The Finite Harmonic Oscillator and Its Applications to Sequences, Communication, and Radar
Shamgar Gurevich, Ronny Hadani, Nir Sochen · IEEE Transactions on Information Theory · 2008
A novel system, called the oscillator system, consisting of order of p3functions (signals) on the finite field Fp, with p an odd prime, is described and studied. The new functions are proved to satisfy good autocorrelation, 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.