter bank based on the optimized structure are improved compared to the traditional system.The symbol error rate(SER)and peak to average power ratio(PAPR)are better than the system based on the traditional shift operator when the high performance filter is applied to the finite length filter bank system.The simulation results show that the new system has good performance in resisting finite word length.