PolarH10Windows-first telemetry toolkit
PolarH10 Developer Reference

Coherence Formula Sheet

Use this sheet when you want the fixed spectral constants, the paper ratio, the normalized UI score, and the runtime adaptations behind the coherence tab.

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Data Path

  • input stream: accepted RR intervals from the Heart Rate Measurement characteristic
  • physical H10: those RR intervals are device-derived from ECG beat timing
  • synthetic transport: the coherence solve still uses RR, while synthetic PMD ECG is emitted separately so the waveform view stays aligned to the same beat schedule

Fixed Spectral Model

The app keeps the paper-defined spectral constants fixed:

  • peak search band: 0.04-0.26 Hz
  • peak integration window: 0.030 Hz centered on the dominant peak
  • total-power band: 0.0033-0.4 Hz

These formulas operate on the RR-derived tachogram after the irregular beat-interval stream has been resampled into a continuous time series. In the notation below, f is frequency in hertz, PSD(f) is the power spectral density at that frequency, f_peak is the strongest oscillation in the allowed coherence band, P_peak is the power concentrated around that oscillation, and P_total is the broader band power used as the paper's reference total.

fpeak=arg⁡max⁡f∈[0.04,0.26]PSD(f)f_{peak} = \arg\max_{f \in [0.04, 0.26]} PSD(f)

This step finds the dominant rhythm inside the coherence search band instead of across the entire spectrum.

Ppeak=∫fpeak−0.015fpeak+0.015PSD(f) dfP_{peak} = \int_{f_{peak} - 0.015}^{f_{peak} + 0.015} PSD(f)\,df

This integrates a narrow window around the dominant peak so the metric rewards concentrated narrowband power rather than diffuse nearby energy.

Ptotal=∫0.00330.4PSD(f) dfP_{total} = \int_{0.0033}^{0.4} PSD(f)\,df

This is the total reference power across the wider HRV band used by the cited method.

paper coherence ratio=(PpeakPtotal−Ppeak)2\text{paper coherence ratio} = \left(\frac{P_{peak}}{P_{total} - P_{peak}}\right)^2

This ratio rises when one narrow resonance-like peak dominates the spectrum and falls when power is spread across the rest of the band.

UI-Facing Normalized Score

The app also publishes a bounded score for the headline readout and summary charts:

normalized coherence0..1=clamp⁡(PpeakPtotal,0,1)\text{normalized coherence}_{0..1} = \operatorname{clamp}\left(\frac{P_{peak}}{P_{total}}, 0, 1\right)

Here the app is simply reporting the fraction of tracked power that sits in the dominant peak window, then clamping that fraction to a display-friendly range.

This normalized score is an app-side presentation choice. It is not the McCraty paper ratio itself.

Runtime Choices Around The Paper Formula

The cited source fixes the spectral constants above, but it does not define the operator-side runtime details used by this app. The current implementation uses:

  • a rolling RR window
  • cubic-spline resampling of the RR tachogram
  • a 128-point Hann-windowed spectrum solve
  • a smoothed headline 0..1 display value
  • a separate confidence score based on RR count and window coverage

Those runtime choices describe how the app gets from incoming RR intervals to PSD(f) and to a stable operator readout. They affect warmup, smoothness, and confidence behavior, but not the core paper ratio formula shown above.

Alignment Status

The implementation is aligned to the cited reference at the formula level for:

  • peak search band
  • peak-window width
  • total-band limits
  • paper coherence ratio

The display normalization, smoothing, and confidence telemetry are explicit application-level additions.

References