The Game

• Signals and Systems

The Game as mentioned in class starts with a Linear time invariant system and the impulse response of that system

Mathematical Property	$Input⟹Output$
Given	$$\begin{gathered} \delta \\ (t)⟹h(t) \end{gathered}$$
Time Invariance	$$\begin{gathered} \delta \\ (t-u)⟹h(t-u) \end{gathered}$$
Proportionality	$$\begin{gathered} f(u)*\delta \\ (t-u)⟹f(u)*h(t-u) \end{gathered}$$
Linearity	$$\begin{gathered} \underset{-\mathrm{\infty }}{\overset{\mathrm{\infty }}{\int }}f(u)*\delta \\ (t-u)du⟹\underset{-\mathrm{\infty }}{\overset{\mathrm{\infty }}{\int }}f(u)*h(t-u)du \end{gathered}$$

Nathan Sherman