A NEW OPTIMAL WINDOW

A new optimal window is presented in this paper. It can provide the best tradeoff between the peak sidelobe level and the total sidelobe energy. Necessary and sufficient conditions are established for the optimal window. A design algorithm is presented and examples are discussed. The examples demonstrate that the new window is capable of much better performance than previously available windows, such as the Hamming window. Relationships between the maximum error and the mean-squared error are explored for optimization problems. It is concluded that minimax and least squares approximations are both fundamentally inefficient. This conclusion is supported by experimental evidence and mathematical analyses.