Applied harmonic analysis
Abstract
Recent work by the CUNY group under the direction of Professor Louis Auslander has continued to study application of the Weil transform to radar signal processing and, in a parallel effort, to multi-access spread spectrum communications. The main thrust of the work is the relationship between the Weil transform of a waveform and the ambiguity surface of the wave-form. The study of this relationship has led to a fundamental observation: the cancellation properties of a waveform necessary for the creation of a thumbtack-like ambiguity surface may be viewed as arising from the pattern of zeros and the non-trivial winding numbers of the Weil transform of the waveform. This point of view is exposited and used to reinterpret classical radar waveform design techniques, while also providing a new method for radar waveform design. Additionally, a new technique for modifying or shaping waveforms has been developed. This consists of changing a waveforms has been developed. This consists of changing a waveform by multiplying its Weil transform by doubly-periodic functions and taking the inverse Weil transform to produce a new signal.
- Publication:
-
NASA STI/Recon Technical Report N
- Pub Date:
- August 1993
- Bibcode:
- 1993STIN...9433353A
- Keywords:
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- Harmonic Analysis;
- Multiple Access;
- Signal Processing;
- Spread Spectrum Transmission;
- Waveforms;
- Winding;
- Communications and Radar