Toolbox · real tools, not GIFs

Drag a slider. Watch the math respond.

Three interactive widgets. Drag a slider, watch the math respond. No libraries — the FFT, the detector, and the BP model are all written from scratch.

BP reasoner FFT explorer R-peak detector Cuff physics demo Source on GitHub →

Oscillometric BP reasoner

How a cuff turns oscillations into SBP/MAP/DBP. Try four estimator methods.

cuff pressure + arterial volume oscillations during deflation

extracted oscillogram envelope vs cuff pressure · truth (solid) vs estimate (dashed)

True SBP120mmHg

True MAP100mmHg

True DBP80mmHg

Est. SBP—mmHg

Est. MAP—mmHg

Est. DBP—mmHg

SBP error—mmHg

MAP error—mmHg

DBP error—mmHg

Peak amp—

Peak at—mmHg

Confidence—

true SBP 120 mmHg true DBP 80 mmHg

HR 72 bpm deflation 3.0 mmHg/s

compliance c 15 mmHg pulse shape 0.50

noise 0.05 method

SBP ratio 0.55 DBP ratio 0.75

FFT explorer

Pick a preset, add noise, change the window. The spectrum updates live with the top-three peaks labeled.

time domain · windowed (ghost = unwindowed)

magnitude spectrum (dB)

Peak 1—

Peak 2—

Peak 3—

THD—

preset window

F_s 1000 Hz N samples

noise σ 0.05

f₁ 5 Hz A₁ 1.00

f₂ 17 Hz A₂ 0.60

f₃ 42 Hz A₃ 0.30

HR 70 bpm

SAW decay 5.0

chirp f₀ 5 Hz chirp f₁ 100 Hz

AM f_c 60 Hz AM f_m 3 Hz

Pan–Tompkins R-peak detector

Synthetic ECG, real Pan–Tompkins detector. Add noise, watch detection break.

synthetic ECG · truth (rings) vs detector (dots) · motion bursts shaded

integrated signal with adaptive thresholds (this is what the detector sees)

True HR—bpm

Detected HR—bpm

Sensitivity—%

PPV—%

Mean RR—ms

RMSSD—ms

pNN50—%

Latency—ms

SNR—dB

HR 75 bpm RMSSD jitter 30 ms

baseline drift 0.10 EMG noise 0.10

powerline powerline amp 0.10

motion bursts 0.00

inject PVC every 10 beats

Try the research

The physics behind the cuff: arterial blood volume.

An arm cuff doesn't measure pressure directly — it reads volume oscillations from the artery underneath, mapped through a sigmoidal volume–transmural-pressure curve. Drag the cuff pressure: invasive arterial pressure rolls in along the X-axis, gets mapped through the curve, and rolls out as volume on the Y-axis. The output is loudest when the cuff sits exactly at MAP.

Cuff pressure 150 mmHg

Transmural P (mean) −57 mmHg

Volume DC 0 % V_max

Pulse AC (pk-pk) 0 % V_max

State artery collapsed

Cuff pressure drag to deflate — watch the artery reopen

0 80 (DBP) 100 (MAP) 120 (SBP) 200

● SBP 120 ● MAP 100 ● DBP 80