Calculator Inputs
Provide paired phase samples for two channels. You can paste values, paste a two-column list, or upload a file with two numeric columns.
Example Data Table
Copy this two-column example into the “Two-column phase list” input.
| Phase A (rad) | Phase B (rad) |
|---|---|
| 0.10 | 0.05 |
| 0.35 | 0.20 |
| 0.60 | 0.55 |
| 0.85 | 0.70 |
| 1.15 | 1.05 |
| 1.40 | 1.25 |
Formula Used
The Phase Locking Value (PLV) quantifies how consistent the phase difference is over time.
For paired instantaneous phases \(\phi_A(k)\) and \(\phi_B(k)\), define \(\Delta\phi(k)=\phi_A(k)-\phi_B(k)\).
The PLV is the magnitude of the average unit phasor:
PLV = | (1/N) Σ exp( i · Δφ(k) ) |
With \(C=Σcos(Δφ)\) and \(S=Σsin(Δφ)\), you can compute:
PLV = √(C² + S²) / N, mean lag = atan2(S, C)
How to Use This Calculator
- Choose an input mode: two lists, two-column text, or file upload.
- Select units that match your data: radians or degrees.
- Optionally skip early samples and limit the maximum samples used.
- Click Calculate PLV to view results above the form.
- Use Download CSV or Download PDF to export the report.
Tip: If you only have raw signals, first extract instantaneous phase using a bandpass filter and Hilbert transform in your analysis software.
Technical Article
1) What PLV measures
Phase Locking Value (PLV) summarizes how stable the phase difference between two oscillatory signals remains across time. It uses unit phasors exp(i·Δφ) so amplitude changes do not dominate the metric. PLV ranges from 0 (random phase differences) to 1 (perfectly constant phase lag).
2) Interpreting typical ranges
In practical recordings, PLV depends on bandwidth, noise, and coupling strength. Values around 0.1–0.3 often indicate weak or intermittent synchrony, 0.3–0.6 moderate coupling, and above 0.6 strong alignment. These ranges are context dependent and should be compared within the same preprocessing pipeline.
3) Preparing phase time series
PLV requires instantaneous phase estimates. A common workflow is bandpass filtering to the target band, then computing the analytic signal and phase angle. Use consistent filter order and edge handling. If phases are in degrees, this calculator converts them internally to radians for computation.
4) Why sample count matters
PLV is an average over N samples, so the estimate becomes more stable as N increases. Very small N can inflate variability and make significance tests unreliable. For long recordings, it is typical to compute PLV in windows (for example, 1–10 seconds) and then summarize the distribution across time.
5) Wrapping and mean phase lag
Δφ can be wrapped to the interval [−π, π] so the mean phase lag is interpretable near the discontinuity at ±π. Wrapping does not change the PLV magnitude because exp(i·Δφ) is periodic, but it helps when reporting the average lag direction in radians or degrees.
6) Significance with the Rayleigh statistic
The Rayleigh test evaluates whether phase differences are uniformly distributed on the circle. This calculator reports z = N·PLV² and an approximate p-value. A small p-value suggests non-random alignment, but it does not prove causality and can be influenced by nonstationarity and shared references.
7) Common pitfalls to avoid
Volume conduction or shared sensors can create artificially high synchrony. Consider referencing choices, spatial filtering, or controls. Also avoid mixing mismatched sampling points; PLV assumes paired samples. If one series is longer, the calculator trims to the shortest matched length after optional skipping.
8) Reporting results clearly
When reporting PLV, include the frequency band, window length, overlap, filtering approach, and whether wrapping was used. Provide N and the mean phase lag alongside PLV. The CSV and PDF exports support transparent documentation so results can be reproduced and audited later.
FAQs
1) Can I compute PLV from raw voltage signals?
No. First estimate instantaneous phase, usually after bandpass filtering. PLV is defined on phase values, not on amplitudes or raw samples.
2) What is a good window length for PLV?
Choose a window that contains many cycles of the target frequency. For 10 Hz activity, 1–2 seconds often works; slower rhythms may need longer windows to stabilize the estimate.
3) Does wrapping Δphase change the PLV value?
No. PLV uses exp(i·Δφ), which is periodic. Wrapping mainly improves the readability of the mean phase difference near ±π.
4) Why does PLV sometimes increase with more samples?
More samples reduce estimator variance, so the measured PLV can become less noisy. However, true coupling can also vary over time, so windowed analysis is recommended.
5) How should I handle missing or uneven data lengths?
PLV requires paired samples. This calculator trims to the matched length and lets you skip initial samples. For gaps, clean the data first or interpolate cautiously with a documented method.
6) Is a small Rayleigh p-value always meaningful?
Not always. Nonstationarity, shared references, or filtering artifacts can produce small p-values. Use controls, surrogate tests, and appropriate referencing to support interpretation.
7) How do I cite PLV results in a report?
State PLV, N, mean phase lag, frequency band, windowing choices, and preprocessing. Include exported tables for transparency, and describe any subject-level averaging or statistical comparisons.