Design Of FIR Filters Using L_p Elliptic Error Minimization And RUL Reweighting Techniques

Nowadays,digital signal processing technology has been applied to almost all fields of engineering and technology in the wake of developments in information science and technology.Since digital filtering is a basic part of digital signal processing,the design of digital filter is of importance in digital signal processing.Compared with infinite impulse response(IIR)digital filter,finite impulse response(FIR)digital filter has intrinsic stability and can achieve exact linear phase,which makes the FIR digital filter design problem widely concerned by scholars and has been applied to the many industrial fields.However,the exact linear phase FIR filter usually has large signal delay,which is undesirable in many practical applications.Compared with linear phase FIR filters,FIR filters with magnitude performance but without phase response specifications can be achieved in accordance with the minimum-phase system,and magnitude response characteristics can be guaranteed at the same time,and they have lowest group delay in all the filters.In this paper,we consider the aforementioned design of FIR digital filters.First of all,the background and significance of the research is summarized,and then the research actuality of FIR digital filters is reviewed.In this paper we focus on the following three aspects to carry out the research.1.An iterative reweighted least-squares(IRLS)algorithm for the minimum L_p norm approximation problem is studied.The original IRLS algorithm proposed by Lawson is for linear minimax approximation problems,and the weight function updated in each iteration is in a multiplicative way by the absolute value of the approximation error function obtained by the last iteration and the current weighting function.But the original Lawson algorithm often converges slowly and needs to restart sometimes when applied to digital filter designs.Based on the original Lawson algorithm,J.Rice and K.Usow presented a modified Lawson algorithm for general L_p norm minimization problems,which we call RUL-IRLS algorithm.In this paper we focuses on the IRLS algorithm.2.The iterative constrained minimization of L_p elliptic error(ICMEE-p)method of FIR digital filters is studied and combined with RUL-IRLS algorithm to solve the minimization problems of the L_p elliptic error.The minimization problems of L_p elliptic error obtained by each iteration could be solved with the basic IRLS algorithm.But the basic IRLS algorithm is only for the design examples with small p values,and it will not converge when p takes largevalues.In this paper,we use the RUL-IRLS algorithm to solve the minimization problems of constrained L_p elliptic error and combine with the ICMEE-p method to get a new design algorithm,which we call ICMEE-p-RUL algorithm.Simulation results show that the ICMEE-p-RUL algorithm converges fast even when p takes large values,and is effective for the minimization problems of constrained L_p magnitude error of FIR digital filters.3.The minimization problem of constrained L_p magnitude error of FIR digital filters with time-domain constrains is studied,and the ICMEE-p-RUL algorithm is proposed to solve the problems.When the filter's impulse response coefficient is constrained by time-domain,the design problem of FIR digital filters is highly nonconvex,and then it's very difficult to solve.Linear time-domain constraints are easily incorporated into the ICMEE-p method and this can converts the approximation problems of constrained L_p magnitude error of FIR digital filters with linear time-domain constrains into a series of convex problem.In this paper,RUL-IRLS algorithm is combined with ICMEE-p method to obtain the ICMEE-p-RUL algorithm for solving the minimization problems of constrained L_p magnitude error of FIR Nyquist digital filters.Simulation results show the effectiveness of ICMEE-p-RUL algorithm.