Spectral entropy as a diagnostic gate for whitening quality and false-positive cross-coherence

Data Analysis
1

Hi everyone,

Following up on my earlier posts regarding template-free cross-correlation statistics and residual conditioning, I wanted to share a brief diagnostic observation on using Spectral Entropy (H_{\text{spec}}) as a fast quality gate for residual strain data.

Context & Motivation

When probing residual strain r(t) = d(t) - h_{\text{template}}(t) for unmodeled excess power or phase modifications, uncleaned low-frequency drift or imperfect PSD estimation can artificially inflate inter-detector cross-correlation, producing false-positive coherence between independent sites.

Diagnostic Metric & Minimal Implementation

We evaluate normalized spectral entropy H_{\text{spec}} over the conditioned frequency domain spectrum P(f):

H_{\text{spec}} = -\frac{1}{\ln N} \sum_{f} P(f) \ln P(f)
  • H_{\text{spec}} \approx 1.0: Residual matches stationary, ideal whitened Gaussian noise.
  • H_{\text{spec}} \ll 1.0: Residual retains narrow-band lines, unwhitened low-frequency tilt, or non-stationary noise features.

A minimal helper function in Python:

import numpy as np
from scipy.stats import entropy

def compute_spectral_entropy(residual_fd):
    """Computes normalized spectral entropy H_spec over frequency-domain residual."""
    psd = np.abs(residual_fd) ** 2
    psd_norm = psd / np.sum(psd)
    return entropy(psd_norm) / np.log(len(psd_norm))
Empirical Example (GW150914 Residual Test)
In a recent test evaluating residual cross-coherence between H1 and L1 around GW150914:

Unwhitened / Poorly Conditioned Residual: Residual retains significant low-frequency power (H 
spec
​
 ≈0.17). This produced a false-positive inter-detector cross-correlation peak of C 
H1,L1
​
 =0.2774.

Properly Whitened Residual: Spectral entropy recovers to H 
spec
​
 ≈0.68. The cross-correlation collapses to C 
H1,L1
​
 =0.0531—completely consistent with uncorrelated baseline noise.

Stage	H 
spec
​
 	Inter-Detector C 
H1,L1
​
 	Coherence Interpretation
Unwhitened Residual	~0.17	0.2774	False Positive (Low-frequency leakage)
Whitened Residual	~0.68	0.0531	Null / Pure Noise
Takeaway
Using H 
spec
​
  as a pre-check before calculating cross-site correlation statistics provides a light, deterministic guardrail against spectral leakage artifacts.

Curious to hear if others in DetChar or unmodeled search pipelines use similar information-theoretic bounds for low-latency data verification.

Best regards,

Dimitar
2

A propagation-Λ dispersion model and its mapping onto the standard LVK α=4 MDR test

Following up on my earlier post regarding template-free cross-correlation statistics, I want to share a separate line of work: a phenomenological frequency-dependent phase correction to the GW propagation phase,

ΔΨ(f,Λ) = -4π³ΛK(z)f³/c³

derived from an independent FLRW-dispersion argument (manuscript in preparation; distinct from the near-horizon Hamiltonian in Kretski (2026), A Hamiltonian Oscillator Extension of Wave Propagation in Schwarzschild Spacetime: Dispersion Index, Radial Wavenumber Dynamics, Covariant Derivation, and Observational Constraints on a Single Parameter, which uses a dimensionally different Λ), where K(z) is a standard cosmological distance-type integral.

Connection to the standard LVK dispersion test: This f³ phase form is mathematically identical to the α=4 case of the standard Mirshekari-Yunes-Will modified dispersion relation (E²=p²c²+Aₐp^αc^α), routinely tested by the LVK collaboration in each GWTC catalog. Comparing the two phase formulas directly gives an exact conversion (no residual z-dependence, since both models share the same cosmological distance-integral structure — verified numerically, D₄=c·K(z)/(1+z)³ to machine precision):

Λ = h²c³/(4π²) · A₄

Result: Applying this conversion to the published GWTC-4.0 combined bound on A₄ (83 cumulative events, Table 5 of arXiv:2603.19020) gives:

Λ ∈ [-7.2×10⁻³, +2.2×10⁻³] m³/s (90% CI)

consistent with Λ=0 (GR). This is, to my knowledge, the first translation of the standard LVK MDR bound into this parametrization.

I also independently tested whether Λ≠0 measurably affects detection characteristics of a template-free H1/L1 cross-correlation statistic (TriAxis V5, Zenodo 10.5281/zenodo.22210847): injecting Λ-deformed signals at fixed SNR and scanning detection AUC and delay-reconstruction accuracy against Λ=0 controls showed no measurable dependence on Λ in either metric — consistent with the geometric/coherence nature of that statistic.

Happy to share the conversion derivation or discuss further.