Peak frequency

The peak frequency of a band is the frequency inside it where the spectrum is highest, in hertz (cycles per second).

Why this measure exists

Band power says how much variation a band holds; the peak says what rhythm is making it. The 1996 Task Force asks studies using autoregressive spectra to report the central frequency of LF LF LF power The variance of the heartbeat intervals that falls in the 0.04 to 0.15 Hz band, in ms²: rhythms repeating every 7 to 25 seconds. Once read as sympathetic activity, which is now disputed. More about LF power and HF HF HF power The variance of the heartbeat intervals that falls in the 0.15 to 0.40 Hz band, in ms²: the range of normal breathing. It mainly reflects vagal activity when breathing is 9 to 24 breaths a minute. More about HF power , and Shaffer and Ginsberg define the LF peak as the highest-amplitude frequency in the LF band, the HF peak likewise. In a resting recording the HF peak is the breathing rate breathing rate Breathing rate How many breaths you take a minute. It moves HRV on its own: slower, deeper breathing makes the beat-to-beat swing larger, and below about 9 breaths a minute it shifts from the HF band into LF. More about Breathing rate : 0.25 Hz is 15 breaths a minute. The LF peak sits near 0.1 Hz, the period of the blood-pressure waves the baroreflex baroreflex Baroreflex The reflex that steadies blood pressure from beat to beat by changing heart rate. Its built-in delay makes heart rate rise and fall about every 10 seconds, the 0.1 Hz rhythm in LF power. More about Baroreflex produces, and paced breathing at 6 a minute puts a spectral peak at exactly that frequency, which is the basis of resonance breathing resonance breathing HRV biofeedback A breathing practice in which you watch your heart rate live and breathe slowly, often near 6 breaths a minute, to make the heart's rise and fall with each breath as large as possible. More about HRV biofeedback and of HeartMath’s coherence score coherence score Coherence A HeartMath score for how much of the HRV spectrum sits in one narrow peak between 0.04 and 0.26 Hz. Slow breathing at about 6 a minute produces it, so it largely measures breathing pace. More about Coherence .

The formula

$$f_{\mathrm{peak}} = \arg\max_{f \in \text{band}} P(f)$$

Within the band’s frequency limits, find the frequency $f$ at which the power spectral density $P(f)$ is largest. To turn it into a breathing rate, multiply by 60: 0.25 Hz × 60 = 15 breaths a minute.

Worked example

Take the rhythm apart

Five minutes of the teaching recording

Power at each frequency, Hz Breathing

VLFLFHF

0 0.1 0.2 0.3 0.4 0.5

ULF

needs 24 h

VLF

3 ms²

LF

120 ms²

HF

635 ms²

Total

758 ms²

LF nu

15.9

HF nu

84.1

LF/HF

0.19

Peak

0.250 Hz, HF

Rested, 15 breaths a minute (0.250 Hz), 5 minutes, Welch's method after detrending. The breathing peak sits at 0.250 Hz in the HF band, with the ~0.1 Hz blood-pressure wave as a smaller LF peak. LF/HF is 0.19.

Rested Stressed Drifting Ectopic beats

Breathing rate 15 breaths a minute Recording length 5 minutes

Welch (FFT) Lomb–Scargle

Detrend first (smoothness priors, λ = 500)

The controls work when JavaScript is on.

A line chart of power against frequency from 0 to 0.5 Hz with the VLF (0.003–0.04 Hz), LF (0.04–0.15 Hz) and HF (0.15–0.4 Hz) bands shaded and a marker at the breathing frequency. Readouts give ULF, VLF, LF, HF and total power in ms squared, LF and HF in normalised units, the LF/HF ratio and the peak frequency, followed by a sentence explaining what changed. Controls: a breathing-rate slider from 5 to 20 breaths a minute, a recording-length slider, a detrending checkbox, Welch or Lomb–Scargle buttons, and four preset buttons for a rested, stressed, drifting or ectopic recording.

The five minutes of the teaching recording, breathing at 15 a minute, show a peak at 0.250 Hz in the HF band. Set the breathing rate to 6 a minute and the peak moves to 0.100 Hz, right where the ~0.1 Hz blood-pressure wave already sits, and the two rhythms merge into one tall LF peak.

What moves it

Breathing rate sets the HF peak directly, and Kubios HRV estimates a respiration rate from the ECG ECG ECG A recording of the heart's electrical activity, taken with electrodes on the skin. ECG-based RR intervals are the reference standard for measuring HRV. More about ECG and the beat series. The LF peak moves less at rest, though the Task Force notes that the central frequencies of both LF and HF are not fixed and shift with autonomic changes. The frequency resolution of the method sets how finely a peak can be placed: a 256-sample window at 4 Hz gives bins 1/64 Hz apart, so a peak is only known to about 0.016 Hz.

When it misleads

When breathing is irregular there is no single HF peak, and the reported frequency is whichever bin happened to win. When breathing is slow the breathing peak sits in the LF band and the “LF peak” is breathing, not the baroreflex. And a peak frequency says nothing about how much power is under it: a tall narrow peak and a low broad hump can share one peak frequency.

Where you will see it

Kubios HRV prints a peak frequency for VLF VLF VLF power The variance of the heartbeat intervals in the 0.003 to 0.04 Hz band, in ms²: rhythms repeating every 25 seconds to 5 minutes. It needs at least a 5-minute recording and is best read over 24 hours. More about VLF power , LF and HF in Hz beside each band’s power, and, from ECG, an ECG-derived respiration rate. Breathing-trainer apps show the breathing peak when they draw a spectrum. Coherence is a score built around the peak’s share of the spectrum.