[Paper Review] Cerebral Signal Instantaneous Parameters Estimation MATLAB Toolbox - User Guide Version 2.3

Esmaeil Seraj|arXiv (Cornell University)|Oct 7, 2016

EEG and Brain-Computer Interfaces3 references4 citations

TL;DR

This paper introduces the Cerebral Signal Instantaneous Parameters Estimation MATLAB Toolbox, a free, open-source tool for estimating instantaneous phase, frequency, and amplitude in EEG and MEG signals using conventional, ZPPP, and Transfer Function Perturbation (TFP) methods. It enables robust analysis of phase synchronization, phase locking value (PLV), and other neurophysiological features, with validated performance across synthetic and real EEG data.

ABSTRACT

This document is meant to help individuals use the Cerebral Signal Phase Analysis toolbox which implements different methods for estimating the instantaneous phase and frequency of a signal and calculating some related popular quantities.The toolbox -- which is distributed under the terms of the GNU GENERAL PUBLIC LICENSE as a set of MATLAB routines -- can be downloaded at the address http://oset.ir/category.php?dir=Tools.The purpose of this toolbox is to calculate the instantaneous phase and frequency sequences of cerebral signals (EEG, MEG, etc.) and some related popular features and quantities in brain studies and Neuroscience such as Phase Shift, Phase Resetting, Phase Locking Value (PLV), Phase Difference and more, to help researchers in these fields.

Motivation & Objective

• To provide a reliable, open-source MATLAB toolbox for estimating instantaneous parameters of cerebral signals such as phase, frequency, and amplitude.
• To address limitations in conventional phase estimation by introducing robust statistical frameworks like TFP and ZPPP for improved accuracy in noisy or non-stationary EEG/MEEG signals.
• To support neuroscience research by enabling computation of key phase-related metrics such as PLV, phase resetting, and phase differences.
• To facilitate reproducible research through comprehensive test files, user guides, and integration with the Open-Source Electrophysiological Toolbox (OSET).
• To enable synthetic EEG generation using AR modeling for cross-validation and benchmarking of phase analysis methods.

Proposed method

• Employs three core phase estimation methods: conventional Hilbert transform (Phase_Ex_Trad.m), Zeros-Poles Perturbation Procedure (ZPPP) (Phase_Ex_ZPPP.m), and Transfer Function Perturbation (TFP) (Phase_Ex_TFP.m).
• Applies statistical frameworks based on random perturbations of filter zeros and poles to enhance robustness against noise and artifacts in phase estimation.
• Uses the Hilbert transform and analytic signal approach to compute instantaneous phase, frequency, and amplitude from bandpass-filtered signals.
• Implements phase locking value (PLV) calculation via both phase sequences (PLV_PhaseSeq.m) and raw signals (PLV_RawSig.m), with support for multi- and single-channel analysis.
• Generates synthetic EEG signals using an autoregressive (AR) model and innovation filtering (Synth_EEG.m), preserving spectral characteristics of real EEG.
• Integrates with the OSET framework and supports modular use via test scripts (e.g., Test_Phase_Ex_TFP.m) for validation and demonstration.

Experimental results

Research questions

• RQ1 How can instantaneous phase, frequency, and amplitude be robustly estimated in noisy or non-stationary EEG and MEG signals?
• RQ2 What is the performance gain of the TFP and ZPPP methods over conventional Hilbert-based phase estimation in real and synthetic EEG data?
• RQ3 To what extent can the toolbox accurately compute phase synchronization metrics like PLV across multiple EEG channels?
• RQ4 How well does the synthetic EEG generation function (Synth_EEG.m) reproduce the spectral and temporal characteristics of real EEG signals?
• RQ5 Can the toolbox reliably detect phase reset events and phase shift dynamics in neural time series?

Key findings

• The TFP and ZPPP methods significantly improve phase estimation robustness compared to conventional Hilbert-based methods, especially in low signal-to-noise conditions.
• Phase Locking Value (PLV) matrices computed using both phase sequences and raw signals show consistent results, validating the reliability of the PLV calculation functions.
• Synthetic EEG signals generated using the AR model and innovation filter closely match the power spectral density (PSD) of real EEG signals, as confirmed by Welch’s PSD analysis.
• The toolbox successfully captures alpha rhythm dynamics (8–12 Hz) with accurate instantaneous phase, frequency, and amplitude sequences, as demonstrated in sample figures.
• The Phase_Ex_TFP.m function enables detection of phase shift and phase reset events through statistical perturbation of filter responses, enhancing sensitivity to transient neural dynamics.
• The user guide and test files (e.g., Test_PLV_RawSig.m, Test_Synth_EEG.m) confirm the toolbox’s usability and reproducibility across different EEG datasets and analysis scenarios.