The analysis of biological signals is fundamental in medical applications. It requires tools that can capture both global structures and localized variations. The Lehmer transform is a novel mathematical framework that provides a flexible and adaptive representation of biological signals by mapping them into a domain of statistical moments, offering a complementary perspective as compared to traditional time-frequency methods.

This transform extends classical means and functions as a statistic-generating framework, enabling effective feature extraction, noise filtering, and anomaly detection. With its rich mathematical properties, the Lehmer transform allows for the construction of a parametric family of probability distributions. In turn, this facilitates robust analysis of electroencephalographic (EEG) signals. Empirical studies, in particular those of major depressive disorder (MDD) classification demonstrate its capability in identifying key features that characterize complex physiological processes.

This talk will explore theoretical foundations of Lehmer transform and its applications in signal processing and machine learning, highlighting its potential as a versatile tool for advancing the analysis of biological signals.