Signal Filtering and Prediction

This research theme focuses on the development and analysis of advanced filtering algorithms that enable accurate tracking and prediction of time-varying signals corrupted by noise. It examines the optimality, computational efficiency, and robustness of filters such as Kalman filters, adaptive filters (LMS, RLS), and their combinations, with particular attention to their performance in nonstationary or uncertain environments where parameter variation occurs. Understanding and improving filter tracking capabilities directly impact real-time signal estimation tasks in communications, navigation, and control systems.

This theme explores the mathematical and optical foundations of fractional Fourier transforms (FrFT) and their applications to signal processing, particularly in filtering chirp signals, synthesizing mutual intensity distributions, and performing filtering and multiplexing in fractional domains. By generalizing classical Fourier analysis via fractional orders, these approaches enable enhanced handling of signals with time-frequency characteristics, providing advanced filtering capabilities and novel perspectives on signal representation and transformation relevant to both theoretical analysis and optical implementations.

This theme highlights the application of fractal dimension measures and nonlinear dynamical system embeddings to extract robust, noise-resistant features from signals such as speech and biomedical data. By embedding signals in reconstructed phase spaces and applying nonlinear filtering informed by local geometry and fractal characteristics, these approaches seek to improve the discriminative and predictive performance under noisy conditions, supplementing or enhancing classical linear feature extraction methods.