SAR Window Functions: A Review and Analysis of the Notched Spectrum Problem

Abstract

Imaging systems such as Synthetic Aperture Radar collect band-limited data from which an image of a target scene is rendered. The band-limited nature of the data generates sidelobes, or 'spilled energy' most evident in the neighborhood of bright pointlike objects. It is generally considered desirable to minimize these sidelobes, even at the expense of some generally small increase in system bandwidth. This is accomplished by shaping the spectrum with window functions prior to inversion or transformation into an image. A window function that minimizes sidelobe energy can be constructed based on prolate spheroidal wave functions. A parametric design procedure allows doing so even with constraints on allowable increases in system bandwidth. This approach is extended to accommodate spectral notches or holes, although the guaranteed minimum sidelobe energy can be quite high in this case. Interestingly, for a fixed bandwidth, the minimummean-squared-error image rendering of a target scene is achieved with no windowing at all (rectangular or boxcar window).

Generating nonlinear FM chirp waveforms for radar.

“…A question remains, however, "How well can we do with polynomial phase of order N if we don't necessarily try to match a specific weighting function?" This begs the question of whether and how some 'optimum' polynomial can be found for a phase function to generate minimum sidelobe energy in a manner similar to the technique for weighting functions presented by Dickey, et al 15 The answer to this question, regardless of how interesting it might be, is however beyond the scope of this report.…”