Research On FRM Filter Designing Methods

Finite-length impulse response filter with linear phase has many well-known advantages,such as stability,free of phase distortion and low coefficient sensitivity.A fatal disadvantage of it is high complexity.The problem will become particularly acute in sharp transition bandwidth filters.Because when the transition bandwidth is narrow,filter length will be long.For example,transition bandwidth of 0.01? may lead to filter length of several hundreds.Such a high order filter will have serious quantization errors and long wordlength will be used to represent the coefficients.Frequency response masking(FRM)method proposed by Y.C.Lim in 1986 is used to implement sharp transition bandwidth filter.For a given designing specification its effective filter length is slightly longer than minimax optimum filter.Since only a few non-zero filter coefficients are used,it achieves a saving as high as 25%in terms of arithmetic operations.Especially when FRM method is combined with multiplierless design method,the complexity of resulting filter will reduced to a minimum.Although interpolated prototype filter in FRM method has multiple frequency bands,single frequency band can only be extracted by using traditional FRM method.So,to extract overall frequency bands,it's necessary to redesign appropriate masking filter constantly,which greatly increases design complexity.In this paper,designing method of variable masking filter based on frequency warping is proposed.Firstly,only a prototype masking filter is designed based on traditional FRM structure.Then,multiple masking filters in the upper and lower branches are realized by introducing frequency warping method and control a single frequency parameter.Secondly,the prototype masking filter is designed to be as half-band prototype filter in order to reduce the designing complexity.What's more,the frequency parameter is set to be as the power of two in order to reduce the number of multipliers.The simulation result show that the design complexity is reduced by 75.38%comparing with traditional FRM method.With FRM methods applied widely,a series of optimization algorithms are gradually used to improve the performance of sharp transition filter,such as semi-definite programming and cone programming.Based on the deep research of feedback neural network,this brief proposed optimization designing method of FRM filter based on continuous Hopfield neural network.The core of the method is to obtain optimal filter coefficients by mapping error function to energy function of neural network and minimizing the energy function.When designing two-stage FRM filter,layer-by-layer optimization method is adopted.The initial weight values are adjusted according to the parity of interpolation factor.The interpolated filter coefficients of second layer are generated firstly and used as inputs to the first layer,optimizing final filter coefficients.The basic principle and stable convergence of Hopfield neural network are described in detail,and ReLU function is used as activation function by comparing the advantages and disadvantages of various activation functions.Finally,the design example demonstrated that the FRM filter designed by this method has higher stopband attenuation and better performance.