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This letter presents a new extended active set strategy for optimum finite impulse response (FIR) window design by semi-infinite quadratic programming. The windows may be asymmetric corresponding to frequency responses with general nonlinear phase. The optimality criterion is to minimize the sidelobe energy (L/sub 2/-norm) subject to a peak sidelobe magnitude-constraint (L/sub /spl infin//-constraint). Additional linear constraints are used to form the mainlobe (unity DC gain). Numerical examples involving group delay specifications are used to illustrate the usefulness of the algorithm.