Cross-correlation antenna systems with modified principal solution spatial frequency transfer functions

The principal solution type of spatial frequency transfer function (SFTF) for a linear antenna system, e.g., line source or linear array, is constant (flat) over its entire spatial frequency (SF) passband and drops abruptly to zero at the edges of the band. Such a SFTF is obtainable with cross-correlation (multiplicative) techniques. The associated power pattern, of the
sin (Lu)/Lu
type, has high sidelobes diminishing asymptotically as
u^{-1}
. Moreover, the weighting distribution for the line source has an inverse taper with end point singularities. A modified principal solution SFTF, flat over most of the SF passband but with a smoothly varying transition function of the quadratic-linear-quadratic type at the edges of the passband is introduced. This engenders a power pattern whose sidelobes diminish asymptotically as
u^{-3}
instead of
u^{-1}
. The line source weighting distributions, moreover, are continuous and free of singularities, making physical realizability no longer a problem.