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#Two Key Transforms

Two essential transforms are when the signal of interest consists of delta function in time or a delta function in frequency.

If `$z(t)=\delta(t-t_o)$` then we have

`\begin{align}w(t,s) &=\int_{-\infty}^\infty \frac{1}{s} \psi^*\left(\frac{\tau-t}{s}\right) z(\tau) d\tau\\
&=\int_{-\infty}^\infty \frac{1}{s} \psi^*\left(\frac{\tau-t}{s}\right) \delta(\tau-t_o) d\tau=\frac{1}{s} \psi^*\left(\frac{t_o-t}{s}\right)
\end{align}`

while if `$Z(\omega)=2\pi \delta(\o