Memory-Related Input-Space Partition Within Band-Limited Regression for Spectral Extrapolation

Partition in the input domain is shown to explain why band-limited regression is a spectral extrapolation, and it rises from the memory terms in dynamic DPD models. Transforming the basis functions, the input space can be partitioned into two areas, visualized in certain examples. The supervised area is convex and unsupervised output cannot be interpolated from the supervised input-output pairs. Therefore, it is not an overfitting problem and the spectral extrapolation cannot be improved by adding or selecting training samples. This understanding may improve the regularization for DPDs with band-limited feedback, validated by simulations based on real measurements.