Fractional Order Convex Linear Prediction for Signal Modelling

This paper introduces and analyzes three innovative Linear Prediction (LP) models, consisting of two Fractional Order (FO) LP models and an integer LP model. The closed-form expressions for the proposed methods-namely, Two Parameter FO Linear Prediction (TP-FLP), FO Convex Linear Prediction (FCLP), and integer Convex Linear Prediction (CLP)-are derived for derivative order \( 0 \le \alpha \le 2 \). These derivations contribute to a more profound understanding of underlying mathematical principles of the proposed predictor. The foundation of our proposed methodologies is based on the presentation of the current signal sample as a linear combination of the FO derivative of two past samples, coupled with the utilization of the convex combination technique. An extensive set of experiments is conducted to compare the effectiveness of the proposed models with baseline methods involving two traditional LP models: First- and Second-order LP, along with the One Parameter FO Linear Prediction (OP-FLP) model. The performance evaluation encompasses a diverse range of signal types, including sinusoidal waves, damped sine waves, electroencephalogram (EEG), and speech signals. The simulation results demonstrate significant advancements achieved by the proposed models. Notably, the proposed FCLP exhibits a remarkable prediction gain of 24.74 dB, outperforming baseline methods such as OP-FLP, First- and Second-order LP models, that achieve prediction gains of 23.17, 23.15, and 10.14 dB, respectively.