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 F_p; with p an odd prime, 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.