Group Representation Design of Digital Signals and Sequences

  • Authors:
  • Shamgar Gurevich;Ronny Hadani;Nir Sochen

  • Affiliations:
  • Department of Mathematics, University of California, Berkeley, USA CA 94720;Department of Mathematics, University of Chicago, USA 60637;School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel 69978

  • Venue:
  • SETA '08 Proceedings of the 5th international conference on Sequences and Their Applications
  • Year:
  • 2008

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Abstract

In this survey a novel system, called the oscillator system, consisting of order of p3functions (signals) on the finite field $\mathbb{F}_{p},$ is described and studied. The new functions are proved to satisfy good auto-correlation, cross-correlation and low peak-to-average power ratio properties. Moreover, the oscillator system is closed under the operation of discrete Fourier transform. Applications of the oscillator system for discrete radar and digital communication theory are explained. Finally, an explicit algorithm to construct the oscillator system is presented.