Self-similar decomposition of digital signals

Abstract

The behaviour of a physical quantity in time is described by signals. Traditionally, signals are analysed in the time domain either as time - amplitude relationship or in the frequency domain as frequency - signal power dependency. Both traditional representations have substantial limitations. New algorithms for signal representation and processing are required in order to give some additional useful information about observed processes. The present paper proposes a self-similar decomposition of digital signals, which gives rise to a multiscale description, preserving all features of the signals. The proposed description does not depend on predefined basis functions like sine waves, basic wavelets, etc. Instead, the newly proposed approach looks for self-similar associations of signal segments. The proposed signal description can be considered as an attempt to combine signal representation in time domain with signal representation in frequency domain