Construction of Sparse Representations of Perfect Polyphase Sequences in Zak Space with Applications to Radar and Communications. (26th September 2010)

• Record Type: Journal Article
• Authors: Brodzik Brodzik, Andrzej K. Andrzej K.
• Other Names: Napolitano Napolitano Antonio Antonio Academic Editor.
• Is Part Of: EURASIP journal on advances in signal processing. Volume 2011(2011)
• Publication Date: 2010-09-26
• Subjects: Signal processing -- Periodicals; Traitement du signal; Signal processing; Periodicals; 621.3822
• DOI: 10.1155/2011/214790
• Languages: English
• ISSNs: 1687-6172

Abstract

Abstract : 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.