The design of frequency sampling filters by the method of Lagrange multipliers

A technique is developed for designing linear phase frequency sampling filters where the interpolation errors between frequency samples are controlled by minimizing the mean square error between the desired and actual frequency responses in the stopband subject to constraints on the passband frequency response. The frequency sampling filter design problem is defined as a constrained optimization problem, which is solved using the Lagrange multiplier optimization method. The Lagrange multiplier optimization method results in a set of linear equations, the solution of which determines the filter´s coefficients