Relaxed Linear Fractional Programming for Implementing Allpass Phase Equalizers

This paper reveals a relaxed linear fractional-programming (LFP) method for the design of an allpass digital phase equalizer. The cost function used in the design is a linear fractional function, which approximates the phase-error function. The problem of minimizing the maximum of the linear fractional function is first transformed into a generalized LFP problem. Unfortunately, the resulting problem contains an infinite number of equality constraints which render the problem infeasible. To solve this problem, we relax the equality constraints to inequality constraints. This relaxation produces a relaxed LFP, which is actually a linear programming problem. Therefore, the allpass phase equalizer design can be achieved by solving the relaxed LFP problem. An illustrative example is introduced in the paper for demonstrating the efficiency of the relaxed LFP tactic.