On the Use of Gini Coefficient for Measuring Time-Frequency Distribution Concentration and Parameters Selection

Abstract

The energy concentration in the time-frequency analysis has been used as an important feature in many signal processing tasks such as detection, reconstruction, feature extraction, and classification, especially in applications with nonstationary signals. Consequently, when considering the energy concentration as a feature, it is of great importance to provide the time-frequency representation that provides the highest possible concentration for a certain signal type. Measuring time-frequency distribution concentration allows an appropriate selection of distribution parameters that mostly correspond to the analyzed signal. Different types of concentration measures have been applied for automatic parameters set up in time-frequency based signal analysers. Here, we propose to use the Gini coefficient as an efficient concentration measure for an appropriate choice of time-frequency distribution and its parameters. It is proven that the Gini coefficient can be more suitable than other commonly used measures. The advantage of using the Gini coefficient is demonstrated in examples.