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. In the extreme case where all degrees of freedom are used in achieving the maximum SLFOR a simple closed-form expression is derived for the temporal weights thus formalizing and generalizing the results of Nuttall (1981). The other extreme case where all degrees of freedom are used in creating many SSLD has been recently treated by Zhong et al. (see ibid. vol.40, no.6, p.1452-1459, 1992) combining both desired features in one unified mathematical framework is the main objective of this paper. Simulation results demonstrate the superior performance of a window having both features to that of a window having only one feature in extracting a weak sinusoidal signal dominated by a leakage from another stronger signal