Frequently Asked Questions

What is QSignature?

QSignature is a model-free framework for classifying dynamical regimes from causal response data. It uses signed and unsigned centroid timescales (τ_s and τ_u) to compute diagnostic ratios R_su and Δ_su.

For theoretical background, see :cite:`qsignature2026_isdfs` and :cite:`qsignature2026_theorems`.

Does QSignature require model fitting?

No. QSignature is completely model-free. It computes directly from the time series without any fitting, training, or parametric assumptions.

What types of data can QSignature analyze?

QSignature works on any oscillatory time series, including:

  • Climate data (temperature, humidity, pressure)

  • Quantum systems (coherence decay)

  • Financial data (market cycles)

  • Forensic data (network traffic)

  • Engineering (vibration, control systems)

How do I interpret R_su?

  • R_su < 0 → Strong decay (weakly damped)

  • 0 < R_su < 1 → Decay (underdamped)

  • R_su ≈ 1 → Stable (exponential)

  • R_su > 1 → Growth

What is Λ (envelope growth rate)?

Λ is the average logarithmic growth rate of the amplitude envelope. It is phase-invariant and provides independent validation of the trend inferred from R_su.

Why is τ_u phase-invariant?

τ_u uses absolute values |dR/dt|, so sign cancellations from phase shifts do not affect it. This makes τ_u robust for oscillatory signals where τ_s may become negative.

How do I cite QSignature?

Please cite the ISDFS 2026 paper and the Research Square preprint. See the Acknowledgments page for BibTeX entries.

Where can I find examples?

See the Examples page and the examples/ folder in the GitHub repository.

What if my data is noisy?

Use QSmooth before computing diagnostics:

qs = QSignature.QSmooth()
R_smooth = qs.savgol(t, R, window_frac=0.1, polyorder=3)