ABSTRACT
The application of the Fourier transform representation by series leads to the concept of a wavelet-type unitary transform, which we call the paired transform. This transform is considered as a part of the mathematical structure of the discrete Fourier transform, which allows for minimizing not only the computation cost of the fast Fourier and other transforms [9]-[13]. The paired transform represents the signal as a unique set of separate short and independent signals that can be processed separately for effectively solving different problems of signal and image processing. The splitting-signals have different lengths and carry the spectral information of the represented signal in disjoint sets of frequencies. The paired transform is fast and leads to an effective decomposition of signals. In this chapter, we consider the decomposition of 1-D and 2-D signals by introduced section basis signals and derive the inverse formula. Examples of the application of paired transforms for signal detection and noise filtration, and image enhancement are described.
