Spectrum Transformation in the System of Discrete Fibonacci Functions

The basis system of discrete functions based on Fibonacci numbers has been little studied from the point of view of its application in discrete signal simulation algorithms. The purpose of the study is to analyze the matrix operator that transforms the harmonic trigonometric spectrum into the Fibonacci spectrum as one of the stages of the simulation algorithm. The analysis of the structure of the Fourier kernel matrix has shown that the kernel matrix is non-factorizable, which prevents reducing the computational complexity of spectrum transformation. The matrix elements are such that in the Fibonacci basis it is difficult to preserve the main advantage of the method of canonical expansions – the high accuracy of reproducing signals during simulation modeling. However, the considered spectrum transformation operator provides the possibility of qualitative spectrum estimates in spectral analysis and the development of new signal simulation algorithms.