# Phase demodulation with iterative Hilbert transform embeddings

## TL;DR

This paper introduces an iterative Hilbert transform embedding method for more accurate phase demodulation of complex, fast-modulated signals, surpassing traditional single-application approaches.

## Contribution

The authors develop an iterative approach that significantly improves phase demodulation accuracy for complex waveforms, with theoretical convergence analysis for simple cases.

## Key findings

- Iterative method enhances phase accuracy beyond traditional approaches.
- Applicable to complex and fast modulated waveforms.
- Convergence proven for simple cosine waveforms.

## Abstract

We propose an efficient method for demodulation of phase modulated signals via iterated Hilbert transform embeddings. We show that while a usual approach based on one application of the Hilbert transform provides only an approximation to a proper phase, with iterations the accuracy is essentially improved, up to precision limited mainly by the discretization effects. We demonstrate that the method is applicable to arbitrarily complex waveforms, and to modulations fast compared to the basic frequency. Furthermore, we develop a perturbative theory applicable to simple cosine waveforms, showing convergence of the technique.