Design Of 2-D FIR Digital Filter Based On ADMM Algorithm

With the rapid development of computer technology and information science,the ability of computers and related hardware to process data has been greatly improved,and the memory capacity has increased rapidly,which also brings more and more broad application and development prospects for two-dimensional digital filters.Compared to the Infinite Impulse Response(IIR)filter,the Finite Impulse Response(FIR)filter has attracted the attention of experts and scholars due to its intrinsic stability and the remarkable characteristics of achieving accurate linear phase.At the same time,it is widely used in the industrial field.The optimal design of a two-dimensional FIR digital filter is a classic but still challenging problem in the field of signal processing.When the order of the filter is large,the number of impulse response coefficients and approximation frequency points is large,which results in high computational complexity of the algorithm.At this time,the large amount of computation is one of the main challenges of the design problem.In recent years,the Alternation Direction Method of Multipliers(ADMM)has become a hot topic for many scholars due to its strict theoretical guarantee and good performance in handling large-scale convex optimization problems.In this paper,by virtue of the alternation direction method of multipliers,the Least Square(LS)and Constrained Least Square(CLS)designs of two-dimensional FIR filters are studied.Through maximal splitting of the optimization model and incorporating with a relaxation technology,Maximally Split and Relaxed ADMM(MS-RADMM)algorithms for least square and constrained least square designs of two-dimensional FIR filters are obtained.This thesis mainly does the following work:1.The LS design of two-dimensional FIR digital filter based on MS-RADMM algorithm is studied.For the least square designs of two-dimensional linear phase and nonlinear phase FIR filters,the alternation direction method of multipliers is applied to study the parallel optimization in the design problems.By maximally splitting the optimization model and using a recently proposed acceleration technique,a maximally split and relaxed ADMM algorithm with scalarwise variable updates is proposed.The computational complexity of the algorithm is analyzed,the convergence of the algorithm is discussed,and the parameter setting for quick converge is given.The simulation results show that the maximally split and relaxed ADMM algorithm has a highly parallel structure and very high computational efficiency,and can be applied to the design based on non-matrix frequency grid.2.The CLS design of linear phase two-dimensional FIR digital filter based on MS-RADMM algorithm is studied.On the basis of the above LS design,the CLS design of the linear phase two-dimensional FIR filter is further studied.The maximally split and relaxed ADMM algorithm for LS design is extended to the CLS design by imposing constraints on the magnitude error of the filter.The convergence of the algorithm is analyzed,the parameter setting of the algorithm is discussed,and the effect of the upper bound of the error constraint on the convergence of the algorithm is studied by simulation.Through comparison with existing CLS design methods of two-dimensional FIR digital filters,it is shown that the proposed method has reduced the dimension of the optimization model,can be easily implemented in parallel,and has higher computational efficiency.At the same time,because it can be applied to non-matrix frequency grids,filters with better performance have been designed by the proposed method.