An exact solution for incorporating boundary continuity constraints in subband all-pole modelling

Subband all-pole modelling is a flexible, scalable, and powerful approach for parsimoniously modelling rational transfer functions. Its advantage lies in its ability to model frequency bands independently of one another, thereby resulting in lower model orders in each subband and an overall reduction in the required number of parameters. To alleviate discontinuities in the spectrum at subband boundaries, it is necessary to increase slightly the computational complexity of the problem by incorporating continuity constraints. Previous solutions for implementing these constraints have been formulated for mathematical tractability and convenience; however, they are approximate and introduce modelling artifacts. This paper outlines an exact solution to the constrained modelling problem by using Lagrangian multipliers. The modelling results improve on the approximate formulations previously published