a mechanical Fourier analyzer — gravity does the summing
Top view looking down on the paper
▾
End view looking along the axis
▾
Signal f(t)
Helix
Procedure
i · Record the signal
1
Record — lay each rod flat and slide its red slider to where the rod crosses the curve
ii · Analyse — phase and amplitude
1
Phase — release the lock; gravity turns the heavy side down
2
Amplitude — raise the diameter D of the blue sliders on top until the helix balances
red heavier
blue heavier
iii · Synthesise the harmonic
1
Read — lay each rod flat, half a turn on, and mark the paper below its blue slider
2
Join — draw a smooth periodic curve through the marks
Bearing & lock
How it works
Rod k points at angle φk = nωtk and carries the sample f(tk) as a distance along it. The centre of mass of all sliders is therefore ½(an, bn): gravity forms the Fourier sum and turns that point to the bottom. Blue sliders on the light side, lying on a circle of diameter D through the axis, cancel it exactly when D equals the amplitude; read back, they draw the harmonic.
the series
recording — one rod per sample
the coefficients
gravity forms the sum
the blue sliders balance it
synthesis
the numbers
exact ∫
helix Σ
device
Spectrum An: outline = exact integral, filled = sum over the N rods. A helix with N rods cannot tell harmonic n from N±n (aliasing).
Controls
Mouse — drag empty space to orbit · wheel to zoom · right-drag to pan Turn — drag the helix, the dial or the knurled knob · click the black lever to lock or release Sliders — drag a red or blue ball along its rod · click a bare rod to put a slider on it Keys — Space lock/release · N record or read the selected rod and step to the next (⇧N all) · B auto-balance · T test balance · J join · ← → rods (⇧ ±1°) · 1 2 3 modes · O V E D F views · Esc stop