A new optimal window [signal processing]

An optimal window that can provide the best tradeoff between the peak sidelobe level and the total sidelobe level is presented. Necessary and sufficient conditions are established for the optimal window. A design algorithm is presented, and examples are discussed. The examples demonstrate that the 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 the window optimization problem. It is concluded that the minimax and least squares approximations are both fundamentally inefficient. This conclusion is supported by experimental evidence and mathematical analyses