Scale Theorem

Fourier Transform of a scaled function $f\left(\frac{t}{a}\right)$

$$\mathcal{F}\left(f\left(\frac{t}{a}\right)\right)=|a|F(a\omega )$$

• $a\in \mathbb{C}$ is allowed
• Implies that the shorter the Pulse of a Wave, the broader the Frequency Spectrum
• Implies Uncertainty Principle