Research And Application Of Low Complexity Finite Impulse Response Filter Design Method

The performance of a finite impulse response(FIR)digital filter can be measured by the two indicators of the bandwidth of the transition band and the attenuation of the pass band and stop band.Since the implementation complexity of direct form FIR filters is inversely proportional to the transition bandwidth,high-performance FIR filtering requires extremely high implementation complexity.There are some typical low-complexity filter structures including interpolated finite impulse response(IFIR)filter,frequency response masking(FRM)filter,and extrapolated impulse response(EIR)filter.Based on these kind of low-complexity filter structures,FIR filter with extremely narrow transition band can be implemented with few multiplier resources.This paper focuses on the research on low-complexity filter structure,starting with extrapolated impulse response filter,and coefficients solution method in filter designing.The main work is as follows:1.The structure of extrapolated impulse response(EIR)filter is researched.By limiting the main lobe parameter M and introducing odd-even component decomposition on the basic side lobe,the transfer function of EIR filter is transformed into a Parallel structure consist of a direct FIR filter and two interpolated impulse response filters.The problem of solving the coefficients of the EIR filter is converted into the problem of solving the coefficients of the IFIR filter.Three restrictions hiding in the traditional EIR filter structure are revealed.2.A novel parallel filter structure based on EIR filter is proposed.In the traditional EIR filter structure,the side lobe continuation period T needs to be equal to the side-lobe length N_D.In the weighted extension process,the weights of the odd-symmetrical components must be equal to the weights of the even-symmetrical components.The new filter structure presented in this paper breaks the above limitations and solves the defect that the EIR filter cannot design high-order FIR filters.According to the parity of the order of the prototype filter in the two IFIR filters,the improved EIR filters are divided into the first type and the second type.The conventional EIR filter can be regarded as a special case in which the continuation period T is equal to the side-lobe length N_D,and the weighting coefficient of the odd component is the same as the weighting coefficient of the even component.Combined with the nonlinear joint optimization algorithm,the improved EIR filter can reduce the group delay of the filter while further reducing the implementation complexity.3.Single branch EIR filter structure and its design method is proposed.Compared with the improved EIR filter,the single branch EIR filter only needs to keep the odd component branch in the parallel structure.The single branch EIR filter has lower implementation complexity as if the filter design index meets the condition thatk??_c is integer.The single-branch EIR filter structure is particularly suitable for the design of half-band filter.