Center of Pressure (CoP) Frequency-Domain Analysis: Reading Balance Ability Through the Spectral Centroid
Whether someone stands steady can't be judged by how much the body sways alone. Center of pressure (CoP) is one of the most overlooked parameters in a plantar pressure system. Traditional indicators track only path length and envelope area. The numbers are easy to read, but they don't show how the body produced the adjustment.
A newer approach moves the CoP signal into the frequency domain and looks at the spectral centroid frequency (Centroid Frequency). It shows which sensory system the body is leaning on to stay balanced. This article explains how to use it and how to read it.
What Traditional Indicators Miss
Path length is the total distance the CoP travels, and envelope area is the region the trajectory covers. Both are simple and intuitive, but both ignore how fast the sway happens. Fatigue or injury can leave path length identical while the frequency distribution changes, and traditional indicators can't tell the two apart.
Frequency-domain analysis uses power spectral density (PSD) to split the CoP signal into frequencies, and each band maps to a different physiological mechanism. Cutting the bands finer than a simple low/high split shows more clearly which sensory system the problem sits in.
Three Bands, Three Systems
The CoP power spectrum is usually divided into three bands:
- Low frequency (<0.1 Hz): mainly shaped by vision and slow postural adjustments
- Mid frequency (0.1–0.5 Hz): reflects vestibular function and automatic postural regulation
- High frequency (>0.5 Hz): reflects fast muscle responses and proprioceptive feedback
Take the eyes-closed foam stance test. Vision is blocked and the foam disturbs foot sensation, so the body can only rely on the vestibular system to stay upright. The share of energy in each band indicates whether vision, the vestibular system or the muscles are doing the work, which is more precise than area-based indicators.
In a healthy person under this condition, the mid-frequency share rises clearly. A high mid-frequency share means the vestibular system has taken over normally and automatic regulation is running smoothly.
Spectral Centroid: One Number for Your Regulation Strategy
The spectral centroid frequency is the key figure in frequency-domain analysis, calculated as a weighted average:
fc = Σ fk · P(fk) / Σ P(fk)
fk is the frequency and P(fk) is the power at that frequency. Put simply, it is the balance point of the power spectrum. A centroid shifted toward high frequency means frequent micro-adjustments, which may relate to fatigue or injury. A centroid shifted toward low frequency means slow adjustment, or a strategy that still has room to improve.
Stable Group vs. Higher Fall-Risk Group: Power Spectral Density
Test condition: eyes closed, standing on foam, using 30 seconds of raw anterior-posterior CoP data.
| Indicator | Stable group | Higher fall-risk group |
|---|---|---|
| Low frequency (drift) | 3.04% | 67.86% |
| Mid frequency (vestibular compensation) | 96.27% | 0.04% |
| High frequency (muscle correction) | 0.30% | 26.56% |
| MPF (centroid) | 0.2824 Hz | 0.7485 Hz |
Stable group: Energy sits in the 0.1–0.5 Hz mid-frequency band. The body relies mainly on the vestibular system and proprioception for smooth regulation, at low cost and high efficiency.
Higher fall-risk group:
- Low frequency: the blue area is narrow, but its value is extremely high (close to 10^2 on the log scale). The body is swaying with large amplitude and at very slow speed.
- Mid frequency: the green area almost disappears. The vestibular strategy, the sturdiest automatic regulation mechanism, is not doing its job.
- High frequency: the pink area is large with several sharp peaks. The moment the brain senses the center of gravity is about to tip, it sends the ankle muscles into rapid corrective twitches.
How to Use It in Practice
In rehabilitation training, the spectral centroid can steer the direction of training: strengthen proprioceptive training when the high-frequency share is high, and use more visual feedback when low-frequency activity is abnormal. It reflects change earlier than path length, which makes it a good fit for balance assessment systems.
The computational threshold is low. MATLAB or Python is enough (sampling rate above 50 Hz, with pre-filtering). Pairing it with nonlinear methods such as sample entropy gives a fuller result.
