Design of FIR digital phase networks

The problem of the minimax design of FIR digital filters with prescribed phase characteristics and unit magnitude is a nonlinear optimization problem. In this paper it is approximated by a linear programming problem, and it is shown that the solution of this linear program is optimal to first order. That is, if δ0and ε0are optimal deviations of magnitude and phase characteristics, then the actual deviations obtained from the linear program solution satisfyδ ≤ δ₀ + εmin{0}max{2}andε ≤ ε₀ (1 + δ₀)/(1 - δ₀). Numerical examples are given, including design results for full-band M-term chirp filters which (like linear phase filters) can be implemented with (M + 1)/2 multiplications per point.