Quantized Information in Spectral Cyberspace

Area of Science:

• Signal Processing
• Information Theory
• Time-Frequency Analysis

Background:

• Traditional spectral analysis methods face limitations in quantifying information and uncertainty.
• Time-frequency representations are crucial for analyzing complex signals but require robust quantification techniques.

Purpose of the Study:

• To develop a novel method for spectral power, information, and uncertainty quantification using constant-Q Gabor atoms.
• To establish stable multiresolution spectral entropy algorithms for enhanced signal analysis.
• To provide sensor-agnostic transformations for signal processing, pattern recognition, and machine learning.

Main Methods:

• Utilized constant-Q Gabor atoms for time-frequency analysis.
• Developed stable multiresolution spectral entropy algorithms employing continuous wavelet and Stockwell transforms.
• Applied processing and scaling methods tailored to signal signatures, desired information, and uncertainty levels.

Main Results:

• Demonstrated the efficacy of the constant-Q Gabor atom for spectral quantification.
• Successfully constructed stable multiresolution spectral entropy algorithms.
• Presented case studies using Lamb wave signatures and information spectra from the 2022 Tonga eruption.

Conclusions:

• The developed methods provide resilient transformations from physical to information metrics.
• The approach is suitable for sensor-agnostic signal processing, pattern recognition, and machine learning.
• The choice of processing and scaling is adaptable based on signal characteristics and analytical goals.