Remez Multiple Exchange Algorithm Research Articles

Use Of The Remez Algorithm For Designing FRM Based FIRr Filters

A very efficient technique for drastically reducing the number of multipliers and adders in narrow transition-band linear-phase finite impulse response (FIR) filters is to use the one-stage or multistage frequency-response masking (FRM) approach as originally introduced by Lim. In the original synthesis techniques developed by Lim and Lian, the subfilters in the overall approach were designed using time-consuming linear programming. In order to perform the overall synthesis faster, this paper shows how these subfilters can be designed with the aid of the the Remez multiple exchange algorithm, the most powerful technique for designing arbitrary-magnitude linear-phase FIR filters in the minimax sense. In addition to speeding up the overall procedure, the use of the Remez algorithm enables one to generate a very fast MATLAB program for the overall synthesis so that after being given the filter specifications as well as the number of stages, the program automatically provides the solution with the minimum number of multipliers and adders required in the overall implementation. This is possible because the MATLAB Remez routine is directly available and thus can be used for this purpose after appropriate modifications.

Complex Chebyshev approximation for IIR digital filters based on eigenvalue problem

This paper presents an efficient method for designing complex infinite impulse response digital filters in the complex Chebyshev sense. The proposed method is based on the formulation of a generalized eigenvalue problem by using the Remez multiple exchange algorithm. Hence, the filter coefficients can be easily obtained by solving the eigenvalue problem to find the absolute minimum eigenvalue, and then the complex Chebyshev approximation is attained through a few iterations starting from a given initial guess. The proposed algorithm is computationally efficient because it not only retains the speed inherent in the Remez exchange algorithm but also simplifies the interpolation step. Some design examples are presented and compared with the conventional methods. It is shown that the results obtained by using the method proposed in this paper are better than those obtained by the conventional methods.

Design of computationally efficient interpolated FIR filters

The number of multipliers required in the implementation of interpolated FIR (Finite-impulse response) filters in the form H(Z)=F(z/sup L/)G(z) is studied. Both single-stage and multistage implementations of G(z) are considered. Optimal decompositions requiring fewest number if multipliers are given for some representative low-pass cases. An efficient algorithm for designing these filters is described. It is based on iteratively designing F(z/sup L/) and G(z) using the Remez multiple-exchange algorithm until the difference between the successive stages is within the given tolerance limits. A novel implementation for G(z) based on the use of recursive running sums is given. The design of this class of filters is converted into another design problem to which the Remez algorithm is directly applicable. The results show that the proposed methods result in significant improvements over conventional multiplier efficient implementations of FIR digital filters. >