Signal Parameters
Freq 2.0
Amp 1.0
Width 0.5
Phase 0
Harmonics 5
Noise & Filter
Noise 0
Cutoff 5.0
Window Function
Real Domain f(x)
Fourier Domain F(k)
Theory
Math
Data
Wave
Decomposes a wave into frequency components.
Physics
Each peak in F(k) is a constituent wave. Narrow in x implies spread in k.
Draw Mode
Toggle Draw Mode and drag on the left canvas to draw a custom function. Drag on the right canvas to edit frequencies directly.
Transform
$$ F(k) = \int f(x) e^{-ikx} dx $$
$$ f(x) = \frac{1}{2\pi} \int F(k) e^{ikx} dk $$
Uncertainty Principle
$$ \Delta x \cdot \Delta k \ge \frac{1}{2} $$
Parseval's Theorem
$$ \sum |f(n)|^2 = \frac{1}{N} \sum |F(k)|^2 $$
| $ \Delta x $ (spread) | 0.000 |
| $ \Delta k $ (spread) | 0.000 |
| $ \Delta x \cdot \Delta k $ | 0.000 |
| Peak Frequency | 0 |
| Parseval L2 (Real) | 0.000 |
| Parseval F2 (Freq) | 0.000 |