Design of linear phase FIR filters with a maximally flat passband

The design of linear phase FIR digital filters having symmetric or antisymmetric impulse response is formulated as a constrained minimization problem. The constraints express the maximal flatness of the frequency response at the origin in the case of a low-pass filter or at an arbitrary frequency in the passband in the case of a bandpass filter. The objective function, which is a quadratic form in the filter coefficients, is formed as a convex combination of two objective functions representing the energy of the error between the frequency response of the designed filter and a scaled version of the frequency response of the ideal filter in both the stop and passbands.