From the Bench · Explainer
Before you can trust a measurement, it helps to know what a signal even is. First we take a wave apart, piece by piece. Then you wrestle with the real trade-off. You sample and filter a noisy impact from a single shoe-mounted sensor, where the number you read is only as honest as the choices behind it.
Part 1 · The parts of a wave
Underneath all the jargon, a signal has only a handful of moving parts. Tap through them and drag the slider; the wave answers back.
Part 2 · The bench
Now the harder problem. A real impact is noisy, brief, and full of high frequencies, and three knobs decide whether the peak you read is real.
How messy the world is. Real sensors are never clean.
How often you read the sensor. Too slow and the spike slips between samples.
How hard you smooth. Kills noise, but lean on it and the real peak smears away.
That is the whole job of signal processing in one screen. The body does something real and brief, a foot hits the ground and the shin spikes, and all you ever get is a noisy, sampled shadow of it. Read the sensor too slowly and the impact peak falls between two samples and you under-read it; that is exactly why one of my papers nails down the minimum sampling frequency you need before a tibial-acceleration number means anything. Filter too little and random noise invents a peak that was never there. Filter too much and you smear the spike flat. Somewhere in the middle is an honest measurement, and knowing where that is, for one accelerometer in the real world, is most of what I do.
A stylized model for intuition, not a clinical dataset. The impact waveform and noise are representative of shoe- or shank-mounted accelerometry during running, simplified for clarity. Filtering here is a zero-lag moving average; real pipelines use carefully designed low-pass filters, but the trade-off is the same.