Physics Models and Analysis Theory

This page explains the advanced models and analytical theories implemented in gwexpy for handling specific physical phenomena and hardware responses.

Response and Coupling Functions

Automatic Excitation Detection

Extracts stable intervals for analysis from data containing injections (such as swept sine or stepped sine). By tracking power in specific frequency bands on a spectrogram, it identifies segments that exceed thresholds, eliminating the need for manual time-range specification.

Coupling Function (:term:`Coupling Function`; CF)

Estimates coupling functions while accounting for background noise. By comparing power during injection and background periods for both the target and witness signals, it isolates the true coupling degree.

\[ \text{CF}(f) = \sqrt{\frac{P_{\text{tgt,inj}}(f) - P_{\text{tgt,bkg}}(f)}{P_{\text{wit,inj}}(f) - P_{\text{wit,bkg}}(f)}} \]

Variable	Definition	Physical Meaning
\(f\)	Frequency	Frequency point for analysis
\(P_{\text{tgt,inj}}(f)\)	Target signal power (during injection)	Power distribution of the main signal during excitation
\(P_{\text{tgt,bkg}}(f)\)	Target signal power (during background)	Noise floor of the main signal without excitation
\(P_{\text{wit,inj}}(f)\)	Witness signal power (during injection)	Power of the reference signal (e.g., environmental noise)
\(P_{\text{wit,bkg}}(f)\)	Witness signal power (during background)	Noise floor of the reference signal without excitation

Related API: Time Series (TimeSeriesDict.calculate_coupling)

Built-in Noise Models

Provides physically motivated noise generators for use as initial models in simulations or fitting.

1. Schumann Resonance (:term:`Schumann Resonance`)

Models magnetic noise corresponding to the resonance modes of the Earth-ionosphere cavity. It reproduces the low-frequency magnetic background by superimposing multiple independent Lorentzian profiles.

Related API: Signal Processing (generate_schumann_model)

2. Voigt Profile

Generates peak shapes found in atomic physics or high-Q mechanical resonances, which combine Gaussian (Doppler broadening, etc.) and Lorentzian (collision/natural broadening, etc.) characteristics. It is calculated efficiently using the Faddeeva function.

Related API: Signal Processing (voigt_profile)

Advanced Analysis Engines and Algorithms

1. Independent and Principal Component Analysis (ICA/PCA)

The ICA/PCA implementation in gwexpy is optimized for physical data characteristics:

Unit Variance Standardization: Standardizes data to unit variance internally to improve convergence, then restores (re-scales) the original physical scale after computation.
Spatio-temporal Metadata Inheritance: Automatically inherits the GPS time conventions from the input data for each statistically extracted component.
Related API: Signal Processing (ICA, PCA)

2. Fast Correlation Engine (:term:`Bruco`)

The FastCoherenceEngine scans thousands of auxiliary channels for contributions to a target signal with extreme speed.

FFT Caching: Reuses FFT results for a common target signal in memory.
Sparse-like Computation: Skips non-correlated channels early to focus resources on significant contributors.
Related API: Time Series (TimeSeriesDict.scan_coherence)

3. Bayesian Inference and GLS Fitting

Handles parameter estimation for multidimensional data with complex error structures.

GLS (Generalized Least Squares): Applies statistically justified weighting when bins at different frequencies have correlated (non-diagonal) covariance.
MCMC Integration: Uses emcee for posterior sampling, enabling robust fitting even for non-linear physical models.
Related API: ../reference/api/stats