Skip to main content


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

Article metrics

  • 7230 Accesses

  • 4 Citations


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.

Publisher note

To access the full article, please see PDF.

Author information

Correspondence to Andrzej K. Brodzik.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and Permissions

About this article


  • Radar
  • Discrete Fourier Transform
  • Space Sequence
  • Sparse Representation
  • Correlation Property