Time Domain High Order Spectral Analysis

This repository provides tools for performing Time Domain High Order Spectral Analysis (TD-HOSA), a technique used to analyze non-linear and non-Gaussian signals by extending traditional spectral analysis beyond second-order statistics. This method is particularly useful in applications where standard Fourier-based techniques fall short, such as detecting system nonlinearities, identifying transient behaviors, and reducing Gaussian noise interference.

What is Time Domain High Order Spectral Analysis?

Traditional spectral analysis, such as Fourier or wavelet transforms, primarily focuses on second-order statistics (power spectra), which assume that the underlying process is linear and Gaussian. However, many real-world signals exhibit nonlinearity and non-Gaussian properties. High Order Spectral Analysis (HOSA) extends the analysis to higher-order statistics (such as bispectrum and trispectrum), which help reveal phase relationships and suppress Gaussian noise components.

Time Domain HOSA, as opposed to frequency domain methods, directly analyzes signals in the time domain, allowing for a more detailed characterization of transient and nonlinear features.

Applications of TD-HOSA

• Industrial Process Monitoring: Detecting anomalies and faults in mechanical and electrical systems.
• Biomedical Signal Processing: Analysis of EEG and ECG signals to detect abnormal brain and heart activities.
• Structural Health Monitoring: Identifying nonlinear vibrations in materials and infrastructures.
• Seismic Signal Analysis: Understanding nonlinear interactions in geophysical data.
• Communication Systems: Enhancing signal processing in non-Gaussian noise environments.

Repository Context

This repository was designed to be used as a package for processing neural signals, meaning that the tools and analysis techniques implemented here aimed to identify complex signal patterns in neural electrophysiological data.

Setup Guide

Prerequisites

To run this repository, ensure you have the following installed:

• Python 3.11+
• Pip 3.11+

Python 101

For those new to Python, we recommend the following interactive tutorials:

Learn Python - Interactive Tutorials

Library Versioning

All library dependencies are managed and versioned in the pyproject.toml file using Poetry.

IDE

The recommended IDE for this project is VS Code.

Installation and Setup

Installing Python 3.11+

To install Python 3.11+ on Ubuntu, follow these steps:

shell sudo apt install software-properties-common -y sudo add-apt-repository ppa:deadsnakes/ppa sudo apt install python3.11

Verify the installation:

shell python3.11 --version

Installing Pip

Install the latest version of pip for Python 3.11:

shell curl -sS https://bootstrap.pypa.io/get-pip.py | python3.11

Verify installation:

shell python3.11 -m pip --version

Upgrade pip:

shell python3.11 -m pip install --upgrade pip

Installing Poetry

Poetry is used for package and dependency management. Install it with:

bash curl -sSL https://install.python-poetry.org | python3 - --version 1.8.3

Creating a Virtual Environment

To create a virtual environment within the project directory:

bash poetry config virtualenvs.in-project true

Explicitly create the environment using Python 3.11:

bash poetry env use python3.11

Activating the Virtual Environment

To activate (or create) the virtual environment:

bash poetry shell

Installing Dependencies

Once inside the virtual environment, install dependencies with:

bash poetry install

If using VS Code, set the interpreter to the newly created virtual environment.

More details about Poetry can be found HERE.

Authors

• Matheus Anjos - matheusvra@hotmail.com - https://github.com/matheusvra