S-Transform Polarization Analysis of Three-Component Signals
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Solution Overview
Problem
Standard Fourier analysis is inadequate for processing time-varying three-component signals, particularly in applications requiring polarization analysis and filtering, as it fails to provide sufficient information about frequency changes over time or space, which are crucial for understanding elliptically polarized motions in 3D space.
Innovation Solution
A signal processing method and system utilizing the S-transform to analyze and filter time-varying three-component signals by transforming each component into the time-frequency and space-frequency domains, determining polarization-dependent features based on polarization ellipses that depend on both time and frequency, and employing a system with a processor to execute these transformations and calculations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If standard Fourier analysis is used to process three-component signals, then frequency components can be identified, but time-varying frequency information and polarization analysis capability are lost
Solution Approach 1:
The patent applies the S-transform, which uses a frequency-adapted Gaussian window that dynamically adjusts its width based on frequency. This dynamic windowing allows the transform to provide both time and frequency localization, capturing time-varying frequency information while maintaining polarization analysis capability for three-component signals
Solution Approach 2:
The patent transitions from standard Fourier analysis (frequency domain only) to S-transform analysis by adding the time dimension. This creates a time-frequency representation that preserves both frequency component identification and time-varying information, enabling comprehensive polarization analysis
2Ease of operation
If standard Fourier analysis is used, then computational simplicity is maintained, but polarization analysis and filtering capability is insufficient
Solution Approach 1:
The S-transform provides a dynamic time-frequency representation that adapts to local signal characteristics through frequency-adapted windowing. This enables reliable polarization analysis of time-varying three-component signals while maintaining computational efficiency through the inherent structure of the transform
Solution Approach 2:
The patent introduces the S-transform as an intermediary between standard Fourier analysis and time-domain signal processing. This intermediary transform provides the necessary time-frequency localization and polarization analysis capability while maintaining computational tractability through its mathematical structure
Data Source
AI summary
The present invention relates to a method and system for processing time-varying three-component signals to determine polarization dependent features therefrom. Relation data indicative of a predetermined expression relating ellipse elements describing an ellipse in three dimensional space to the components of the three-component signal are provided. Received signal data indicative of a three-component signal are processed for transforming each component of the three-component signal into time-frequency domain providing second signal data. Data indicative of polarization dependent features are then determined using the relation data and the second signal data. The method and system for processing time-varying three-component signals according to the invention are highly beneficial in numerous applications for evaluating three-component signal data such as seismology.