Exact Least Squares Algorithm for Signal Matched Synthesis Filter Bank: Part II

TL;DR

This paper introduces a fast recursive algorithm for constructing signal-matched synthesis filter banks that reconstruct specific signals and explores their use in stochastic process modeling, validated through simulations.

Contribution

It defines the concept of signal matched synthesis filter banks and develops a recursive algorithm for their design, extending the previous work on whitening filter banks.

Findings

Developed a lattice-like recursive algorithm for synthesis filter bank coefficients.

Validated the approach through simulation results.

Demonstrated the use of synthesis filter banks in stochastic process modeling.

Abstract

In the companion paper, we proposed a concept of signal matched whitening filter bank and developed a time and order recursive, fast least squares algorithm for the same. Objective of part II of the paper is two fold: first is to define a concept of signal matched synthesis filter bank, hence combining definitions of part I and part II we obtain a filter bank matched to a given signal. We also develop a fast time and order recursive, least squares algorithm for obtaining the same. The synthesis filters, obtained here, reconstruct the given signal only and not every signal from the finite energy signal space (i.e. belonging to L^2(R)), as is usually done. The recursions, so obtained, result in a lattice-like structure. Since the filter parameters are not directly available, we also present an order recursive algorithm for the computation of signal matched synthesis filter bank coefficients from the lattice parameters. The second objective is to explore the possibility of using synthesis side for modeling of a given stochastic process. Simulation results have also been presented to validate the theory.