The finite harmonic oscillator and its applications to sequences, communication and radar

A novel system, called the oscillator system, consisting of order of p 3 functions (signals) on the finite field p; with p an odd prime, is described and studied. The new functions are proved to satisfy good autocorrelation, cross-correlation, and low peak-toaverage 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.

• Type: Journal
• Year: 2008
• Where: CORR
• Authors: Shamgar Gurevich, Ronny Hadani, Nir A. Sochen
• Keywords: CORR 2008, Discrete Fourier Transform, Education, Low Peak-toaverage Power, Oscillator