fourier drawing

Press and drag to draw · wheel zooms · middle-drag pivots

Curve inspector● LIVE

Input state: READY
Source samples: 0
Resampled count: 0
harmonic pairs: —
periodic resolution: 256 points
Closure gap: —
normalized rms error: —

Live mathematics

p · raw p̂ · reconstruction p̂ − p · residual

Inspect the derivations

Closure between start and final point

Δx — Δy — Δz —

Periodic reconstruction

Normalized RMS error derivation

Error energy———

Reference energy———

Squared error sum: —
Reference energy: —
Periodic samples: —

learn moresix paths into the math

follow the sampled points into rotating frequencies, then inspect what the approximation leaves behind.

definitions to inspect

fourier series · synthesis how sine and cosine terms rebuild a periodic curve
discrete fourier transform · definition how finite samples become finite frequency coefficients
root mean square deviation · normalized the error measure beside the reconstruction

watch the idea move · 3blue1brown

use the arrows or slider to step through harmonic pairs in powers of two. auto mode reaches at least 128 pairs, then loops. use the wheel to zoom and middle-drag to orbit.