Some advantages of non-binary Galois fields for digital signal processing

It is shown that the convenient processing facilities of digital signals varying in a finite range amplitudes are non-binary Galois fields, numbers which elements equal to prime numbers. Within choosing sampling interval corresponding such field, it becomes possible construct field Fourier transform, distinctive feature exact correspondence with ranges variation original signal and its spectrum. This favorably distinguishes Field Transform proposed type from spectra, calculated using, for example, Walsh basis. also shown, Transforms have same properties as transform associated expansion terms basis harmonic functions. In particular, an analogue classical correlation, connected spectrum derivative, was obtained. On this proved, using fields makes develop complete transfer function apparatus, but only presented form.