Self-Similar Decomposition of Digital Signals

摘要

Traditionally, the engineers analyze signals in the time domain and in thefrequency domain. These signal representations discover different signalcharacteristics and in many cases, the exploration of a single signal presentation isnot sufficient. In the present paper, a new self-similar decomposition of digital signalsis proposed. Unlike some well-known approaches, the newly proposed method forsignal decomposition and description does not use pre-selected templates such assine waves, wavelets, etc. It is realized in time domain but at the same time, it containsinformation about frequency signal characteristics. Good multiscale characteristicsof the algorithm being proposed are demonstrated in a series of examples. It can beused for compact signal presentation, restoration of distorted signals, eventdetection, localization, etc. The method is also suitable for description of highlyrepetitive continuous and digital signals.