This paper presents a new and versatile framework to window design based on a semi-infinite linear programming approach by using the Dual Nestled Complex Approximation (DNCA) algorithm. The paper considers a practical problem formulation, the general window design specification and the corresponding optimum solution. The DNCA linear programming algorithm is presented and several highly optimized window design examples included. Furthermore, the capability of the design method by enhancing the sidelobe attenuation of existing windows such as Flattop windows is illustrated as well. Flattop windows are commonly available in frequency analyzers for accurate amplitude measurements of harmonic tones in presence of noise. However, the design method can be directly applied to any other existing window, in purpose to enhance its performance. With the proposed method it is possible to design windows with more than 150dB sidelobe attenuation. A relevant application where such high precision windows is needed are in today's 24bit equivalent 1bit-Sigma-Delta ADC:s, where high frequency noise is generated.