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Open Access

Construction of Sparse Representations of Perfect Polyphase Sequences in Zak Space with Applications to Radar and Communications

EURASIP Journal on Advances in Signal Processing20102011:214790

Received: 1 July 2010

Accepted: 9 September 2010

Published: 26 September 2010


Sparse representations of sequences facilitate signal processing tasks in many radar, sonar, communications, and information hiding applications. Previously, conditions for the construction of a compactly supported finite Zak transform of the linear FM chirp were investigated. It was shown that the discrete Fourier transform of a chirp is, essentially, a chirp, with support similar to the support of the time-domain signal. In contrast, the Zak space analysis produces a highly compactified chirp, with support restricted to an algebraic line. Further investigation leads to relaxation of the original restriction to chirps, permitting construction of a wide range of polyphase sequence families with ideal correlation properties. This paper contains an elementary introduction to the Zak transform methods, a survey of recent results in Zak space sequence design and analysis, and a discussion of the main open problems in this area.


RadarDiscrete Fourier TransformSpace SequenceSparse RepresentationCorrelation Property

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Authors’ Affiliations

The MITRE Corporation, Emerging Technologies, Bedford, USA


© Andrzej K. Brodzik. 2011

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.