Construction of generalized Rademacher functions in terms of ternary logic: solving the problem of visibility of using Galois fields for digital signal processing
Abstract
Using generalized Rademacher functions, constructed as a sequence of elements of Galois fields , and intended to find the spectral representation of signals with n levels, the expediency of using the concept of "logical imaginary unit" is substantiated. These functions form a complete basis on the interval corresponding to 3^n -1 discrete time intervals and for n=1 passing into the classical Rademacher functions. The advantage of such spectra obtained using Galois Fields Fourier Transform is that the range of variation of the spectrum amplitudes remains the same as the range of variation of the original signal, which is modeled on discrete time functions taking values in the Galois field.
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