MISAR: Waveform Design and Filtering in Zak Space

Abstract : In this report, the authors document their ongoing effort to develop the Finite Zak Transform (FZT) into a framework for adaptive signal and filter design. The general idea is that by representing one-dimensional signals in multi-dimensional spaces, the underlying geometry in these multi-dimensional spaces can lead to new signal decompositions and processing methods. The specific application outlined in this report is spatial localization and scattering co-efficient computation from the noisy echoes of chirp waveforms interrogating a point target environment. The methods developed will be extended in future efforts to materials identification from chirp pulse echoes, including the determination of the scattering delays due to dielectric materials. Numerical experiments are included to emphasize the feasibility of this approach. Zak space representation provides a geometric, time-frequency setting for developing tools for solving this problem. In this setting, the authors have established geometric conditions for choosing optimal or nearly optimal sampling rates for the echoes of the chirp waveforms, and methods for processing and interpreting the information contained in the resulting sampled echoes. (61 figures, 4 refs.)