Windows with rapidly decaying sidelobes and steerable sidelobe dips

A window in the form of a sum of cosine terms is considered and the temporal weights are evaluated analytically so that it can have rapidly decaying sidelobes as well as steerable sidelobe dips. An analytic expression is derived so that the window designer can exploit the trade-off between a high sidelobe falloff rate (SLFOR) and many steerable sidelobe dips (SSLD). The treatment is based on using the L degrees of freedom inherent in the L temporal weights of the L+1 term window in partially achieving the goals of a high SLFOR and many SSLD. The extreme case when all degrees of freedom are used in creating many SSLD has been treated by Zhong et al. (1992). Combining both desired features in one unified mathematical framework is the main objective of the present paper