Measures of complexity in signal analysis

Abstract

Observational data of natural systems, as measured in astrophysical, geophysical or physiological experiments are typically quite different from those obtained in laboratories. Due to the peculiarities with these data, well‐known characteristics processes, such as periodicities or fractal dimension, often do not provide a suitable description. To study such data, we present here the use of measures of complexity, which are mainly basing on symbolic dynamics. We distinguish two types of such quantities: traditional measures (e.g. algorithmic complexity) which are measures of randomness and alternative measures (e.g. ε‐complexity) which relate highest complexity to some critical points. It is important to note that there is no optimum measure of complexity. Its choice should depend on the context. Mostly, a combination of some such quantities is appropriate. Applying this concept to three examples in astrophysics, cardiology and cognitive psychology, we show that it can be helpful also in cases where other tools of data analysis fail.