Formation of a frequency representation of a one-dimensional signal, invariant to the processing direction, based on a discrete cosine transform
Abstract
Formation of a frequency representation of a one-dimensional signal, invariant to the processing direction, based on a discrete cosine transform
Incoming article date: 10.07.2025The article examines the influence of the data processing direction on the results of the discrete cosine transform (DCT). Based on the theory of groups, the symmetries of the basic functions of the DCT are considered, and the changes that occur when the direction of signal processing is changed are analyzed. It is shown that the antisymmetric components of the basis change sign in the reverse order of counts, while the symmetric ones remain unchanged. Modified expressions for block PREP are proposed, taking into account the change in the processing direction. The invariance of the frequency composition of the transform to the data processing direction has been experimentally confirmed. The results demonstrate the possibility of applying the proposed approach to the analysis of arbitrary signals, including image processing and data compression.
Keywords: discrete transforms, basic functions, invariance, symmetry, processing direction, matrix representation, correlation