Design Of Sparse FIR Filters With Low Order

With the rapid development of digital technology,the demand for low-complexity and low-power digital filter design is becoming more and more obvious.Various digital filter design and optimization technologies have received much more attention in the fields of signal systems and communication applications.Compared with infinite impulse response(IIR)filters,finite impulse response(FIR)filters have absolute linear phase and there is no problem of stability.However,the implementation cost and power consumption of FIR filters are usually higher than the corresponding IIR filters,so the design of FIR filters with low complexity and low-power consumption is particularly important.The optimization of sparse FIR filter design is a hot topic in the research area of low-complexity digital filter design.Essentially,the sparse optimization problem is an L0-norm optimization problem,and its non-convexity is the difficulty of designing the optimal sparse filter.In addition,experiments show that the filter order has an effect on sparsity.To increase the sparsity of coefficients often requires a larger filter order.However,as the filter order increases to a certain length,it cannot continue to increase the sparsity,which only increases additional delay units.This thesis analyzes the existing sparse FIR filter design methods,and proposes a new algorithm to design sparse FIR filters with reduced effective order.The paper is mainly composed of two parts,which respectively correspond to the two proposed low-order sparse FIR filter design methods:(1)For the single-stage sparse FIR filter design,the L0-norm design problem of sparse FIR filter is re-formulated by encoding the filter coefficients using a binary encoding vector to transform it into a convex optimization sub-problem.An iterative0-1 exchange algorithm is proposed to propel the minimax approximation error toward the specified upper bound of error for sparsity maximization.In this process,the proposed algorithm maximizes the number of zero coefficients and reduces the effective length on the basis of maximum sparsity.(2)By decomposing a single-stage FIR filter into two sub-filters,the cascade form sparse filter design problem is reformulated and the coefficients of the two sub-filters are optimized simultaneously by the proposed optimization algorithm,so that the cascade coefficient sparsity is greater than that of a single-stage FIR filter design.Theproposed design algorithms are suitable for all types of sparse FIR filter design problems.Experimental results show that the proposed algorithms can improve the sparsity with comparable or even lower effective filter order than any other existing algorithms.