Optimal windowing for wideband linear arrays

The problem of constructing a wideband beam pattern that is concentrated in both angle and frequency is discussed. This paper is a direct extension of the work of Slepian and co-workers on time- and frequency-limited functions. It is shown that the singular vectors and singular functions of the mapping relating the set of weights of a linear wideband array to its far-field directivity pattern have both concentration properties and double orthogonality properties and so they can be thought of as the wideband equivalents of the discrete prolate spheroidal sequences and wave functions. These singular functions are used to obtain approximations to a frequency-invariant beam pattern