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 which is optimal to first order. That is, if δ
0
and ε
0
are optimal deviations of magnitude and phase characteristics, then the actual deviations obtained from the linear program solution satisfy
\delta \leq \delta_{0} + εmin{0}\max{2}
and
εleq ε_{0}(1+\delta_{0})/(1-\delta_{0})
. Design results are given for full-band M-term chirp filters, which (like linear phase filters) can be implemented with (M+1)/2 multiplications per point.