Spectral representations of digital signals using non-binary Galois fields.

Abstract

The article shown that for digital signal processing varying in a limited range of amplitudes it is advisable to consider a set of signal levels through its mapping into certain Galois field, i.e., finite commutative body. In this case, the signal coding differs from binary, however, this creates quite definite advantages. In particular, a modified Walsh basis where the elements +1 and -1 are treated as elements of a non-binary Galois field can be used. The main difference of such use of the Walsh basis is that the elements of the Galois field corresponding to the spectral components belong to the same set as the original signal levels do. This provides a significant reduction in the amount of information when transmitting information about the signal, presented in the form of its spectrum. A specific example of using the Galois field for processing a time series of data that simulates a digital signal is presented