SpO2-estimation

SpO2 Library (Windowed Double-FFT)

Estimate blood-oxygen saturation (SpO2) from a dual-wavelength PPG (a RED and an IR photoplethysmogram), following:

R. Jin et al., "Windowed Double-FFT Algorithm for SpO2 Measurement in Areas of Low Vascular Density," IEEE Sensors Journal, 25(1), 2025.

Idea

SpO2 comes from the ratio-of-ratios of the two PPG colours:

R = (AC_red / DC_red) / (AC_ir / DC_ir)
SpO2 = A·R² + B·R + C        (empirical calibration)

The hard part is measuring AC (the pulsatile amplitude) and DC (the mean light level) cleanly. This algorithm does it in the frequency domain:

moving-average filter (3-pt, 8-pt)
  → DC = 0-frequency bin of the plain FFT (≈ mean)
  → remove DC, remove baseline drift (piecewise linear fit)
  → Hann window → FFT                      ← the second "double" FFT
  → AC = amplitude at the cardiac fundamental, found by the harmonic rule

The window (Hann) cuts spectral leakage; the double FFT keeps that windowing from corrupting the DC term; the harmonic rule picks the true heart-rate peak (only a peak whose 2×/3× harmonics also exist), which rejects noise so the RED and IR frequencies agree.

How to use

from spo2 import spo2_from_ppg

res = spo2_from_ppg(red, ir, fs)     # red, ir = PPG samples; fs in Hz
res.spo2            # estimated SpO2 (%)
res.R               # ratio-of-ratios
res.valid_fraction  # fraction of windows where RED & IR frequencies agreed

method="wfft_harmonic" (default, paper's Test3) is recommended; "wfft_peak" (Test2) and "fft_peak" (Test1) are the simpler baselines. Pass your own calibration=(A, B, C) — fit it for your device with fit_calibration(R, spo2).

Files

File	What it is
spo2.py	The library
datasets.py	Loads dataset_primer_1 and PhysioNet PTT-PPG (RED+IR) + SpO2
evaluate.py	Validity + accuracy evaluation on both datasets
spo2_gui.py	GUI: visualises the pipeline (time, double-FFT spectrum, R→SpO2)

GUI

python spo2_gui.py

Pick a dataset folder and record to see the algorithm step by step:

1. Time domain — the RED and IR PPG of the analysed segment.
2. Frequency domain — the windowed double-FFT spectrum of each channel, with the cardiac fundamental (the AC location) marked, the IR harmonics shown (the harmonic rule), and whether the RED/IR fundamentals agree (validity).
3. Per-window R across the whole record, the median R, and the SpO2 it maps to vs the ground truth.

"Evaluate all" runs the whole folder, fits the SpO2 calibration, reports MAE, and applies that calibration to subsequent single-record estimates. The "Segment start"/"Window" controls move the analysed slice (time + FFT panels) live. Works with both the primer (*_ppg.csv) and PhysioNet (*.hea) layouts.

Testing

python evaluate.py                      # both datasets
python evaluate.py --dataset physionet  # one dataset

Two datasets carry the dual-wavelength PPG this algorithm needs:

• dataset_primer_1 — MAX30102, PPG_Red/PPG_IR, 125 Hz, 122 records.
• PhysioNet Pulse-Transit-Time PPG — MAX30101, pleth_1=RED / pleth_2=IR, 500 Hz, 66 records (22 subjects × sit/walk/run). Needs the wfdb package.

Validity (the paper's primary metric)

Fraction of windows where the RED and IR cardiac frequencies agree (a mismatch makes the reading invalid). The Test1→Test2→Test3 trend reproduces the paper — windowing gives the big jump:

Method	primer	PhysioNet
Test1 — FFT + peak	86.6%	86.8%
Test2 — windowed double-FFT + peak	94.7%	94.0%
Test3 — windowed double-FFT + harmonic	94.9%	94.0%

(Absolute validity is higher than the paper's because both are strong fingertip PPGs, not the low-vascular-density forearm/sacral signals the paper targets; PhysioNet's walk/run records do show validity dropping on heavy motion.)

SpO2 accuracy (MAE)

A device-specific calibration SpO2 = A·R² + B·R + C is fitted per dataset (the raw R scale differs by sensor). MAE is reported by leave-one-out CV against the trivial "predict the mean" baseline:

Dataset	n	corr(R, SpO2)	MAE (LOO)	baseline
primer (MAX30102)	122	−0.03	0.86%	0.85%
PhysioNet (MAX30101)	66	−0.24	0.69%	0.66%

Both MAEs are sub-1%, but that is mostly because SpO2 barely varies in these healthy subjects (primer 95–100%, PhysioNet 94.5–98.5%). Neither fitted calibration beats predicting the mean in cross-validation, so the MAE reflects the narrow range, not validated accuracy. The encouraging sign is that on PhysioNet R shows the physiologically correct negative correlation with SpO2 (−0.24, vs −0.03 on primer) — evidence the ratio-of-ratios captures real information; it just needs subjects with genuine desaturation to be validated.

Why BIDMC is not tested

The ratio-of-ratios needs two wavelengths. The BIDMC dataset has a single PLETH channel (one wavelength), so R cannot be formed. BIDMC stores the monitor's SpO2 number, but not the raw RED/IR signals this algorithm needs.