Design of multiplierless minimum-phase FIR filters using palindromic polynomials and sharpening

Abstract

Minimum phase (MP) filters have all zeros inside the unit circle and have a minimum group delay and a minimum energy delay properties, especially useful in communication systems. The special class of MP filters has all zeros inside and on the unit circle. This paper presents a method for design of this class of MP FIR (Finite Impulse Response) digital filters without multipliers The method is based on palindromic polynomials and sharpening technique. The coefficients of palindromic polynomials are presented as a sum of powers of two, and consequently can be implemented by using only adders and shifts, resulting in a multiplierless design. Two classes of palindromic polynomials, having all zeros on the unit circle, are considered. Next, the sharpening technique was applied to improve the magnitude characteristic and to move zeros inside of unit circle. The choice of the design parameters is also presented. All zeros, of the designed MP filter, are inside or on the unit circle. Method is illustrated with one example.