Self-Similar Decomposition of Digital Signals

Traditionally, the engineers analyze signals in the time domain and in the frequency domain. These signal representations discover different signal characteristics and in many cases, the exploration of a single signal presentation is not sufficient. In the present paper, a new self-similar decomposition of digital signals is proposed. Unlike some well-known approaches, the newly proposed method for signal decomposition and description does not use pre-selected templates such as sine waves, wavelets, etc. It is realized in time domain but at the same time, it contains information about frequency signal characteristics. Good multiscale characteristics of the algorithm being proposed are demonstrated in a series of examples. It can be used for compact signal presentation, restoration of distorted signals, event detection, localization, etc. The method is also suitable for description of highly repetitive continuous and digital signals.