Generalized Rademacher functions, constructed as a sequence of elements of Galois fields are intended to find the spectral representation of signals with levels. These functions form a complete basis on the interval corresponding to -1 discrete time intervals and for 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.

It is shown that the predicted energy crisis in Kazakhstan makes the issue of small-scale energy and complementary civil society institutions more than relevant. This crisis, caused by the deterioration of heating networks built during the former USSR, can be more than large-scale, as evidenced by the events in the city of Ekibastuz, where a significant proportion of the population was left without heating in the winter of 2022/2023. It is proven that the development of small-scale power generation should be complex, i.e. in the foreseeable future, one should focus attention on a combination of renewable and traditional energy sources, which implies a gradual increase in the share of renewable energy. The expediency of using the concept of “energy freedom”, at least in relation to the Republic of Kazakhstan, is substantiated. It is shown that the goal of the development of small green energy should be precisely the achievement of energy freedom for households, oriented towards the institutions of civil society. This implies, inter alia, the development of a wide range of non-trivial technical solutions that provide, for example, direct heat generation without an intermediate stage of conversion into electrical current. A specific example is considered, demonstrating the adequacy of the proposed approach. It is also shown that the primary measures to ensure the energy freedom of households can be implemented even when using equipment available on the market. Specific calculations are presented which prove that the transition to decentralized heat supply is economically feasible using available equipment.