 These constraints are as shown below

formula_270

formula_271

formula_272

formula_273

If the passband and stopband are defined, then we can replace each positive polynomial formula_274 by a weighted sum of squares expression.Limiting the degrees of the sum-of-squares polynomials to formula_78 then gives sufficient conditions for feasibility.We call the resulting optimization problem a sum-of-squares program and can be solved via semidefinite programming.