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 Spectrum Implies Uncertainty Principle