Non-iterative Filter Bank Phase (Re)Construction

TL;DR

This paper introduces a non-iterative method for reconstructing phase information in filter banks from magnitude measurements, leveraging phase-gradient techniques and Gaussian filter properties for efficient signal recovery.

Contribution

It extends phase-gradient heap integration to filter banks with uniform decimation, providing an explicit phase-magnitude relationship for generalized translation-invariant systems.

Findings

Effective phase reconstruction demonstrated on real and synthetic signals

The method outperforms iterative approaches in speed and accuracy

Explicit phase-magnitude relationship derived for admissible filter banks

Abstract

Signal reconstruction from magnitude-only measurements presents a long-standing problem in signal processing. In this contribution, we propose a phase (re)construction method for filter banks with uniform decimation and controlled frequency variation. The suggested procedure extends the recently introduced phase-gradient heap integration and relies on a phase-magnitude relationship for filter bank coefficients obtained from Gaussian filters. Admissible filter banks are modeled as the discretization of certain generalized translation-invariant systems, for which we derive the phase-magnitude relationship explicitly. The implementation for discrete signals is described and the performance of the algorithm is evaluated on a range of real and synthetic signals.