Polynomial Fourier transforms

A discrete polynomial Fourier transform that leads to a family of Chrestenson-related transforms is disclosed. The polynomial spectrum of a p-valued function can be calculated without requiring complex multiplication. Former known expressions for Chrestenson spectra can be obtained from the polynomial spectra by a simple modulo reduction. The coefficients of the spectral polynomials give exact information on the correlation between p-valued and linear functions. It is shown that the coefficients of selected spectral polynomials characterize the p-valued threshold functions uniquely.<>