This study looks at how machine learning (ML) and polynomial math can be used together to improve advanced signal processing. The study creates new mathematical models that use the polynomial structures that are already present in signal data. These models combine vector metric spaces and orthogonal polynomial sequences to find features and show signals.  The suggested way is based on quickly getting polynomial features that keep the purity of the signal and allow for strong learning. Combining machine learning algorithms with polynomial algebraic structures makes it easier to analyse and handle complex signals. This solves problems with convergence and orthogonality in very large vector spaces.  The method offers better accuracy in jobs like signal classification, noise reduction, and rebuilding.