The Game: Difference between revisions

Revision as of 19:33, 9 October 2006

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

Mathematical Property	$I n p u t ⟹ O u t p u t$
Given	$δ (t) ⟹ h (t)$
Time Invariance	$δ (t - u) ⟹ h (t - u)$
Proportionality	$f (u) * δ (t - u) ⟹ f (u) * h (t - u)$
Linearity	$\int_{- \infty}^{\infty} f (u) * δ (t - u) d u ⟹ \int_{- \infty}^{\infty} f (u) * h (t - u) d u$

@@ Line 1: / Line 1: @@
 The Game as mentioned in class starts with a Linear time invariant system and the impulse response of that system
-u(t)------->h(t)
+<br>
+<table border="1">
+<tr>
+   <td><b><U>Mathematical Property</u></b></td>
+   <td><math>Input \Longrightarrow Output</math></td>
+</tr>
+<tr>
+   <td>Given</td>
+   <td><math>\delta\ (t)\Longrightarrow h(t)</math></td>
+</tr>
+<tr>
+   <td>Time Invariance</td>
+   <td><math>\delta\ (t-u)\Longrightarrow h(t-u)</math></td>
+</tr>
+<tr>
+   <td>Proportionality</td>
+   <td><math>f(u)*\delta\ (t-u)\Longrightarrow f(u)*h(t-u)</math></td>
+</tr>
+<tr>
+   <td>Linearity</td>
+   <td><math>\int_{-\infty}^{\infty}f(u)*\delta\ (t-u)\,du\Longrightarrow \int_{-\infty}^{\infty}f(u)*h(t-u)\,du</math></td>
+</tr>
+</table>
 [[user:sherna|Nathan Sherman]]