Wearable PPG Heart-Rate & SpO2 Monitor

Patient (ground truth)

True heart rate 72 bpm

True SpO₂ 98%

Motion artifact 10%

Ambient light noise 5%

Waveform (IR channel)

Red 660nm IR 940nm

-6snow

Monitor readout

Measured HR

-- bpm

Measured SpO₂

-- %

Signal quality index

-- %

How it works

A pulse oximeter shines red (660nm) and infrared (940nm) light through the skin and measures how much is transmitted through the finger/wrist. Arterial blood volume rises and falls with every heartbeat, so absorption oscillates around a steady baseline (Beer–Lambert law):

I(t) = I_DC − I_AC(t),  AC = pulsatile arterial blood
Ratio of ratios:  R = (AC_red/DC_red) / (AC_ir/DC_ir)
Empirical calibration:  SpO2(%) ≈ 110 − 25·R

This simulator generates a real two-lobe systolic-peak + dicrotic-notch PPG waveform for each wavelength from the true heart rate and SpO2 you set, then independently re-derives the monitor's readout from that noisy signal the same way real firmware does:

Heart rate is recovered by peak-picking the filtered IR trace over a rolling window and averaging the inter-beat intervals.
SpO₂ is recovered by tracking the AC (peak−trough) and DC (mean) envelope of both channels over each cardiac cycle and applying the ratio-of-ratios formula above — the same empirical curve used in commercial pulse oximeters.
Motion artifact injects low-frequency baseline wander and high-frequency jitter that swamps the true pulsatile signal, exactly as an arm swing does on a real wearable — watch the measured values drift and the signal-quality index collapse.
Ambient light noise adds a random DC offset per sample, mimicking stray light leaking under a loose wristband.

Real-world relevance: this red/IR ratio-of-ratios pipeline is the exact principle behind every clinical pulse oximeter and consumer wearable (smartwatches, fitness bands) that reports heart rate and blood oxygen from the wrist or fingertip.

Artery (pulsing) Sensor LEDs

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