Generalized Linear-Fractional Programming (LFP) for Designing Phase-Compensation System

Abstract

This paper shows a novel approach to the design of a digital allpass phase-compensation system. This approach extends the linear-fractional programming (LFP) method to the case of designing an allpass phase-compensation system and solves the system design problem as a linear-programming (LP) minimization. Originally, the LFP is used to minimize an objective function that is a ratio of two affine functions over a polyhedron. The LFP first transforms the original minimization problem to a linear-programming (LP) one, where the affine functions have constant coefficients. This paper extends this transformation to the minimax design of an allpass phase-compensation system, where the objective function is a ratio of two affine functions, but the coefficients are non-constant. This paper discusses how to extend the LFP to the case where the coefficients are non-constant and then design an allpass phase-compensation system by using the LFP approach. A demonstrative example is given to show the feasibility of the extended LFP.