The Game: Difference between revisions

Revision as of 18:33, 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	$Input\Longrightarrow Output$
Given	$\delta \ (t)\Longrightarrow h(t)$
Time Invariance	$\delta \ (t-u)\Longrightarrow h(t-u)$
Proportionality	$f(u)\delta \ (t-u)\Longrightarrow f(u)h(t-u)$
Linearity	$\int _{-\infty }^{\infty }f(u)\delta \ (t-u)\,du\Longrightarrow \int _{-\infty }^{\infty }f(u)h(t-u)\,du$

@@ Line 1: / Line 1: @@
 The Game as mentioned in class starts with a Linear time invariant system and the impulse response of that system
+<br>
-u(t)------->h(t)
+<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]]