Radar waveform design and the Heisenberg group (Q1907303)

The paper under review is in the spirit of a recent paper on the deformation theory of radar ambiguity functions published by the same authors [Weyl multipliers. J. Fourier Anal. Appl. 2, 191-215 (1995)]. It begins with a presentation of the Heisenberg group theoretic setting [\textit{W. Schempp}, Radar reception and nilpotent harmonic analysis. I--IV. C. R. Math. Acad. Sci., Soc. R. Can. 4, 43-48, 139-144, 219-224, 287-292 (1982; Zbl 0485.94007, Zbl 0485.94008, Zbl 0518.94002, Zbl 0509.94002)] which is of particular value for quantum holographic processes such as synthetic aperture radar (SAR) imagery, sonoluminescence, and magnetic resonance imaging [\textit{W. Schempp}, Result. Math. 28, No. 3-4, 303-344 (1995)]. The Heisenberg group approach to the radar ambiguity function leads into a study of the Weyl transform. Specifically a discrete data structure called winding number data of the Weyl transform are introduced and some of its properties, and the computation of the data are discussed.