ulf
Ultra-Low Frequency Power (0-0.003 Hz)
| Aliases | ultra_low_frequency |
| Domain | frequency |
| Distribution family | Gamma |
| Equation | integral(PSD; 0; 0.003) Hz |
| Resource intensity | ◍◍◍◌◌ moderate, Frequency subgraph (requires a Welch/Lomb–Scargle periodogram first). Warm (shared representation cached) is 3× cheaper. (measured, see §Resources) |
Definition
Ultra-low frequency power (0-0.003 Hz). Formally: integral(PSD; 0; 0.003) Hz.
What does normal look like?
Fitted normative prior: Gamma(α = 2.166, θ = 1736), KS p = 0.28, n = 184.
Empirical distribution over the NSRDB normative windows (27000-beat windows, 6750-beat stride), overlaid with the fitted Gamma prior density. Vertical lines mark the median and the 5–95% range.
Normal-range summary (NSRDB)
| statistic | value |
|---|---|
| median | 2956 |
| IQR (25–75%) | 1739 – 4824 |
| 5–95% range | 997.8 – 9405 |
| mean ± sd | 3761 ± 2878 |
| n windows | 184 |
n varies by feature only through per-window validity over the full pooled nsrdb+nsr2db table (n up to 61 715; e.g. sampen/mse drop windows where the statistic is undefined). ulf is the one exception: a 360-beat (~5 min) window contains no ULF-band power, so it uses a long-window NSRDB-only extraction (see its own page).
Use cases
- Autonomic balance via spectral bands (LF/HF interpretation with care).
- Baroreflex and respiratory-sinus-arrhythmia studies.
- Longer recordings where spectral resolution is adequate.
Applications by area
Evidence is reported at the measure-family level; a specific variant may not be the exact index measured in every cited study.
Clinical
Coverage: statistics. A pooled literature; reviews or meta-analyses exist.
ULF/VLF power is extensively studied in mortality risk stratification: lower ULF/VLF consistently predicts higher all-cause/cardiac/arrhythmic mortality post-MI, in CHF, ACS and elderly cohorts. A 2024 meta-analysis, however, found time-domain measures (SDNN, HTI) the strongest post-MI predictors rather than VLF/ULF specifically, and the band's own physiological interpretation (thermoregulation vs. renin–angiotensin vs. artifact) remains unsettled.
Dominant reported direction: down: lower ULF/VLF → higher mortality (contested against time-domain predictors).
Key references: (Shaffer and Ginsberg, 2017); (Rueda-Ochoa et al., 2024); (Yuda et al., 2021).
Sports & peak performance
Coverage: individual papers. A small, scattered literature with no pooled meta-analysis.
Uncommon as a headline sports metric. Acute dose-response is consistent and strong (ULF/VLF falls monotonically with rising exercise intensity; ambulatory ULF rises sharply with movement, largely a motion-artifact/thermoregulatory effect), but chronic-training/overtraining findings are weak, inconsistent, and even sex-reversed within a single small study.
Dominant reported direction: down acutely with intensity; chronic/training direction unsettled.
Key references: (Shaffer and Ginsberg, 2017).
Contemplative practice
Coverage: individual papers. A small, scattered literature with no pooled meta-analysis.
A minor, seldom-isolated component of meditation HRV research: one classic study reports dramatic, exaggerated VLF-spanning oscillations tied to extremely slow breathing during Chi/Kundalini meditation, while a more careful spectral study found no change in normalized VLF power but a significant drop in the residual (non-harmonic) component: illustrating strong method-dependence (raw vs. normalized vs. residual power).
Dominant reported direction: method-dependent (raw vs. normalized vs. residual).
Key references: (Shaffer and Ginsberg, 2017).
See the effect-distribution meta-analysis page for the harvested per-study effect sizes/p-values behind these domain summaries (docs/zoo_gen/effect_stats.csv).
Resources
Resource-intensity rank ◍◍◍◌◌ moderate is measured: median wall-clock time and allocations over a 360-beat window on synthetic realistic RR (docs/zoo_gen/bench_resources.jl; full grid in resource_bench.csv).
| metric (360-beat window) | value |
|---|---|
| cold median wall-time | 0.1031 ms |
| warm median wall-time | 0.03 ms |
| allocations (cold) | 48.6 KiB |
Cold = fresh memoization caches (builds every shared representation from scratch); warm = shared representations (diff, periodogram, Poincaré coords, DFA fluctuation) already cached, so only this feature is recomputed. The tier is derived from the cold cost; see Frequency subgraph (requires a Welch/Lomb–Scargle periodogram first). Warm (shared representation cached) is 3× cheaper.
Citation
Ultra-low-frequency 1/f power-law scaling, Bigger et al. (1996); band per Task Force (1996); Lomb (1976) least-squares periodogram estimator.
Seminal reference(s): (Bigger et al., 1996); (Task Force, European Society of Cardiology / North American Society of Pacing & Electrophysiology, 1996); (Lomb, 1976).
See the References page for the full bibliography.