The Structure and Properties of the Transformation Operators for a Trigonometric Fourier Spectrum to a Generalized Hartley Spectrum

To solve the complex tasks of digital signal processing, it is important to use effective spectrum transformation procedures. This article discusses the operator of spectrum transformation from the trigonometric basis to the generalized Hartley basis. The structure of the Fourier kernel matrix for this transformation is analyzed. A method to combining non-zero matrix elements into independent groups to reduce the number of computational operations is described. Based on the proposed method, spectrum transformation equations are obtained that linearly reduce the algorithm computational complexity depending on the number system used. The results of the paper can be used for spectrum transformation in signal simulation algorithms, as well as for the development of spectral conversion procedures in other bases.