This section, based on a class project by EE graduate student Tatsuki Kashitani, illustrates the use of linprog in Matlab for designing variations on the Chebyshev window (§3.10). In addition, some comparisons between standard linear programming and the Remez exchange algorithm (firpm) are noted.
If we can get our filter or window design problems in the form
The linprog function in Matlab Optimization Toolbox solves LP problems. In Octave, one can use glpk instead (from the GNU GLPK library).