MONAD GRAPhi-X
Vedecké laboratórium · jeden graf na stránku
Funkcie a vlny
Science lab page · one study surface at a time.
Sinus · living wave
f(x) = 1·sin(1x + 0) + 0
f(x) = 1·sin(1x + 0) + 0
right-click · record
f(x) = 1·sin(1x + 0) + 0
Periodic, odd function. Period = 2π/b, range [d−a, d+a]. It is the projection of uniform circular motion onto the vertical axis — the base of every soundwave in this engine.
Fourier synthesis · spectrum
f(t) = a₀/2 + Σ [aₖ·cos(2πkt) + bₖ·sin(2πkt)] — stack coefficients and read both domains at once.
b_k = 2/(πk) for every k. All harmonics present with 1/k decay — the brightest classic waveform; Gibbs overshoot ≈ 9 % stays at the jump no matter how many terms you add.
Fourier synthesis · living signal
f(t) = a₀/2 + Σₖ [ aₖ·cos(2πkt) + bₖ·sin(2πkt) ]
f(t) = a₀/2 + Σ aₖcos(2πkt) + bₖsin(2πkt) · N = 8
right-click · record
- Harmonics N
- 8
- Peak
- 1.066
- RMS
- 0.556
- Energy (Parseval)
- 0.310
- THD
- 72.6 %
Live coefficients · aₖ (cos) / bₖ (sin)
Every drag rewrites the series in place — the reconstruction, the |cₖ| spectrum and the Parseval metrics recompute on the same frame.